Oscillatory enzyme reactions and Michaelis-Menten kinetics.
Goldbeter, Albert
2013-09-02
Oscillations occur in a number of enzymatic systems as a result of feedback regulation. How Michaelis-Menten kinetics influences oscillatory behavior in enzyme systems is investigated in models for oscillations in the activity of phosphofructokinase (PFK) in glycolysis and of cyclin-dependent kinases in the cell cycle. The model for the PFK reaction is based on a product-activated allosteric enzyme reaction coupled to enzymatic degradation of the reaction product. The Michaelian nature of the product decay term markedly influences the period, amplitude and waveform of the oscillations. Likewise, a model for oscillations of Cdc2 kinase in embryonic cell cycles based on Michaelis-Menten phosphorylation-dephosphorylation kinetics shows that the occurrence and amplitude of the oscillations strongly depend on the ultrasensitivity of the enzymatic cascade that controls the activity of the cyclin-dependent kinase. Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.
Enzymatic reactions in microfluidic devices: Michaelis-Menten kinetics.
Ristenpart, William D; Wan, Jiandi; Stone, Howard A
2008-05-01
Kinetic rate constants for enzymatic reactions are typically measured with a series of experiments at different substrate concentrations in a well-mixed container. Here we demonstrate a microfluidic technique for measuring Michaelis-Menten rate constants with only a single experiment. Enzyme and substrate are brought together in a coflow microfluidic device, and we establish analytically and numerically that the initial concentration of product scales with the distance x along the channel as x5/2. Measurements of the initial rate of product formation, combined with the quasi-steady rate of product formation further downstream, yield the rate constants. We corroborate the x5/2 scaling result experimentally using the bioluminescent reaction between ATP and luciferase/luciferin as a model system.
Liao, Fei; Tian, Kao-Cong; Yang, Xiao; Zhou, Qi-Xin; Zeng, Zhao-Chun; Zuo, Yu-Ping
2003-03-01
The reliability of kinetic substrate quantification by nonlinear fitting of the enzyme reaction curve to the integrated Michaelis-Menten equation was investigated by both simulation and preliminary experimentation. For simulation, product absorptivity epsilon was 3.00 mmol(-1) L cm(-1) and K(m) was 0.10 mmol L(-1), and uniform absorbance error sigma was randomly inserted into the error-free reaction curve of product absorbance A(i) versus reaction time t(i) calculated according to the integrated Michaelis-Menten equation. The experimental reaction curve of arylesterase acting on phenyl acetate was monitored by phenol absorbance at 270 nm. Maximal product absorbance A(m) was predicted by nonlinear fitting of the reaction curve to Eq. (1) with K(m) as constant. There were unique A(m) for best fitting of both the simulated and experimental reaction curves. Neither the error in reaction origin nor the variation of enzyme activity changed the background-corrected value of A(m). But the range of data under analysis, the background absorbance, and absorbance error sigma had an effect. By simulation, A(m) from 0.150 to 3.600 was predicted with reliability and linear response to substrate concentration when there was 80% consumption of substrate at sigma of 0.001. Restriction of absorbance to 0.700 enabled A(m) up to 1.800 to be predicted at sigma of 0.001. Detection limit reached A(m) of 0.090 at sigma of 0.001. By experimentation, the reproducibility was 4.6% at substrate concentration twice the K(m), and A(m) linearly responded to phenyl acetate with consistent absorptivity for phenol, and upper limit about twice the maximum of experimental absorbance. These results supported the reliability of this new kinetic method for enzymatic analysis with enhanced upper limit and precision.
Michaelis-Menten kinetics in shear flow: Similarity solutions for multi-step reactions.
Ristenpart, W D; Stone, H A
2012-03-01
Models for chemical reaction kinetics typically assume well-mixed conditions, in which chemical compositions change in time but are uniform in space. In contrast, many biological and microfluidic systems of interest involve non-uniform flows where gradients in flow velocity dynamically alter the effective reaction volume. Here, we present a theoretical framework for characterizing multi-step reactions that occur when an enzyme or enzymatic substrate is released from a flat solid surface into a linear shear flow. Similarity solutions are developed for situations where the reactions are sufficiently slow compared to a convective time scale, allowing a regular perturbation approach to be employed. For the specific case of Michaelis-Menten reactions, we establish that the transversally averaged concentration of product scales with the distance x downstream as x(5/3). We generalize the analysis to n-step reactions, and we discuss the implications for designing new microfluidic kinetic assays to probe the effect of flow on biochemical processes.
Non-Michaelis-Menten kinetics in cytochrome P450-catalyzed reactions.
Atkins, William M
2005-01-01
The cytochrome P450 monooxygenases (CYPs) are the dominant enzyme system responsible for xenobiotic detoxification and drug metabolism. Several CYP isoforms exhibit non-Michaelis-Menten, or "atypical," steady state kinetic patterns. The allosteric kinetics confound prediction of drug metabolism and drug-drug interactions, and they challenge the theoretical paradigms of allosterism. Both homotropic and heterotropic ligand effects are now widely documented. It is becoming apparent that multiple ligands can simultaneously bind within the active sites of individual CYPs, and the kinetic parameters change with ligand occupancy. In fact, the functional effect of any specific ligand as an activator or inhibitor can be substrate dependent. Divergent approaches, including kinetic modeling and X-ray crystallography, are providing new information about how multiple ligand binding yields complex CYP kinetics.
Liao, Fei; Zhu, Xiao-Yun; Wang, Yong-Mei; Zuo, Yu-Ping
2005-01-31
The estimation of enzyme kinetic parameters by nonlinear fitting reaction curve to the integrated Michaelis-Menten rate equation ln(S(0)/S)+(S(0)-S)/K(m)=(V(m)/K(m))xt was investigated and compared to that by fitting to (S(0)-S)/t=V(m)-K(m)x[ln(S(0)/S)/t] (Atkins GL, Nimmo IA. The reliability of Michaelis-Menten constants and maximum velocities estimated by using the integrated Michaelis-Menten equation. Biochem J 1973;135:779-84) with uricase as the model. Uricase reaction curve was simulated with random absorbance error of 0.001 at 0.075 mmol/l uric acid. Experimental reaction curve was monitored by absorbance at 293 nm. For both CV and deviation kinetic parameters and applicable for the characterization of enzyme inhibitors.
Michaelis-Menten kinetics under non-isothermal conditions.
Lervik, Anders; Kjelstrup, Signe; Qian, Hong
2015-01-14
We extend the celebrated Michaelis-Menten kinetics description of an enzymatic reaction taking into consideration the presence of a thermal driving force. A coupling of chemical and thermal driving forces is expected from the principle of non-equilibrium thermodynamics, and specifically we obtain an additional term to the classical Michaelis-Menten kinetic equation, which describes the coupling in terms of a single parameter. A companion equation for the heat flux is also derived, which actually can exist even in the absence of a temperature difference. Being thermodynamic in nature, this result is general and independent of the detailed mechanism of the coupling. Conditions for the experimental verification of the new equation are discussed.
Tang, J. Y
2015-01-01
The Michaelis-Menten kinetics and the reverse Michaelis-Menten kinetics are two popular mathematical formulations used in many land biogeochemical models to describe how microbes and plants would...
Amyloid-like fibril elongation follows michaelis-menten kinetics
Milto, Katazyna; Botyriute, Akvile; Smirnovas, Vytautas
2013-01-01
... are. We obtained experimental data on insulin amyloid-like fibril elongation at the conditions where other processes which may impact kinetics of fibril formation are minor and fitted it using Michaelis-Menten equation...
Liu, Ai-Lin; Zhou, Ting; He, Feng-Yun; Xu, Jing-Juan; Lu, Yu; Chen, Hong-Yuan; Xia, Xing-Hua
2006-06-01
We firstly transformed the traditional Michaelis-Menten equation into an off-line form which can be used for evaluating the Michaelis-Menten constant after the enzymatic reaction. For experimental estimation of the kinetics of enzymatic reactions, we have developed a facile and effective method by integrating an enzyme microreactor into direct-printing polymer microchips. Strong nonspecific adsorption of proteins was utilized to effectively immobilize enzymes onto the microchannel wall, forming the integrated on-column enzyme microreactor in a microchip. The properties of the integrated enzyme microreactor were evaluated by using the enzymatic reaction of glucose oxidase (GOx) with its substrate glucose as a model system. The reaction product, hydrogen peroxide, was electrochemically (EC) analyzed using a Pt microelectrode. The data for enzyme kinetics using our off-line form of the Michaelis-Menten equation was obtained (K(m) = 2.64 mM), which is much smaller than that reported in solution (K(m) = 6.0 mM). Due to the hydrophobic property and the native mesoscopic structure of the poly(ethylene terephthalate) film, the immobilized enzyme in the microreactor shows good stability and bioactivity under the flowing conditions.
Time-dependent corrections to effective rate and event statistics in Michaelis-Menten kinetics
Sinitsyn, N. A.; Nemenman, I.
2010-01-01
We generalize the concept of the geometric phase in stochastic kinetics to a noncyclic evolution. Its application is demonstrated on kinetics of the Michaelis-Menten reaction. It is shown that the nonperiodic geometric phase is responsible for the correction to the Michaelis-Menten law when parameters, such as a substrate concentration, are changing with time. We apply these ideas to a model of chemical reactions in a bacterial culture of a growing size, where the geometric correction qualita...
Noise slows the rate of Michaelis-Menten reactions.
Van Dyken, J David
2017-10-07
Microscopic randomness and the small volumes of living cells combine to generate random fluctuations in molecule concentrations called "noise". Here I investigate the effect of noise on biochemical reactions obeying Michaelis-Menten kinetics, concluding that substrate noise causes these reactions to slow. I derive a general expression for the time evolution of the joint probability density of chemical species in arbitrarily connected networks of non-linear chemical reactions in small volumes. This equation is a generalization of the chemical master equation (CME), a common tool for investigating stochastic chemical kinetics, extended to reaction networks occurring in small volumes, such as living cells. I apply this equation to a generalized Michaelis-Menten reaction in an open system, deriving the following general result: 〈p〉≤p¯ and 〈s〉≥s¯, where s¯ and p¯ denote the deterministic steady-state concentration of reactant and product species, respectively, and 〈s〉 and 〈p〉 denote the steady-state ensemble average over independent realizations of a stochastic reaction. Under biologically realistic conditions, namely when substrate is degraded or diluted by cell division, 〈p〉≤p¯. Consequently, noise slows the rate of in vivo Michaelis-Menten reactions. These predictions are validated by extensive stochastic simulations using Gillespie's exact stochastic simulation algorithm. I specify the conditions under which these effects occur and when they vanish, therefore reconciling discrepancies among previous theoretical investigations of stochastic biochemical reactions. Stochastic slowdown of reaction flux caused by molecular noise in living cells may have functional consequences, which the present theory may be used to quantify. Copyright © 2017 Elsevier Ltd. All rights reserved.
Extending the kinetic solution of the classic Michaelis-Menten model of enzyme action
BISPO, Jose Ailton Conceicao; Bonafe, Carlos Francisco Sampaio; SOUZA, Volnei Brito de; SILVA, Joao Batista de Almeida e; CARVALHO, Giovani Brandao Mafra de
2011-01-01
The principal aim of studies of enzyme-mediated reactions has been to provide comparative and quantitative information on enzyme-catalyzed reactions under distinct conditions. The classic Michaelis-Menten model (Biochem Zeit 49:333, 1913) for enzyme kinetic has been widely used to determine important parameters involved in enzyme catalysis, particularly the Michaelis-Menten constant (K (M) ) and the maximum velocity of reaction (V (max) ). Subsequently, a detailed treatment of the mechanisms ...
Optimal designs for Michaelis-Menten kinetic studies.
Matthews, J N S; Allcock, G C
2004-02-15
Many reactions in enzymology are governed by the Michaelis-Menten equation. Characterising these reactions requires the estimation of the parameters K(M) and V(max) which determine the Michaelis-Menten equation and this is done by observing rates of reactions at a set of substrate concentrations. The choice of substrate concentrations is investigated by determining Bayesian D-optimal designs for a model in which residuals have a normal distribution with constant variance. Designs which focus on alternative quantities, such as K(M) or the ratio V(max)/K(M) are also considered. The effect on the optimal designs of alternative error distributions is also considered.
Reexamining Michaelis-Menten Enzyme Kinetics for Xanthine Oxidase
Bassingthwaighte, James B.; Chinn, Tamara M.
2013-01-01
Abbreviated expressions for enzyme kinetic expressions, such as the Michaelis-Menten (M-M) equations, are based on the premise that enzyme concentrations are low compared with those of the substrate and product. When one does progress experiments, where the solute is consumed during conversion to form a series of products, the idealized conditions…
Reexamining Michaelis-Menten Enzyme Kinetics for Xanthine Oxidase
Bassingthwaighte, James B.; Chinn, Tamara M.
2013-01-01
Abbreviated expressions for enzyme kinetic expressions, such as the Michaelis-Menten (M-M) equations, are based on the premise that enzyme concentrations are low compared with those of the substrate and product. When one does progress experiments, where the solute is consumed during conversion to form a series of products, the idealized conditions…
Amyloid-like fibril elongation follows michaelis-menten kinetics.
Milto, Katazyna; Botyriute, Akvile; Smirnovas, Vytautas
2013-01-01
A number of proteins can aggregate into amyloid-like fibrils. It was noted that fibril elongation has similarities to an enzymatic reaction, where monomers or oligomers would play a role of substrate and nuclei/fibrils would play a role of enzyme. The question is how similar these processes really are. We obtained experimental data on insulin amyloid-like fibril elongation at the conditions where other processes which may impact kinetics of fibril formation are minor and fitted it using Michaelis-Menten equation. The correlation of the fit is very good and repeatable. It speaks in favour of enzyme-like model of fibril elongation. In addition, obtained [Formula: see text] and [Formula: see text] values at different conditions may help in better understanding influence of environmental factors on the process of fibril elongation.
Time-dependent corrections to effective rate and event statistics in Michaelis-Menten kinetics.
Sinitsyn, N A; Nemenman, I
2010-11-01
The authors generalise the concept of the geometric phase in stochastic kinetics to a non-cyclic evolution. Its application is demonstrated on kinetics of the Michaelis-Menten reaction. It is shown that the non-periodic geometric phase is responsible for the correction to the Michaelis-Menten law when parameters, such as a substrate concentration, are changing with time. The authors apply these ideas to a model of chemical reactions in a bacterial culture of a growing size, where the geometric correction qualitatively changes the outcome of the reaction kinetics.
Conformational Nonequilibrium Enzyme Kinetics: Generalized Michaelis-Menten Equation.
Piephoff, D Evan; Wu, Jianlan; Cao, Jianshu
2017-08-03
In a conformational nonequilibrium steady state (cNESS), enzyme turnover is modulated by the underlying conformational dynamics. On the basis of a discrete kinetic network model, we use an integrated probability flux balance method to derive the cNESS turnover rate for a conformation-modulated enzymatic reaction. The traditional Michaelis-Menten (MM) rate equation is extended to a generalized form, which includes non-MM corrections induced by conformational population currents within combined cyclic kinetic loops. When conformational detailed balance is satisfied, the turnover rate reduces to the MM functional form, explaining its general validity. For the first time, a one-to-one correspondence is established between non-MM terms and combined cyclic loops with unbalanced conformational currents. Cooperativity resulting from nonequilibrium conformational dynamics can be achieved in enzymatic reactions, and we provide a novel, rigorous means of predicting and characterizing such behavior. Our generalized MM equation affords a systematic approach for exploring cNESS enzyme kinetics.
Introducing Michaelis-Menten Kinetics through Simulation
Halkides, Christopher J.; Herman, Russell
2007-01-01
We describe a computer tutorial that introduces the concept of the steady state in enzyme kinetics. The tutorial allows students to produce graphs of the concentrations of free enzyme, enzyme-substrate complex, and product versus time in order to learn about the approach to steady state. By using a range of substrate concentrations and rate…
Introducing Michaelis-Menten Kinetics through Simulation
Halkides, Christopher J.; Herman, Russell
2007-01-01
We describe a computer tutorial that introduces the concept of the steady state in enzyme kinetics. The tutorial allows students to produce graphs of the concentrations of free enzyme, enzyme-substrate complex, and product versus time in order to learn about the approach to steady state. By using a range of substrate concentrations and rate…
Chaudhury, Srabanti; Cherayil, Binny J
2007-09-14
Single-molecule equations for the Michaelis-Menten [Biochem. Z. 49, 333 (1913)] mechanism of enzyme action are analyzed within the Wilemski-Fixman [J. Chem. Phys. 58, 4009 (1973); 60, 866 (1974)] approximation after the effects of dynamic disorder--modeled by the anomalous diffusion of a particle in a harmonic well--are incorporated into the catalytic step of the reaction. The solution of the Michaelis-Menten equations is used to calculate the distribution of waiting times between successive catalytic turnovers in the enzyme beta-galactosidase. The calculated distribution is found to agree qualitatively with experimental results on this enzyme obtained at four different substrate concentrations. The calculations are also consistent with measurements of correlations in the fluctuations of the fluorescent light emitted during the course of catalysis, and with measurements of the concentration dependence of the randomness parameter.
Michaelis-Menten kinetics of stiripentol in normal humans.
Levy, R H; Loiseau, P; Guyot, M; Blehaut, H M; Tor, J; Moreland, T A
1984-08-01
Michaelis-Menten kinetic parameters for stiripentol, and anticonvulsant, were assessed in six normal volunteers. Stiripentol was administered orally three times a day in dosage increments of 600, 1,200, and 1,800 mg/day for consecutive periods of 3, 4, and 7 days, respectively. Stiripentol steady-state levels at the three dosing rates increased more than proportionally with dose. The mean +/- SD oral clearance of stiripentol at 600 mg/day (1,090 +/- 624 L/day) was significantly greater (p less than 0.01) than at 1,200 (506 +/- 219 L/day) or 1,800 (405 +/- 151 L/day) mg/day. Average steady-state concentrations predicted from individually determined Vm and Km parameters were in good agreement with experimentally observed levels, indicating that the kinetics of stiripentol are of the Michaelis-Menten type. The mean Vm, Km, and Vm/Km ratio were 2,299 +/- 490 mg/day, 2.20 +/- 1.28 mg/L, and 1,241 +/- 837 L/day, respectively. Neuropsychological tests carried out before and after 14 days of stiripentol treatment showed a significant decline in verbal learning ability (p = 0.038) and a significant improvement in a test of memory and attention (p less than 0.01).
Optimal design for goodness-of-fit of the Michaelis-Menten enzyme kinetic function
Wong, Weng Kee; Melas, Viatcheslav B.; Dette, Holger
2004-01-01
We construct efficient designs for the Michaelis-Menten enzyme kinetic model capable of checking model assumption. An extended model, called EMAX model is also considered for this purpose. This model is widely used in pharmacokinetics and reduces to the Michaelis- Menten model for a specific choice of the parameter setting. Our strategy is to find efficient designs for estimating the parameters in the EMAX model and at the same time test the validity of the Michaelis-Menten model against the ...
A note on the reverse Michaelis-Menten kinetics
Wang, Gangsheng [ORNL; Post, Wilfred M [ORNL
2013-01-01
We theoretically derive a general equation describing the enzyme kinetics that can be further simplified to the typical Michaelis-Menten (M-M) kinetics and the reverse M-M equation (RM-M) proposed by Schimel and Weintraub (2003). We discuss the conditions under which the RM-M is valid with this theoretical derivation. These conditions are contrary to the assumptions of Schimel and Weintraub (2003) and limit the applicability of the model in field soil environments. Nonetheless, Schimel and Weintraub s RM-M model is useful and has the ability to produce a non-linear response of SOM decomposition to enzyme concentration consistent with observations. Regardless of the theoretical basis, if we assume that the M-M and the RM-M could be equivalent, our sensitivity analysis indicates that enzyme plays a more sensitive role in the M-M kinetics compared with in the RM-M kinetics.
Bueno, Paulo R; Watanabe, Ailton M; Faria, Ronaldo C; Santos, Márcio L; Riccardi, Carla S
2010-12-16
A piezoelectric detection of enzyme-modified surface was performed under Michaelis-Menten presumptions of steady-state condition. The approach herein presented showed promise in the study of enzymatic kinetics by measuring the frequency changes associated with mass changes at the piezoelectric crystal surface. Likewise, real-time frequency shifts, that is, dΔf/dt, indicated the rate of products formation from enzymatic reaction. In this paper, acetylcholinesterase was used as the enzymatic model and acetylcholine as substrate. The enzymatic rate has its maximum value for a short time during the kinetic reaction, for instance, during the first ten minutes of the reaction time scale. The values found for the kinetic constant rate and Michaelis-Menten constant were (1.4 ± 0.8) 10(5) s(-1) and (5.2 ± 3) 10(-4) M, respectively, in agreement with the values found in classical Michaelis-Menten kinetic experiments.
Role of substrate unbinding in Michaelis-Menten enzymatic reactions.
Reuveni, Shlomi; Urbakh, Michael; Klafter, Joseph
2014-03-25
The Michaelis-Menten equation provides a hundred-year-old prediction by which any increase in the rate of substrate unbinding will decrease the rate of enzymatic turnover. Surprisingly, this prediction was never tested experimentally nor was it scrutinized using modern theoretical tools. Here we show that unbinding may also speed up enzymatic turnover--turning a spotlight to the fact that its actual role in enzymatic catalysis remains to be determined experimentally. Analytically constructing the unbinding phase space, we identify four distinct categories of unbinding: inhibitory, excitatory, superexcitatory, and restorative. A transition in which the effect of unbinding changes from inhibitory to excitatory as substrate concentrations increase, and an overlooked tradeoff between the speed and efficiency of enzymatic reactions, are naturally unveiled as a result. The theory presented herein motivates, and allows the interpretation of, groundbreaking experiments in which existing single-molecule manipulation techniques will be adapted for the purpose of measuring enzymatic turnover under a controlled variation of unbinding rates. As we hereby show, these experiments will not only shed first light on the role of unbinding but will also allow one to determine the time distribution required for the completion of the catalytic step in isolation from the rest of the enzymatic turnover cycle.
Sinitsyn, Nikolai A [Los Alamos National Laboratory
2008-01-01
We generalize the concept of the geometric phase in stochastic kinetics to a noncyclic evolution. Its application is demonstrated on kinetics of the Michaelis-Menten reaction. It is shown that the noncyclic geometric phase is responsible for the correction to the Michaelis-Menten law when parameters, such as a substrate concentration, are changing with time. We also discuss a model, where this correction qualitatively changes the outcome of reaction kinetics.
Relation between pulmonary clearance and particle burden: a Michaelis-Menten-like kinetic model.
Yu, R. C.; Rappaport, S.M.
1996-01-01
OBJECTIVES: To test the validity of a Michaelis-Menten-like kinetic model of pulmonary clearance of insoluble dusts. METHODS: Data were investigated from studies of pulmonary clearance in F344 rats exposed to antimony trioxide (Sb2O3), photocopy test toner, polyvinyl chloride powder (PVC), and diesel exhaust particles. The Michaelis-Menten-like model was used to develop a relation in which the pulmonary clearance half time was a linear function of lung burden. After combining all data, linear...
Ochab-Marcinek, Anna
2010-04-21
The study of biochemical pathways usually focuses on a small section of a protein interactions network. Two distinct sources contribute to the noise in such a system: intrinsic noise, inherent in the studied reactions, and extrinsic noise generated in other parts of the network or in the environment. We study the effect of extrinsic noise entering the system through a nonlinear uptake reaction which acts as a nonlinear filter. Varying input noise intensity varies the mean of the noise after the passage through the filter, which changes the stability properties of the system. The steady-state displacement due to small noise is independent on the kinetics of the system but it only depends on the nonlinearity of the input function. For monotonically increasing and concave input functions such as the Michaelis-Menten uptake rate, we give a simple argument based on the small-noise expansion, which enables qualitative predictions of the steady-state displacement only by inspection of experimental data: when weak and rapid noise enters the system through a Michaelis-Menten reaction, then the graph of the system's steady states vs. the mean of the input signal always shifts to the right as noise intensity increases. We test the predictions on two models of lac operon, where TMG/lactose uptake is driven by a Michaelis-Menten enzymatic process. We show that as a consequence of the steady state displacement due to fluctuations in extracellular TMG/lactose concentration the lac switch responds in an asymmetric manner: as noise intensity increases, switching off lactose metabolism becomes easier and switching it on becomes more difficult. (c) 2009 Elsevier Ltd. All rights reserved.
Klinman, Judith P
2014-01-01
The final arbiter of enzyme mechanism is the ability to establish and test a kinetic mechanism. Isotope effects play a major role in expanding the scope and insight derived from the Michaelis-Menten equation. The integration of isotope effects into the formalism of the Michaelis-Menten equation began in the 1970s and has continued until the present. This review discusses a family of eukaryotic copper proteins, including dopamine β-monooxygenase, tyramine β-monooxygenase and peptidylglycine α-amidating enzyme, which are responsible for the synthesis of neuroactive compounds, norepinephrine, octopamine and C-terminally carboxamidated peptides, respectively. The review highlights the results of studies showing how combining kinetic isotope effects with initial rate parameters permits the evaluation of: (a) the order of substrate binding to multisubstrate enzymes; (b) the magnitude of individual rate constants in complex, multistep reactions; (c) the identification of chemical intermediates; and (d) the role of nonclassical (tunnelling) behaviour in C-H activation. © 2013 FEBS.
Simon Brown
2010-06-01
Full Text Available The behavior of enzyme-catalyzed reactions is not made clear to many students by the standard mathematical description of enzyme kinetics. An enzyme-machine analogy is described that has made the details of the Michaelis-Menten mechanism and the associated kinetics more accessible with minimal use of mathematics. Students taught using the analogy appear to have fewer of the misconceptions than those taught using a more mathematical approach.
Simon Brown
2010-01-01
The behavior of enzyme-catalyzed reactions is not made clear to many students by the standard mathematical description of enzyme kinetics. An enzyme-machine analogy is described that has made the details of the Michaelis-Menten mechanism and the associated kinetics more accessible with minimal use of mathematics. Students taught using the analogy appear to have fewer of the misconceptions than those taught using a more mathematical approach.
Thiopentone elimination in newborn infants: exploring Michaelis-Menten kinetics.
Larsson, P; Anderson, B J; Norman, E; Westrin, P; Fellman, V
2011-04-01
Thiopentone elimination has been described using Michaelis-Menten pharmacokinetics in adults after prolonged infusion or overdose, but there are few reports of elimination in neonates. Time-concentration profiles for neonates (n=37) given single-dose thiopentone were examined using both first-order (constant clearance) and mixed-order (Michaelis-Menten) elimination processes using nonlinear mixed effects models. These profiles included a 33-week post-menstrual age (PMA) neonate given an overdose. A two-compartment mamillary model was used to fit data. Parameter estimates were standardized to a 70 kg person using allometric models. There were 197 observations available for analysis from neonates with a mean post-menstrual age of 35 (SD 4.5) weeks and a mean weight of 2.5 (SD 0.9) kg. They were given a mean thiopentone dose of 3 (SD 0.4) mg/kg as a rapid bolus. Clearance at 26 weeks PMA was 0.015 l/min/70 kg and increased to 0.119 l/min/70 kg by 42 weeks PMA. The maximum rate of elimination (V(max)) at 26 weeks PMA was 0.22 mg/min/70 kg and increased to 4.13 mg/min/70 kg by 42 weeks PMA. These parameter estimates are approximately 40% adult values at term gestation. The Michaelis constant (K(m)) was 28.3 [between subject variability (BSV) 46.4%, 95% confidence interval (CI) 4.49-99.2] mg/l; intercompartment clearance was 0.44 (BSV 97.5%, 95% CI 0.27-0.63) l/min/70 kg; central volume of distribution was 46.4 (BSV 29.2%, 95% CI 41.7-59.8) l/70 kg; peripheral volume of distribution was 95.7 (BSV 70.3%, 95% CI 61.3-128) l/70 kg. Both first-order and mixed-order processes satisfactorily described elimination. First-order elimination adequately described the time-concentration profile in the premature neonate given an overdose. Clearance is immature in the pre-term neonate although there is rapid maturation around 40 weeks PMA, irrespective of post-natal age. © 2011 The Authors. Acta Anaesthesiologica Scandinavica © 2011 The Acta Anaesthesiologica Scandinavica Foundation.
A Simple Classroom Teaching Technique to Help Students Understand Michaelis-Menten Kinetics
Runge, Steven W.; Hill, Brent J. F.; Moran, William M.
2006-01-01
A new, simple classroom technique helps cell biology students understand principles of Michaelis-Menten enzyme kinetics. A student mimics the enzyme and the student's hand represents the enzyme's active site. The catalytic event is the transfer of marbles (substrate molecules) by hand from one plastic container to another. As predicted, increases…
A Simple Classroom Teaching Technique to Help Students Understand Michaelis-Menten Kinetics
Runge, Steven W.; Hill, Brent J. F.; Moran, William M.
2006-01-01
A new, simple classroom technique helps cell biology students understand principles of Michaelis-Menten enzyme kinetics. A student mimics the enzyme and the student's hand represents the enzyme's active site. The catalytic event is the transfer of marbles (substrate molecules) by hand from one plastic container to another. As predicted, increases…
Reduction for Michaelis-Menten-Henri kinetics in the presence of diffusion.
Kalachev, L.V.; Kaper, H.G.; Kaper, T.J.; Popovic, N.; Zagaris, A.
2007-01-01
Abstract: The Michaelis-Menten-Henri (MMH) mechanism is one of the paradigm reaction mechanisms in biology and chemistry. In its simplest form, it involves a substrate that reacts (reversibly) with an enzyme, forming a complex which is transformed (irreversibly) into a product and the enzyme. Given
Reduction for Michaelis-Menten-Henri kinetics in the presence of diffusion
A. Zagaris (Antonios); L.V. Kalachev; H.G. Kaper; T.J. Kaper (Tasso Joost); N. Popovic
2007-01-01
textabstractThe Michaelis-Menten-Henri (MMH) mechanism is one of the paradigm reaction mechanisms in biology and chemistry. In its simplest form, it involves a substrate that reacts (reversibly) with an enzyme, forming a complex which is transformed (irreversibly) into a product and the enzyme.
Park, Soohyung; Agmon, Noam
2008-05-15
We develop a uniform theory for the many-particle diffusion-control effects on the Michaelis-Menten scheme in solution, based on the Gopich-Szabo relaxation-time approximation (Gopich, I. V.; Szabo, A. J. Chem. Phys. 2002, 117, 507). We extend the many-particle simulation algorithm to the Michaelis-Menten case by utilizing the Green function previously derived for excited-state reversible geminate recombination with different lifetimes (Gopich, I. V.; Agmon, N. J. Chem. Phys. 2000, 110, 10433). Running the simulation for representative parameter sets in the time domain and under steady-state conditions, we find poor agreement with classical kinetics but excellent agreement with some of the modern theories for bimolecular diffusion-influenced reactions. Our simulation algorithm can be readily extended to the biologically interesting case of dense patches of membrane-bound enzymes.
Bozlee, Brian J.
2007-01-01
The impact of raising Gibbs energy of the enzyme-substrate complex (G[subscript 3]) and the reformulation of the Michaelis-Menten equation are discussed. The maximum velocity of the reaction (v[subscript m]) and characteristic constant for the enzyme (K[subscript M]) will increase with increase in Gibbs energy, indicating that the rate of reaction…
Kosmidis, Kosmas; Karalis, Vangelis; Argyrakis, Panos; Macheras, Panos
2004-09-01
Two different approaches were used to study the kinetics of the enzymatic reaction under heterogeneous conditions to interpret the unusual nonlinear pharmacokinetics of mibefradil. Firstly, a detailed model based on the kinetic differential equations is proposed to study the enzymatic reaction under spatial constraints and in vivo conditions. Secondly, Monte Carlo simulations of the enzyme reaction in a two-dimensional square lattice, placing special emphasis on the input and output of the substrate were applied to mimic in vivo conditions. Both the mathematical model and the Monte Carlo simulations for the enzymatic reaction reproduced the classical Michaelis-Menten (MM) kinetics in homogeneous media and unusual kinetics in fractal media. Based on these findings, a time-dependent version of the classic MM equation was developed for the rate of change of the substrate concentration in disordered media and was successfully used to describe the experimental plasma concentration-time data of mibefradil and derive estimates for the model parameters. The unusual nonlinear pharmacokinetics of mibefradil originates from the heterogeneous conditions in the reaction space of the enzymatic reaction. The modified MM equation can describe the pharmacokinetics of mibefradil as it is able to capture the heterogeneity of the enzymatic reaction in disordered media.
Lee, Hye Jin; Wark, Alastair W; Goodrich, Terry T; Fang, Shiping; Corn, Robert M
2005-04-26
Real-time surface plasmon resonance (SPR) imaging measurements of surface enzymatic reactions on DNA microarrays are analyzed using a kinetics model that couples the contributions of both enzyme adsorption and surface enzyme reaction kinetics. For the case of a 1:1 binding of an enzyme molecule (E) to a surface-immobilized substrate (S), the overall enzymatic reaction can be described in terms of classical Langmuir adsorption and Michaelis-Menten concepts and three rate constants: enzyme adsorption (k(a)), enzyme desorption (k(d)) and enzyme catalysis (k(cat)). In contrast to solution enzyme kinetics, the amount of enzyme in solution is in excess as compared to the amount of substrate on the surface. Moreover, the surface concentration of the intermediary enzyme-substrate complex (ES) is not constant with time, but goes to zero as the reaction is completed. However, kinetic simulations show that the fractional surface coverage of ES on the remaining unreacted sites does reach a steady-state value throughout the course of the surface reaction. This steady-state value approaches the Langmuir equilibrium value for cases where k(a)[E] > k(cat). Experiments using the 3' --> 5' exodeoxyribonuclease activity of Exonuclease III on double-stranded DNA microarrays as a function of temperature and enzyme concentration are used to demonstrate how this model can be applied to quantitatively analyze the SPR imaging data.
Moffitt, Jeffrey R; Bustamante, Carlos
2014-01-01
Enzyme-catalyzed reactions are naturally stochastic, and precision measurements of these fluctuations, made possible by single-molecule methods, promise to provide fundamentally new constraints on the possible mechanisms underlying these reactions. We review some aspects of statistical kinetics: a new field with the goal of extracting mechanistic information from statistical measures of fluctuations in chemical reactions. We focus on a widespread and important statistical measure known as the randomness parameter. This parameter is remarkably simple in that it is the squared coefficient of variation of the cycle completion times, although it places significant limits on the minimal complexity of possible enzymatic mechanisms. Recently, a general expression has been introduced for the substrate dependence of the randomness parameter that is for rate fluctuations what the Michaelis-Menten expression is for the mean rate of product generation. We discuss the information provided by the new kinetic parameters introduced by this expression and demonstrate that this expression can simplify the vast majority of published models. © 2013 FEBS.
Tang, Sanyi; Xiao, Yanni
2007-12-01
The purpose of this article is to provide the analytical solutions of one-compartment models with Michaelis-Menten elimination kinetics for three different inputs (single intravenous dose, multiple-dose bolus injection and constant). All analytical solutions obtained in present paper can be described by the well defined Lambert W function which can be easily implemented in most mathematical softwares such as Matlab and Maple. These results will play an important role in fitting the Michaelis-Menten parameters and in designing a dosing regimen to maintain steady-state plasma concentrations. In particular, the analytical periodic solution for multi-dose inputs is also given, and we note that the maximum and minimum values of the periodic solution depends on the Michaelis-Menten parameters, dose and time interval of drug administration. In practice, it is important to maintain a concentration above the minimum therapeutic level at all times without exceeding the minimum toxic concentration. Therefore, the one-compartment model with therapeutic window is proposed, and further the existence of periodic solution, analytical expression and its period are analyzed. The analytical formula of period plays a key role in designing a dose regimen to maintain the plasma concentration within a specified range over long periods of therapy. Finally, the completely analytical solution for the constant input rate is derived and discussed which depends on the relations between constant input rate and maximum rate of change of concentration.
eduction for Michaelis-Menten-Henri kinetics in the presence of diffusion
Leonid V. Kalachev
2007-05-01
Full Text Available The Michaelis-Menten-Henri (MMH mechanism is one of the paradigm reaction mechanisms in biology and chemistry. In its simplest form, it involves a substrate that reacts (reversibly with an enzyme, forming a complex which is transformed (irreversibly into a product and the enzyme. Given these basic kinetics, a dimension reduction has traditionally been achieved in two steps, by using conservation relations to reduce the number of species and by exploiting the inherent fast-slow structure of the resulting equations. In the present article, we investigate how the dynamics change if the species are additionally allowed to diffuse. We study the two extreme regimes of large diffusivities and of small diffusivities, as well as an intermediate regime in which the time scale of diffusion is comparable to that of the fast reaction kinetics. We show that reduction is possible in each of these regimes, with the nature of the reduction being regime dependent. Our analysis relies on the classical method of matched asymptotic expansions to derive approximations for the solutions that are uniformly valid in space and time.
Global stability of enzymatic chains of full reversible Michaelis-Menten reactions.
Belgacem, Ismail; Gouzé, Jean-Luc
2013-09-01
We consider a chain of metabolic reactions catalyzed by enzymes, of reversible Michaelis-Menten type with full dynamics, i.e. not reduced with any quasi-steady state approximations. We study the corresponding dynamical system and show its global stability if the equilibrium exists. If the system is open, the equilibrium may not exist. The main tool is monotone systems theory. Finally we study the implications of these results for the study of coupled genetic-metabolic systems.
Burchardt, Malte; Träuble, Markus; Wittstock, Gunther
2009-06-15
The formalism for simulating scanning electrochemical microscopy (SECM) experiments by boundary element methods in three space coordinates has been extended to allow consideration of nonlinear boundary conditions. This is achieved by iteratively refining the boundary conditions that are encoded in a boundary condition matrix. As an example, the simulations are compared to experimental approach curves in the SECM feedback mode toward samples modified with glucose oxidase (GOx). The GOx layer was prepared by the layer-by-layer assembly of polyelectrolytes using glucose oxidase as one of the polyelectrolytes. The comparison of the simulated and experimental curves showed that under a wide range of experimentally accessible conditions approximations of the kinetics at the sample by first order models yield misleading results. The approach curves differ also qualitatively from curves calculated with first order models. As a consequence, this may lead to severe deviations when such curves are fitted to first order kinetic models. The use of linear approximations to describe the enzymatic reaction in SECM feedback experiments is justified only if the ratio of the mediator and Michaelis-Menten constant is equal to or smaller than 0.1 (deviation less than 10%).
Enzyme Kinetics and the Michaelis-Menten Equation
Biaglow, Andrew; Erickson, Keith; McMurran, Shawnee
2010-01-01
The concepts presented in this article represent the cornerstone of classical mathematical biology. The central problem of the article relates to enzyme kinetics, which is a biochemical system. However, the theoretical underpinnings that lead to the formation of systems of time-dependent ordinary differential equations have been applied widely to…
Enzyme Kinetics and the Michaelis-Menten Equation
Biaglow, Andrew; Erickson, Keith; McMurran, Shawnee
2010-01-01
The concepts presented in this article represent the cornerstone of classical mathematical biology. The central problem of the article relates to enzyme kinetics, which is a biochemical system. However, the theoretical underpinnings that lead to the formation of systems of time-dependent ordinary differential equations have been applied widely to…
Costa, Rafael S; Machado, Daniel; Rocha, Isabel; Ferreira, Eugénio C
2010-05-01
The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis-Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action, convenience kinetics, lin-log and power-law). Using the mechanistic model for Escherichia coli central carbon metabolism as a benchmark, we investigate the alternative modeling approaches through comparative simulations analyses. The good dynamic behavior and the powerful predictive capabilities obtained using the hybrid model composed of Michaelis-Menten and the approximate lin-log kinetics indicate that this is a possible suitable approach to model complex large-scale networks where the exact rate laws are unknown. 2010 Elsevier Ireland Ltd. All rights reserved.
André Rosa Martins
2014-11-01
Full Text Available The enzymatic processes according Michaelis-Menten kinetics have been studied from various approaches to describe the inhibition state. Proposals for inhibition were compared from a generic process, where kinetic constants have received unitary values, and the numeric value of the concentration of substrate was ten (10 times higher than the numerical value of the concentration of enzyme. For each inhibition model proposed, numerical solutions were obtained from nonlinear system of ordinary differential equations, generating results presents by graphs showing the variation of the enzyme and enzyme complexes, also the variation of substrate and product of the reaction. Also, was designed a model with performance, indicating similar behavior to that seen in the Michaelis-Menten kinetics, where complex of reaction is rapidly formed and throughout the process, tends to decay to zero. Thus, in this new proposed model, the effect of inhibition starts at zero and, throughout the process, tends to the nominal value of the initial enzyme concentration. Such responses have proved to be valid for different values of enzyme concentration and process time, showing robustness. The proposed model was applied to the hydrolysis of disaccharides, providing a setting with conservation of mass of the model at the end of the process regarding the responses of the carbohydrate concentration.
Perturbation theory in the catalytic rate constant of the Henri-Michaelis-Menten enzymatic reaction.
Bakalis, Evangelos; Kosmas, Marios; Papamichael, Emmanouel M
2012-11-01
The Henry-Michaelis-Menten (HMM) mechanism of enzymatic reaction is studied by means of perturbation theory in the reaction rate constant k (2) of product formation. We present analytical solutions that provide the concentrations of the enzyme (E), the substrate (S), as well as those of the enzyme-substrate complex (C), and the product (P) as functions of time. For k (2) small compared to k (-1), we properly describe the entire enzymatic activity from the beginning of the reaction up to longer times without imposing extra conditions on the initial concentrations E ( o ) and S ( o ), which can be comparable or much different.
Standardization of α-L-iduronidase enzyme assay with Michaelis-Menten kinetics.
Ou, Li; Herzog, Tyler L; Wilmot, Carrie M; Whitley, Chester B
2014-02-01
The lack of methodological uniformity in enzyme assays has been a long-standing difficulty, a problem for bench researchers, for the interpretation of clinical diagnostic tests, and an issue for investigational drug review. Illustrative of the problem, α-L-iduronidase enzyme catalytic activity is frequently measured with the substrate 4-methylumbelliferyl-α-L-iduronide (4MU-iduronide); however, final substrate concentrations used in different assays vary greatly, ranging from 25 μM to 1425 μM (Km ≈ 180 μM) making it difficult to compare results between laboratories. In this study, α-L-iduronidase was assayed with 15 different substrate concentrations. The resulting activity levels from the same specimens varied greatly with different substrate concentrations but, as a group, obeyed the expectations of Michaelis-Menten kinetics. Therefore, for the sake of improved comparability, it is proposed that α-L-iduronidase enzyme assays should be conducted either (1) under substrate saturating conditions; or (2) when concentrations are significantly below substrate saturation, with results standardized by arithmetic adjustment that considers Michaelis-Menten kinetics. The approach can be generalized to many other enzyme assays. Copyright © 2013 Elsevier Inc. All rights reserved.
Biphasic character of ribosomal translocation and non-Michaelis-Menten kinetics of translation.
Xie, Ping
2014-12-01
We study theoretically the kinetics of mRNA translocation in the wild-type (WT) Escherichia coli ribosome, which is composed of a small 30S and large 50S subunit, and the ribosomes with mutations to some intersubunit bridges such as B1a, B4, B7a, and B8. The theoretical results reproduce well the available in vitro experimental data on the biphasic kinetics of the forward mRNA translocation catalyzed by elongation factor G (EF-G) hydrolyzing GTP, which can be best fit by the sum of two exponentials, and the monophasic kinetics of the spontaneous reverse mRNA translocation in the absence of the elongation factor, which can be best fit by a single-exponential function, in both the WT and mutant ribosomes. We show that both the mutation-induced increase in the maximal rate of the slow phase for the forward mRNA translocation and that in the rate of the spontaneous reverse mRNA translocation result from a reduction in the intrinsic energy barrier to resist the rotational movements between the two subunits, giving the same degree of increase in the two rates. The mutation-induced increase in the maximal rate of the fast phase for the forward mRNA translocation results mainly from the increase in the rate of the ribosomal unlocking, a conformational change in the ribosome that widens the mRNA channel for the mRNA translocation to take place, which could be partly due to the effect of the mutation on the intrasubunit 30S head rotation. Moreover, we study the translation rate of the WT and mutant ribosomes. It is shown that the translation rate versus the concentration of EF-G-GTP does not follow the Michaelis-Menten (MM) kinetics, which is in sharp contrast to the general property of other enzymes that the rate of the enzymatic reaction versus the concentration of a substrate follows the MM kinetics. The physical origin of this non-MM kinetics for the ribosome is revealed.
Garneau-Tsodikova, Sylvie; Shkel, Irina A; Tsodikov, Oleg V
2009-04-15
Most enzyme kinetic experiments are carried out under pseudo-first-order conditions, that is, when one of the reactant species (the enzyme or the substrate) is in a large excess of the other species. More accurate kinetic information about the system can be gained without the restrictions of the pseudo-first-order conditions. We present a practical and general method of analysis of the common two-step rapid equilibrium Michaelis-Menten mechanism. The formalism is exact in that it does not involve any other approximations such as the steady-state, limitations on the reactant concentrations or on reaction times. We apply this method to the global analysis of kinetic progress curves for bovine alkaline phosphatase assays carried out under both pseudo-first-order and pseudo-second-order conditions.
Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches.
Hadeler, Karl Peter
2013-01-01
The Michaelis-Menten (MM) function is a fractional linear function depending on two positive parameters. These can be estimated by nonlinear or linear least squares methods. The non-linear methods, based directly on the defect of the MM function, can fail and not produce any minimizer. The linear methods always produce a unique minimizer which, however, may not be positive. Here we give sufficient conditions on the data such that the nonlinear problem has at least one positive minimizer and also conditions for the minimizer of the linear problem to be positive. We discuss in detail the models and equilibrium relations of a classical operator-repressor system, and we extend our approach to the MM problem with leakage and to reversible MM kinetics. The arrangement of the sufficient conditions exhibits the important role of data that have a concavity property (chemically feasible data).
Pereira, Félix Monteiro; Oliveira, Samuel Conceição
2016-11-01
In this article, the occurrence of dead core in catalytic particles containing immobilized enzymes is analyzed for the Michaelis-Menten kinetics. An assessment of numerical methods is performed to solve the boundary value problem generated by the mathematical modeling of diffusion and reaction processes under steady state and isothermal conditions. Two classes of numerical methods were employed: shooting and collocation. The shooting method used the ode function from Scilab software. The collocation methods included: that implemented by the bvode function of Scilab, the orthogonal collocation, and the orthogonal collocation on finite elements. The methods were validated for simplified forms of the Michaelis-Menten equation (zero-order and first-order kinetics), for which analytical solutions are available. Among the methods covered in this article, the orthogonal collocation on finite elements proved to be the most robust and efficient method to solve the boundary value problem concerning Michaelis-Menten kinetics. For this enzyme kinetics, it was found that the dead core can occur when verified certain conditions of diffusion-reaction within the catalytic particle. The application of the concepts and methods presented in this study will allow for a more generalized analysis and more accurate designs of heterogeneous enzymatic reactors.
Extended Parker-Sochacki method for Michaelis-Menten enzymatic reaction model.
Abdelrazik, Ismail M; Elkaranshawy, Hesham A
2016-03-01
In this article, a new approach--namely, the extended Parker-Sochacki method (EPSM)--is presented for solving the Michaelis-Menten nonlinear enzymatic reaction model. The Parker-Sochacki method (PSM) is combined with a new resummation method called the Sumudu-Padé resummation method to obtain approximate analytical solutions for the model. The obtained solutions by the proposed approach are compared with the solutions of PSM and the Runge-Kutta numerical method (RKM). The comparison proves the practicality, efficiency, and correctness of the presented approach. It serves as a basis for solving other nonlinear biochemical reaction models in the future. Copyright © 2015 Elsevier Inc. All rights reserved.
Müller, R; Babel, W
1980-01-01
Investigations of the 3-hexulosephosphate synthase (HPS) from different methylotrophic bacteria have revealed apparent discrepancies in kinetic behaviour. In all methanol-utilizing species investigated by us the kinetic characteristics showed intermediary plateau regions. Therefore, this behaviour is assumed to be a general feature of the HPS from all non-methane-utilizing methylotrophic bacteria. However, this assumption is in contrast to the results of other authors. Both for Methylomonas M15 (SAHM et al. 1976) and Methylomonas aminofaciens 77a (KATO et al. 1977, 1978) MICHAELIS-MENTEN kinetics of the HPS were stated. To check the validity of our assumption we have analyzed the kinetic data given by others. Indications of the existence of intermediary plateau regions could be found with the enzyme from Arthrobacter globiformis (BYKOVSKAYA and VORONKOV 1977) and Methylomonas aminofaciens 77a (KATO et al. 1978). Furthermore, biphasic ARRHENIUS plots indicate a multiple character of the HPS from these species as could already be demonstrated with the enzyme from Bacterium MB 58 and Pseudomonas oleovorans. In addition, causes which may obscure the detection of intermediary plateau regions are demonstrated.
Kumar, Ashutosh; Dua, Arti
2015-01-01
Recent fluorescence spectroscopy measurements of the turnover time distribution of single-enzyme turnover kinetics of $\\beta$-galactosidase provide evidence of Michaelis-Menten kinetics at low substrate concentration. However, at high substrate concentrations, the dimensionless variance of the turnover time distribution shows systematic deviations from the Michaelis-Menten prediction. This difference is attributed to conformational fluctuations in both the enzyme and the enzyme-substrate complex and to the possibility of both parallel and off-pathway kinetics. Here, we use the chemical master equation to model the kinetics of a single fluctuating enzyme that can yield a product through either parallel or off-pathway mechanisms. An exact expression is obtained for the turnover time distribution from which the mean turnover time and randomness parameters are calculated. The parallel and off-pathway mechanisms yield strikingly different dependences of the mean turnover time and the randomness parameter on the su...
Putz, Mihai V
2011-04-13
The conceptual and practical issues regarding the reduction of the Haldane-Radić enzymic mechanism, specific for cholinesterase kinetics, to the consecrated or logistically modified Michaelis-Menten kinetics, specific for some mutant enzymes, are here clarified as due to the limited initial substrate concentration, through detailed initial rate and progress curve analysis, even when other classical conditions for such equivalence are not entirely fulfilled.
2009-01-01
A different view of Henri-Michaelis-Menten (HMM) enzyme kinetics is presented. In the first part of the paper, a simplified but useful description that stresses the cyclic nature of the catalytic process is introduced. The time-dependence of the substrate concentration after the initial transient phase is derived in a simple way that dispenses the mathematical technique known as quasi-steady-state approximation. In the second part of the paper an exact one-dimensional formulation of HMM kinet...
Mihai V. Putz
2011-04-01
Full Text Available The conceptual and practical issues regarding the reduction of the Haldane-Radić enzymic mechanism, specific for cholinesterase kinetics, to the consecrated or logistically modified Michaelis-Menten kinetics, specific for some mutant enzymes, are here clarified as due to the limited initial substrate concentration, through detailed initial rate and progress curve analysis, even when other classical conditions for such equivalence are not entirely fulfilled.
Legitimacy of the stochastic Michaelis-Menten approximation.
Sanft, K R; Gillespie, D T; Petzold, L R
2011-01-01
Michaelis-Menten kinetics are commonly used to represent enzyme-catalysed reactions in biochemical models. The Michaelis-Menten approximation has been thoroughly studied in the context of traditional differential equation models. The presence of small concentrations in biochemical systems, however, encourages the conversion to a discrete stochastic representation. It is shown that the Michaelis-Menten approximation is applicable in discrete stochastic models and that the validity conditions are the same as in the deterministic regime. The authors then compare the Michaelis-Menten approximation to a procedure called the slow-scale stochastic simulation algorithm (ssSSA). The theory underlying the ssSSA implies a formula that seems in some cases to be different from the well-known Michaelis-Menten formula. Here those differences are examined, and some special cases of the stochastic formulas are confirmed using a first-passage time analysis. This exercise serves to place the conventional Michaelis-Menten formula in a broader rigorous theoretical framework.
Eberwein, Jennifer; Shen, Weijun; Jenerette, G Darrel
2017-05-11
China experiences some of the highest rates of anthropogenic nitrogen deposition globally, with further increases projected. Understanding of soil feedbacks to the combined anthropogenic influences of climate change and nitrogen deposition in these systems is critical to improve predictive abilities for future climate scenarios. Here we used a Michaelis-Menten substrate-based kinetics framework to explore how soil CO2 production (Rsoil) responds to changes in temperature and available soil nitrogen (N) by combining field experiments with laboratory manipulations from sites experiencing elevated rates of anthropogenic N deposition but varying in soil N availabiltiy. The temperature sensitivity of Rsoil was strongly influenced by labile C additions. Furthermore, estimation of the temperature response of the Michaelis-Menten parameters supports the use of substrate-based kinetics in modeling efforts. Results from both field and laboratory experiments demonstrated a general decrease in Rsoil with increasing soil available N that was variably dependent on carbon (C) availability. Both the field and the laboratory measurements demonstrated a consistent decrease in the Michaelis-Menten parameter kM with increasing soil available N, indicating an increase in the efficiency of soil C decomposition with increasing N. Furthermore, these results provide evidence of interactions between N deposition and temperature sensitivity, which could influence C storage under combined anthropogenic global change drivers.
Michaelis-Menten dynamics in protein subnetworks
Rubin, Katy J
2016-01-01
To understand the behaviour of complex systems it is often necessary to use models that describe the dynamics of subnetworks. It has previously been established using projection methods that such subnetwork dynamics generically involves memory of the past, and that the memory functions can be calculated explicitly for biochemical reaction networks made up of unary and binary reactions. However, many established network models involve also Michaelis-Menten kinetics, to describe e.g. enzymatic reactions. We show that the projection approach to subnetwork dynamics can be extended to such networks, thus significantly broadening its range of applicability. To derive the extension we construct a larger network that represents enzymes and enzyme complexes explicitly, obtain the projected equations, and finally take the limit of fast enzyme reactions that gives back Michaelis-Menten kinetics. The crucial point is that this limit can be taken in closed form. The outcome is a simple procedure that allows one to obtain ...
About and beyond the Henri-Michaelis-Menten rate equation for single-substrate enzyme kinetics.
Bajzer, Zeljko; Strehler, Emanuel E
2012-01-20
For more than a century the simple single-substrate enzyme kinetics model and related Henri-Michaelis-Menten (HMM) rate equation have been thoroughly explored in various directions. In the present paper we are concerned with a possible generalization of this rate equation recently proposed by F. Kargi (BBRC 382 (2009) 157-159), which is assumed to be valid both in the case that the total substrate or enzyme is in excess and the quasi-steady-state is achieved. We demonstrate that this generalization is grossly inadequate and propose another generalization based on application of the quasi-steady-state condition and conservation equations for both enzyme and substrate. The standard HMM equation is derived by (a) assuming the quasi-steady-state condition, (b) applying the conservation equation only for the enzyme, and (c) assuming that the substrate concentration at quasi-steady-state can be approximated by the total substrate concentration [S](0). In our formula the rate is already expressed through [S](0), and we only assume that when quasi-steady-state is achieved the amount of product formed is negligible compared to [S](0). Numerical simulations show that our formula is generally more accurate than the HMM formula and also can provide a good approximation when the enzyme is in excess, which is not the case for the HMM formula. We show that the HMM formula can be derived from our expression by further assuming that the total enzyme concentration is negligible compared to [S](0). Copyright © 2011 Elsevier Inc. All rights reserved.
Statistical reconstruction of transcription factor activity using Michaelis-Menten kinetics.
Khanin, R; Vinciotti, V; Mersinias, V; Smith, C P; Wit, E
2007-09-01
The basic building block of a gene regulatory network consists of a gene encoding a transcription factor (TF) and the gene(s) it regulates. Considerable efforts have been directed recently at devising experiments and algorithms to determine TFs and their corresponding target genes using gene expression and other types of data. The underlying problem is that the expression of a gene coding for the TF provides only limited information about the activity of the TF, which can also be controlled posttranscriptionally. In the absence of a reliable technology to routinely measure the activity of regulators, it is of great importance to understand whether this activity can be inferred from gene expression data. We here develop a statistical framework to reconstruct the activity of a TF from gene expression data of the target genes in its regulatory module. The novelty of our approach is that we embed the deterministic Michaelis-Menten model of gene regulation in this statistical framework. The kinetic parameters of the gene regulation model are inferred together with the profile of the TF regulator. We also obtain a goodness-of-fit test to verify the fit of the model. The model is applied to a time series involving the Streptomyces coelicolor bacterium. We focus on the transcriptional activator cdaR, which is partly responsible for the production of a particular type of antibiotic. The aim is to reconstruct the activity profile of this regulator. Our approach can be extended to include more complex regulatory relationships, such as multiple regulatory factors, competition, and cooperativity.
Michaelis-Menten dynamics in protein subnetworks.
Rubin, Katy J; Sollich, Peter
2016-05-07
To understand the behaviour of complex systems, it is often necessary to use models that describe the dynamics of subnetworks. It has previously been established using projection methods that such subnetwork dynamics generically involves memory of the past and that the memory functions can be calculated explicitly for biochemical reaction networks made up of unary and binary reactions. However, many established network models involve also Michaelis-Menten kinetics, to describe, e.g., enzymatic reactions. We show that the projection approach to subnetwork dynamics can be extended to such networks, thus significantly broadening its range of applicability. To derive the extension, we construct a larger network that represents enzymes and enzyme complexes explicitly, obtain the projected equations, and finally take the limit of fast enzyme reactions that gives back Michaelis-Menten kinetics. The crucial point is that this limit can be taken in closed form. The outcome is a simple procedure that allows one to obtain a description of subnetwork dynamics, including memory functions, starting directly from any given network of unary, binary, and Michaelis-Menten reactions. Numerical tests show that this closed form enzyme elimination gives a much more accurate description of the subnetwork dynamics than the simpler method that represents enzymes explicitly and is also more efficient computationally.
Differences in Michaelis-Menten kinetics for different cultivars of maize during cyanide removal.
Yu, Xiao-Zhang; Gu, Ji-Dong
2007-06-01
Knowledge of the kinetic parameters, the half-saturation constant (K(m)) and the maximum metabolic capacity (v(max)), is very useful for the characterization of enzymes and biochemical processes. Little is known about rates of which vegetation metabolizes environmental chemicals. It is known, however, that vascular plants possess an enzyme system that detoxifies cyanide by converting it into the amino acid asparagine. This study investigated the differences in Michaelis-Menten kinetics of cyanide removal by different cultivars of maize. Detached leaves (1.0 g fresh weight) of seven different cultivars of maize (Zea mays L.) were kept in glass vessels with 100mL of aqueous solution spiked with potassium cyanide at 25+/-0.5 degrees C for 28 h. Four treatment concentrations of cyanide were used, ranging from 0.43 to 7.67 mgCNL(-1). The disappearance of cyanide from the aqueous solution was analyzed spectrophotometrically. Realistic values of K(m) and v(max) were estimated by a computer program using non-linear regression treatment. Lineweaver-Burk plots were also used to estimate the kinetic parameters for comparison. Using non-linear regression treatments, values of v(max) and K(m) were found to be between 10.80 and 22.80 mgCNkg(-1)h(-1), and 2.57 and 7.09 mgCNL(-1), respectively. The highest v(max) was achieved by the cultivars HengFen 1, followed by NongDa 108. The lowest v(max) was demonstrated by JingKe 8. The highest K(m) was found in NongDa 108, followed by HengFen 1. The lowest K(m) was associated with JingKe 8. Results from this study indicated that significant removal of cyanide from an aqueous solution was observed in the presence of plant materials without apparent phytotoxicity, even at the high concentration of cyanide used in this study. All maize cultivars used in this study were able to metabolize cyanide efficiently, although with different metabolic capacities. Results also showed a small variation of metabolic rates between the different cultivars
Bezerra, Rui M F; Pinto, Paula A; Fraga, Irene; Dias, Albino A
2016-03-01
To determine initial velocities of enzyme catalyzed reactions without theoretical errors it is necessary to consider the use of the integrated Michaelis-Menten equation. When the reaction product is an inhibitor, this approach is particularly important. Nevertheless, kinetic studies usually involved the evaluation of other inhibitors beyond the reaction product. The occurrence of these situations emphasizes the importance of extending the integrated Michaelis-Menten equation, assuming the simultaneous presence of more than one inhibitor because reaction product is always present. This methodology is illustrated with the reaction catalyzed by alkaline phosphatase inhibited by phosphate (reaction product, inhibitor 1) and urea (inhibitor 2). The approach is explained in a step by step manner using an Excel spreadsheet (available as a template in Appendix). Curve fitting by nonlinear regression was performed with the Solver add-in (Microsoft Office Excel). Discrimination of the kinetic models was carried out based on Akaike information criterion. This work presents a methodology that can be used to develop an automated process, to discriminate in real time the inhibition type and kinetic constants as data (product vs. time) are achieved by the spectrophotometer. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.
Single-molecule Michaelis-Menten equations.
Kou, S C; Cherayil, Binny J; Min, Wei; English, Brian P; Xie, X Sunney
2005-10-20
This paper summarizes our present theoretical understanding of single-molecule kinetics associated with the Michaelis-Menten mechanism of enzymatic reactions. Single-molecule enzymatic turnover experiments typically measure the probability density f(t) of the stochastic waiting time t for individual turnovers. While f(t) can be reconciled with ensemble kinetics, it contains more information than the ensemble data; in particular, it provides crucial information on dynamic disorder, the apparent fluctuation of the catalytic rates due to the interconversion among the enzyme's conformers with different catalytic rate constants. In the presence of dynamic disorder, f(t) exhibits a highly stretched multiexponential decay at high substrate concentrations and a monoexponential decay at low substrate concentrations. We derive a single-molecule Michaelis-Menten equation for the reciprocal of the first moment of f(t), 1/, which shows a hyperbolic dependence on the substrate concentration [S], similar to the ensemble enzymatic velocity. We prove that this single-molecule Michaelis-Menten equation holds under many conditions, in particular when the intercoversion rates among different enzyme conformers are slower than the catalytic rate. However, unlike the conventional interpretation, the apparent catalytic rate constant and the apparent Michaelis constant in this single-molecule Michaelis-Menten equation are complicated functions of the catalytic rate constants of individual conformers. We also suggest that the randomness parameter r, defined as )2> / t2, can serve as an indicator for dynamic disorder in the catalytic step of the enzymatic reaction, as it becomes larger than unity at high substrate concentrations in the presence of dynamic disorder.
Kumar, Ashutosh; Maity, Hiranmay; Dua, Arti
2015-07-09
Recent fluorescence spectroscopy measurements of the turnover time distribution of single-enzyme turnover kinetics of β-galactosidase provide evidence of Michaelis-Menten kinetics at low substrate concentration. However, at high substrate concentrations, the dimensionless variance of the turnover time distribution shows systematic deviations from the Michaelis-Menten prediction. This difference is attributed to conformational fluctuations in both the enzyme and the enzyme-substrate complex and to the possibility of both parallel- and off-pathway kinetics. Here, we use the chemical master equation to model the kinetics of a single fluctuating enzyme that can yield a product through either parallel- or off-pathway mechanisms. An exact expression is obtained for the turnover time distribution from which the mean turnover time and randomness parameters are calculated. The parallel- and off-pathway mechanisms yield strikingly different dependences of the mean turnover time and the randomness parameter on the substrate concentration. In the parallel mechanism, the distinct contributions of enzyme and enzyme-substrate fluctuations are clearly discerned from the variation of the randomness parameter with substrate concentration. From these general results, we conclude that an off-pathway mechanism, with substantial enzyme-substrate fluctuations, is needed to rationalize the experimental findings of single-enzyme turnover kinetics of β-galactosidase.
Reith, David; Medlicott, Natalie J; Kumara De Silva, Rohana; Yang, Lin; Hickling, Jeremy; Zacharias, Mathew
2009-01-01
1. The aim of the present study was to perform an in vivo estimation of the Michaelis-Menten constants of the major metabolic pathways of paracetamol (APAP). 2. A two-occasion, single-dose cross-over trial was performed using 60 and 90 mg/kg doses of APAP in healthy patients undergoing third molar dental extraction. Plasma samples were collected over 24 h and urine was collected for 8 h after dosing. Twenty patients were enrolled in the study and complete data for plasma and urine were available for both doses for 13 volunteers who were included in the analysis; seven of the volunteers were men, the median age (range) was 22 years (19-31) and the median weight (range) was 68 kg (50-86). 3. The mean (95% CI) k(m) for APAP glucuronidation was 6.89 mmol/L (3.57-10.22) and the V(max) was 0.97 mmol/h per kg (0.65-1.28). The k(m) for APAP sulphation was 0.097 mmol/L (0.041-0.152) and the V(max) was 0.011 mmol/h per kg (0.009-0.013). For the combined excretion of APAP-cysteine and APAP-mercapturate, the k(m) was 0.303 mmol/L (0.131-0.475) and the V(max) was 0.004 mmol/h per kg (0.002-0.005). 4. The estimates for in vivo Michaelis-Menten constants for APAP glucuronidation and sulphation were in the order of those reported previously using in vitro methods.
Pulkkinen, O
2016-01-01
Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessi...
Bezerra, Rui M F; Fraga, Irene; Dias, Albino A
2013-01-01
Enzyme kinetic parameters are usually determined from initial rates nevertheless, laboratory instruments only measure substrate or product concentration versus reaction time (progress curves). To overcome this problem we present a methodology which uses integrated models based on Michaelis-Menten equation. The most severe practical limitation of progress curve analysis occurs when the enzyme shows a loss of activity under the chosen assay conditions. To avoid this problem it is possible to work with the same experimental points utilized for initial rates determination. This methodology is illustrated by the use of integrated kinetic equations with the well-known reaction catalyzed by alkaline phosphatase enzyme. In this work nonlinear regression was performed with the Solver supplement (Microsoft Office Excel). It is easy to work with and track graphically the convergence of SSE (sum of square errors). The diagnosis of enzyme inhibition was performed according to Akaike information criterion. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.
Houston, J B; Kenworthy, K E
2000-03-01
Strategies for the prediction of in vivo drug clearance from in vitro drug metabolite kinetic data are well established for the rat. In this animal species, metabolism rate-substrate concentration relationships can commonly be described by the classic hyperbola consistent with the Michaelis-Menten model and simple scaling of the parameter intrinsic clearance (CL(int) - the ratio of V(max) to K(m)) is particularly valuable. The in vitro scaling of kinetic data from human tissue is more complex, particularly as many substrates for cytochrome P450 (CYP) 3A4, the dominant human CYP, show nonhyperbolic metabolism rate-substrate concentration curves. This review critically examines these types of data, which require the adoption of an enzyme model with multiple sites showing cooperative binding for the drug substrate, and considers the constraints this kinetic behavior places on the prediction of in vivo pharmacokinetic characteristics, such as metabolic stability and inhibitory drug interaction potential. The cases of autoactivation and autoinhibition are discussed; the former results in an initial lag in the rate-substrate concentration profile to generate a sigmoidal curve whereas the latter is characterized by a convex curve as V(max) is not maintained at high substrate concentrations. When positive cooperativity occurs, we suggest the use of CL(max), the maximal clearance resulting from autoactivation, as a substitute for CL(int). The impact of heteroactivation on this approach is also of importance. In the case of negative cooperativity, care in using the V(max)/K(m) approach to CL(int) determination must be taken. Examples of substrates displaying each type of kinetic behavior are discussed for various recombinant CYP enzymes, and possible artifactual sources of atypical rate-concentration curves are outlined. Finally, the consequences of ignoring atypical Michaelis-Menten kinetic relationships are examined, and the inconsistencies reported for both different
Alternative Analysis of the Michaelis-Menten Equations
Krogstad, Harald E.; Dawed, Mohammed Yiha; Tegegne, Tadele Tesfa
2011-01-01
Courses in mathematical modelling are always in need of simple, illustrative examples. The Michaelis-Menten reaction kinetics equations have been considered to be a basic example of scaling and singular perturbation. However, the leading order approximations do not easily show the expected behaviour, and this note proposes a different perturbation…
Alternative Analysis of the Michaelis-Menten Equations
Krogstad, Harald E.; Dawed, Mohammed Yiha; Tegegne, Tadele Tesfa
2011-01-01
Courses in mathematical modelling are always in need of simple, illustrative examples. The Michaelis-Menten reaction kinetics equations have been considered to be a basic example of scaling and singular perturbation. However, the leading order approximations do not easily show the expected behaviour, and this note proposes a different perturbation…
Explicit reformulations of time-dependent solution for a Michaelis-Menten enzyme reaction model.
Golicnik, Marko
2010-11-01
The exact closed-form solution to the Michaelis-Menten equation is expressed in terms of the Lambert W(x) function. However, the utility of this solution is limited because the W(x) function is not widely available in curve-fitting software. Based on various approximations to the W(x) function, different explicit equations expressed in terms of the elementary functions are proposed here as useful shortcuts to fit time depletion of substrate concentration directly to progress curves using commonly available nonlinear regression computer programs. The results are compared with those obtained by fitting other algebraic equations that have been proposed previously in the literature. 2010 Elsevier Inc. All rights reserved.
Wu, Xiaotian; Li, Jun; Nekka, Fahima
2015-04-01
The current study aims to provide the closed form solutions of one-compartment open models exhibiting simultaneous linear and nonlinear Michaelis-Menten elimination kinetics for single- and multiple-dose intravenous bolus administrations. It can be shown that the elimination half-time ([Formula: see text]) has a dose-dependent property and is upper-bounded by [Formula: see text] of the first-order elimination model. We further analytically distinguish the dominant role of different elimination pathways in terms of model parameters. Moreover, for the case of multiple-dose intravenous bolus administration, the existence and local stability of the periodic solution at steady state are established. The closed form solutions of the models are obtained through a newly introduced function motivated by the Lambert W function.
Michel, Denis
2013-01-01
The Michaelis-Menten enzymatic reaction is sufficient to perceive many subtleties of network modeling, including the concentration and time scales separations, the formal equivalence between bulk phase and single-molecule approaches, or the relationships between single-cycle transient probabilities and steady state rates. Seven methods proposed by different authors and yielding the same famous Michaelis-Menten equation, are selected here to illustrate the kinetic and probabilistic use of rate constants and to review basic techniques for handling them. Finally, the general rate of an ordered multistep reaction, of which the Michaelis-Menten reaction is a particular case, is deduced from a Markovian approach.
Lee, Byung-Yo; Kwon, Kwang-Il; Kim, Min-Soo; Baek, In-Hwan
2016-08-01
Etanercept was approved by the Food and Drug Administration (FDA) in 2010 as a biologic agent for the treatment of rheumatoid arthritis (RA). The aim of the study was to investigate the pharmacokinetic properties of etanercept after intravenous and subcutaneous injection in rats. The plasma concentration of etanercept was determined using an enzyme-linked immunosorbent assay (ELISA). Intravenous and subcutaneous administration of 2 mg/kg of etanercept to rats showed that etanercept was slowly absorbed (time to reach the peak drug concentration [T max] = 1.60 days, bioavailability [F] = 47.18 %) and slowly eliminated (half-life [t 1/2], 2.33 days after intravenous administration and 3.31 days after subcutaneous administration). The area under the curve values on day 13 (AUC13day) were 121.25 ± 14.37 and 48.56 ± 6.78 μg day/mL after intravenous and subcutaneous administration, respectively. A two-compartment model with Michaelis-Menten elimination kinetics (V max = 94.28 µg/day; K m = 10.88 µg/mL) was used to describe the pharmacokinetic profile of etanercept. Our results describe the pharmacokinetic profile of etanercept, and these results could be used for the development of etanercept biosimilars.
Meyer, Markus R; Orschiedt, Tina; Maurer, Hans H
2013-02-27
The pharmacokinetics of various important drugs are known to be significantly influenced by the human ABC transporter P-glycoprotein (P-gp), which may lead to clinically relevant drug-drug interactions. In contrast to therapeutic drugs, emerging drugs of abuse (DOA) are sold and consumed without any safety pharmacology testing. Only some studies on their metabolism were published, but none about their affinity to the transporter systems. Therefore, 47 DOAs from various classes were tested for their P-gp affinity using human P-gp (hP-gp) to predict possible drug-drug interactions. DOAs were initially screened for general hP-gp affinity and further characterized by modeling classic Michaelis-Menten kinetics and assessing their K(m) and V(max) values. Among the tested drugs, 12 showed a stimulation of ATPase activity. The most intensive stimulating DOAs were further investigated and compared with the known P-gp model substrates sertraline and verapamil. ATPase stimulation kinetics could be modeled for the entactogen 3,4-methylenedioxy-α-ethylphenethylamine (3,4-BDB), the hallucinogen 2,5-dimethoxy-4-iodoamphetamine (DOI), the abused alkaloid glaucine, the opioid-like drugs N-iso-propyl-1,2-diphenylethylamine (NPDPA), and N-(1-phenylcyclohexyl)-3-ethoxypropanamine (PCEPA), with K(m) and V(max) values within the same range as for verapamil or sertraline. As a consequence interactions with other drugs being P-gp substrates might be considered to be very likely and further studies should be encouraged. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
Use of Mushroom Tyrosinase to Introduce Michaelis-Menten Enzyme Kinetics to Biochemistry Students
Flurkey, William H.; Inlow, Jennifer K.
2017-01-01
An inexpensive enzyme kinetics laboratory exercise for undergraduate biochemistry students is described utilizing tyrosinase from white button mushrooms. The exercise can be completed in one or two three-hour lab sessions. The optimal amounts of enzyme, substrate (catechol), and inhibitor (kojic acid) are first determined, and then kinetic data is…
Utilization of Integrated Michaelis-Menten Equation to Determine Kinetic Constants
Bezerra, Rui M. F.; Dias, Albino A.
2007-01-01
Students of biochemistry and related biosciences are urged to solve problems where kinetic parameters are calculated from initial rates obtained at different substrate concentrations. Troubles begin when they go to the laboratory to perform kinetic experiments and realize that usual laboratory instruments do not measure initial rates but only…
Utilization of Integrated Michaelis-Menten Equation to Determine Kinetic Constants
Bezerra, Rui M. F.; Dias, Albino A.
2007-01-01
Students of biochemistry and related biosciences are urged to solve problems where kinetic parameters are calculated from initial rates obtained at different substrate concentrations. Troubles begin when they go to the laboratory to perform kinetic experiments and realize that usual laboratory instruments do not measure initial rates but only…
Pulkkinen, Otto; Metzler, Ralf
2015-12-04
Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessible to experiments and not specific to the exact source of the concentration fluctuations.
The Nuts and Bolts of Michaelis-Menten Enzyme Kinetics: Suggestions and Clarifications
Silverstein, Todd
2011-01-01
Matthew Junker's recent article describes a useful and effective enzyme kinetics application and analogy in which students simulate enzyme activity by unscrewing nut-bolt "substrate molecules", thus, converting them into separate nuts and bolts "products". A number of suggestions and corrections are presented that improve the clarity and accuracy…
The Nuts and Bolts of Michaelis-Menten Enzyme Kinetics: Suggestions and Clarifications
Silverstein, Todd
2011-01-01
Matthew Junker's recent article describes a useful and effective enzyme kinetics application and analogy in which students simulate enzyme activity by unscrewing nut-bolt "substrate molecules", thus, converting them into separate nuts and bolts "products". A number of suggestions and corrections are presented that improve the clarity and accuracy…
Non-Michaelis-Menten kinetics model for conductance of low-conductance potassium ion channels.
Tolokh, Igor S; Tolokh, Illya I; Cho, Hee Cheol; D'Avanzo, Nazzareno; Backx, Peter H; Goldman, Saul; Gray, C G
2005-02-01
A reduced kinetics model is proposed for ion permeation in low-conductance potassium ion channels with zero net electrical charge in the selectivity filter region. The selectivity filter is assumed to be the only conductance-determining part of the channel. Ion entry and exit rate constants depend on the occupancy of the filter due to ion-ion interactions. The corresponding rates are assumed slow relative to the rates of ion motion between binding sites inside the filter, allowing a reduction of the kinetics model of the filter by averaging the entry and exit rate constants over the states with a particular occupancy number. The reduced kinetics model for low-conductance channels is described by only three states and two sets of effective rate constants characterizing transitions between these states. An explicit expression for the channel conductance as a function of symmetrical external ion concentration is derived under the assumption that the average electrical mobility of ions in the selectivity filter region in a limited range of ion concentrations does not depend on these concentrations. The simplified conductance model is shown to provide a good description of the experimentally observed conductance-concentration curve for the low-conductance potassium channel Kir2.1, and also predicts the mean occupancy of the selectivity filter of this channel. We find that at physiological external ion concentrations this occupancy is much lower than the value of two ions observed for one of the high-conductance potassium channels, KcsA.
Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem.
Rotbart, Tal; Reuveni, Shlomi; Urbakh, Michael
2015-12-01
We study the effect of restart, and retry, on the mean completion time of a generic process. The need to do so arises in various branches of the sciences and we show that it can naturally be addressed by taking advantage of the classical reaction scheme of Michaelis and Menten. Stopping a process in its midst-only to start it all over again-may prolong, leave unchanged, or even shorten the time taken for its completion. Here we are interested in the optimal restart problem, i.e., in finding a restart rate which brings the mean completion time of a process to a minimum. We derive the governing equation for this problem and show that it is exactly solvable in cases of particular interest. We then continue to discover regimes at which solutions to the problem take on universal, details independent forms which further give rise to optimal scaling laws. The formalism we develop, and the results obtained, can be utilized when optimizing stochastic search processes and randomized computer algorithms. An immediate connection with kinetic proofreading is also noted and discussed.
Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem
Rotbart, Tal; Reuveni, Shlomi; Urbakh, Michael
2015-12-01
We study the effect of restart, and retry, on the mean completion time of a generic process. The need to do so arises in various branches of the sciences and we show that it can naturally be addressed by taking advantage of the classical reaction scheme of Michaelis and Menten. Stopping a process in its midst—only to start it all over again—may prolong, leave unchanged, or even shorten the time taken for its completion. Here we are interested in the optimal restart problem, i.e., in finding a restart rate which brings the mean completion time of a process to a minimum. We derive the governing equation for this problem and show that it is exactly solvable in cases of particular interest. We then continue to discover regimes at which solutions to the problem take on universal, details independent forms which further give rise to optimal scaling laws. The formalism we develop, and the results obtained, can be utilized when optimizing stochastic search processes and randomized computer algorithms. An immediate connection with kinetic proofreading is also noted and discussed.
Michel, Denis; Ruelle, Philippe
2013-01-01
International audience; The Michaelis-Menten enzymatic reaction is sufficient to perceive many subtleties of network modeling, including the concentration and time scales separations, the formal equivalence between bulk phase and single-molecule approaches, or the relationships between single-cycle transient probabilities and steady state rates. Seven methods proposed by different authors and yielding the same famous Michaelis-Menten equation, are selected here to illustrate the kinetic and p...
Goličnik, Marko
2011-09-01
The exact closed-form solutions to the integrated rate equations for one-compartment pharmacokinetic models that obey Michaelis-Menten elimination kinetics were derived recently (Tang and Xiao in J Pharmacokin Pharmacodyn 34:807-827, 2007). These solutions are expressed in terms of the Lambert W(x)-omega function; however, unfortunately, most of the available computer programs are not set up to handle equations that involve the W(x) function. Therefore, in this article, I provide alternative explicit analytical equations expressed in terms of elementary mathematical functions that accurately approximate exact solutions and can be simply calculated using any optional standard software.
Long, Cormac G; Gilbertson, John D; Vijayaraghavan, Ganesh; Stevenson, Keith J; Pursell, Christopher J; Chandler, Bert D
2008-08-06
Thiol monolayer-protected Au clusters (MPCs) were prepared using dendrimer templates, deposited onto a high-surface-area titania, and then the thiol stabilizers were removed under H2/N2. The resulting Au catalysts were characterized with transmission electron microscopy, X-ray photoelectron spectroscopy, and infrared spectroscopy of adsorbed CO. The Au catalysts prepared via this route displayed minimal particle agglomeration during the deposition and activation steps. Structural data obtained from the physical characterization of the Au catalysts were comparable to features exhibited from a traditionally prepared standard Au catalyst obtained from the World Gold Council (WGC). A differential kinetic study of CO oxidation catalysis by the MPC-prepared Au and the standard WGC catalyst showed that these two catalyst systems have essentially the same reaction order and Arrhenius apparent activation energies (28 kJ/mol). However, the MPC-prepared Au catalyst shows 50% greater activity for CO oxidation. Using a Michaelis-Menten approach, the oxygen binding constants for the two catalyst systems were determined and found to be essentially the same within experimental error. To our knowledge, this kinetic evaluation is the first experimental determination of oxygen binding by supported Au nanoparticle catalysts under working conditions. The values for the oxygen binding equilibrium constant obtained from the Michaelis-Menten treatment (ca. 29-39) are consistent with ultra-high-vacuum measurements on model catalyst systems and support density functional theory calculations for oxygen binding at corner or edge atoms on Au nanoparticles and clusters.
The Michaelis-Menten-Stueckelberg Theorem
Alexander N. Gorban
2011-05-01
Full Text Available We study chemical reactions with complex mechanisms under two assumptions: (i intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS and (ii they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE. Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the “rarefied gas” limit or the “molecular chaos” hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density (low density of elementary events. This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann H-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.
Fowler, Stephen; Guerini, Elena; Qiu, NaHong; Cleary, Yumi; Parrott, Neil; Greig, Gerard; Mallalieu, Navita L
2017-01-01
Basimglurant, a novel mGlu5-negative allosteric modulator under development for the treatment of major depressive disorder, is cleared via cytochrome P450 (P450)-mediated oxidative metabolism. Initial enzyme phenotyping studies indicated that CYP3A4/5 dominates basimglurant metabolism and highlights a risk for drug-drug interactions when it is comedicated with strong CYP3A4/5 inhibitors or inactivators; however, a clinical drug-drug interaction (DDI) study using the potent and selective CYP3A4/5 inhibitor ketoconazole resulted in an area under the curve (AUC) AUCi/AUC ratio of only 1.24. A further study using the CYP3A4 inducer carbamazepine resulted in an AUCi/AUC ratio of 0.69. More detailed in vitro enzyme phenotyping and kinetics studies showed that, at the low concentrations attained clinically, basimglurant metabolic clearance is catalyzed mainly by CYP1A2. The relative contributions of the enzymes were estimated as 70:30 CYP1A2:CYP3A4/5. Using this information, a clinical study using the CYP1A2 inhibitor fluvoxamine was performed, resulting in an AUCi/AUC ratio of 1.60, confirming the role of CYP1A2 and indicating a balanced DDI risk profile. Basimglurant metabolism kinetics show enzyme dependency: CYP1A2-mediated metabolism follows Michaelis-Menten kinetics, whereas CYP3A4 and CYP3A5 follow sigmoidal kinetics [with similar constant (KM) and S50 values]. The interplay of the different enzyme kinetics leads to changing fractional enzyme contributions to metabolism with substrate concentration, even though none of the metabolic enzymes is saturated. This example demonstrates the relevance of non-Michaelis-Menten P450 enzyme kinetics and highlights the need for a thorough understanding of metabolism enzymology to make accurate predictions for human metabolism in vivo. Copyright © 2016 by The American Society for Pharmacology and Experimental Therapeutics.
Moaty Sayed, A A; Hussein, M A; Becker, T
2010-04-01
Lattice Boltzmann models (LBM) are rapidly showing their ability to simulate a lot of fluid dynamics problems that previously required very complex approaches. This study presents a LBM for simulating diffusion-advection transport of substrate in a 2-D laminar flow. The model considers the substrate influx into a set of active cells placed inside the flow field. A new innovative method was used to simulate the cells activity using the LBM by means of Michaelis-Menten kinetics. The model is validated with some numerical benchmark problems and proved highly accurate results. After validation the model was used to simulate the transport of oxygen substrates that diffuse in water to feed a set of active cartilage cells inside a new designed bioreactor.
Coluzzi, Barbara; Bersani, Enrico
2016-01-01
We recall the perturbation expansion for Michaelis-Menten kinetics, beyond the standard quasi-steady-state approximation (sQSSA). Against this background, we are able to appropriately apply the alternative approach to the study of singularly perturbed differential equations that is based on the renormalization group (SPDERG), by clarifying similarities and differences. In the present demanding situation, we directly renormalize the bare initial condition value for the substrate. Our main results are: i) the 2nd order SPDERG uniform approximations to the correct solutions contain, up to 1st order, the same outer components as the known perturbation expansion ones; ii) the differential equation to be solved for the derivation of the 1st order outer substrate component is simpler within the SPDERG approach; iii) the approximations better reproduce the numerical solutions of the original problem in a region encompassing the matching one, because of the 2nd order terms in the inner components, calculated here for ...
Schnell, Santiago
2014-01-01
The Michaelis-Menten equation is generally used to estimate the kinetic parameters, V and K(M), when the steady-state assumption is valid. Following a brief overview of the derivation of the Michaelis-Menten equation for the single-enzyme, single-substrate reaction, a critical review of the criteria for validity of the steady-state assumption is presented. The application of the steady-state assumption makes the implicit assumption that there is an initial transient during which the substrate concentration remains approximately constant, equal to the initial substrate concentration, while the enzyme-substrate complex concentration builds up. This implicit assumption is known as the reactant stationary assumption. This review presents evidence showing that the reactant stationary assumption is distinct from and independent of the steady-state assumption. Contrary to the widely believed notion that the Michaelis-Menten equation can always be applied under the steady-state assumption, the reactant stationary assumption is truly the necessary condition for validity of the Michaelis-Menten equation to estimate kinetic parameters. Therefore, the application of the Michaelis-Menten equation only leads to accurate estimation of kinetic parameters when it is used under experimental conditions meeting the reactant stationary assumption. The criterion for validity of the reactant stationary assumption does not require the restrictive condition of choosing a substrate concentration that is much higher than the enzyme concentration in initial rate experiments. © 2013 FEBS.
Stochastic mapping of the Michaelis-Menten mechanism.
Dóka, Éva; Lente, Gábor
2012-02-07
The Michaelis-Menten mechanism is an extremely important tool for understanding enzyme-catalyzed transformation of substrates into final products. In this work, a computationally viable, full stochastic description of the Michaelis-Menten kinetic scheme is introduced based on a stochastic equivalent of the steady-state assumption. The full solution derived is free of restrictions on amounts of substance or parameter values and is used to create stochastic maps of the Michaelis-Menten mechanism, which show the regions in the parameter space of the scheme where the use of the stochastic kinetic approach is inevitable. The stochastic aspects of recently published examples of single-enzyme kinetic studies are analyzed using these maps.
Bezerra, Rui M F; Dias, Albino A
2004-03-01
The kinetics of exoglucanase (Cel7A) from Trichoderma reesei was investigated in the presence of cellobiose and 24 different enzyme/Avicel ratios for 47 h, in order to establish which of the eight available kinetic models best explained the factors involved. The heterogeneous catalysis was studied and the kinetic parameters were estimated employing integrated forms of Michaelis-Menten equations through the use of nonlinear least squares. It was found that cellulose hydrolysis follows a model that takes into account competitive inhibition by cellobiose (final product) with the following parameters: Km = 3.8 mM, Kic = 0.041 mM, kcat = 2 h-1 (5.6 x 10-4 s-1). Other models, such as mixed type inhibition and those incorporating improvements concerning inhibition by substrate and parabolic inhibition, increased the modulation performance very slightly. The results support the hypothesis that nonproductive enzyme substrate complexes, parabolic inhibition, and enzyme inactivation (Selwyn test) are not the principal constraints in enzymatic cellulose hydrolysis. Under our conditions, the increment in hydrolysis was not significant for substrate/enzyme ratios <6.5.
Michaelis-Menten equation and detailed balance in enzymatic networks.
Cao, Jianshu
2011-05-12
Many enzymatic reactions in biochemistry are far more complex than the celebrated Michaelis-Menten scheme, but the observed turnover rate often obeys the hyperbolic dependence on the substrate concentration, a relation established almost a century ago for the simple Michaelis-Menten mechanism. To resolve the longstanding puzzle, we apply the flux balance method to predict the functional form of the substrate dependence in the mean turnover time of complex enzymatic reactions and identify detailed balance (i.e., the lack of unbalanced conformational current) as a sufficient condition for the Michaelis-Menten equation to describe the substrate concentration dependence of the turnover rate in an enzymatic network. This prediction can be verified in single-molecule event-averaged measurements using the recently proposed signatures of detailed balance violations. The finding helps analyze recent single-molecule studies of enzymatic networks and can be applied to other external variables, such as force-dependence and voltage-dependence.
Li, Albert P; Schlicht, Kari E
2014-01-01
A higher throughput platform was developed for the determination of K(M) values for isoformselective P450 substrates in human hepatocytes via incubation of the hepatocytes with substrates in 384- well plates and metabolite quantification by RapidFire™ mass spectrometry. Isoform-selective P450 substrates were incubated at 8 concentrations in triplicate with cryopreserved human hepatocytes from 16 donors. The metabolic pathways examined were the CYP1A2-catalyzed tacrine 1-hydroxylation, CYP2B6-catalyzed bupropion hydroxylation, CYP2C8-catalyzed amodiaquine N-deethylation, CYP2C9- catalyzed diclofenac 4'-hydroxylation, CYP2D6-catalyzed dextromethorphan O-demethylation, and CYP3A4-catalyzed midazolam 1'-hydroxylation. Typical saturation enzyme kinetics was observed for all the pathways evaluated. Individual differences in the apparent V(max) and K(M) values were observed among the human hepatocytes from each of the 16 individual donors, with no statistically significant gender- or age-associated differences. A "composite" K(M) value was calculated for each of the pathways via normalizing the individual activities to their respective V(max) values to develop "relative activities" followed by Michaelis-Menten analysis of the mean relative activities of the 16 donors at each of the 8 substrate concentrations. The resulting "composite" K(M) values for the P450 substrates may be used to guide in vitro P450 inhibition and induction studies and kinetic modeling of in vivo drug-drug interaction.
Single molecule Michaelis-Menten equation beyond quasistatic disorder.
Xue, Xiaochuan; Liu, Fei; Ou-Yang, Zhong-Can
2006-09-01
The classic Michaelis-Menten equation describes the catalytic activities for ensembles of enzyme molecules very well. But recent single-molecule experiments showed that the waiting time distribution and other properties of single enzyme molecules were not consistent with the prediction based on the ensemble viewpoint. They have contributed to the slow conformational changes of a single enzyme in the catalytic processes. In this work, we study the general dynamics of single enzymes in the presence of dynamic disorder. We find that, within the time separation regimes, i.e., the slow reaction and nondiffusion limits, the Michaelis-Menten equation holds exactly. In particular, by employing the decoupling approximation we demonstrate analytically that the classic Michaelis-Menten equation is still an excellent approximation in the presence of general dynamic disorder.
Blum, Philipp; Hunkeler, Daniel; Weede, Matthias; Beyer, Christof; Grathwohl, Peter; Morasch, Barbara
2009-04-01
At a former wood preservation plant severely contaminated with coal tar oil, in situ bulk attenuation and biodegradation rate constants for several monoaromatic (BTEX) and polyaromatic hydrocarbons (PAH) were determined using (1) classical first order decay models, (2) Michaelis-Menten degradation kinetics (MM), and (3) stable carbon isotopes, for o-xylene and naphthalene. The first order bulk attenuation rate constant for o-xylene was calculated to be 0.0025 d - 1 and a novel stable isotope-based first order model, which also accounted for the respective redox conditions, resulted in a slightly smaller biodegradation rate constant of 0.0019 d - 1 . Based on MM-kinetics, the o-xylene concentration decreased with a maximum rate of kmax = 0.1 µg/L/d. The bulk attenuation rate constant of naphthalene retrieved from the classical first order decay model was 0.0038 d - 1 . The stable isotope-based biodegradation rate constant of 0.0027 d - 1 was smaller in the reduced zone, while residual naphthalene in the oxic part of the plume further downgradient was degraded at a higher rate of 0.0038 d - 1 . With MM-kinetics a maximum degradation rate of kmax = 12 µg/L/d was determined. Although best fits were obtained by MM-kinetics, we consider the carbon stable isotope-based approach more appropriate as it is specific for biodegradation (not overall attenuation) and at the same time accounts for the dominant electron-accepting process. For o-xylene a field based isotope enrichment factor ɛfield of - 1.4 could be determined using the Rayleigh model, which closely matched values from laboratory studies of o-xylene degradation under sulfate-reducing conditions.
Blum, Philipp; Hunkeler, Daniel; Weede, Matthias; Beyer, Christof; Grathwohl, Peter; Morasch, Barbara
2009-04-01
At a former wood preservation plant severely contaminated with coal tar oil, in situ bulk attenuation and biodegradation rate constants for several monoaromatic (BTEX) and polyaromatic hydrocarbons (PAH) were determined using (1) classical first order decay models, (2) Michaelis-Menten degradation kinetics (MM), and (3) stable carbon isotopes, for o-xylene and naphthalene. The first order bulk attenuation rate constant for o-xylene was calculated to be 0.0025 d(-1) and a novel stable isotope-based first order model, which also accounted for the respective redox conditions, resulted in a slightly smaller biodegradation rate constant of 0.0019 d(-1). Based on MM-kinetics, the o-xylene concentration decreased with a maximum rate of k(max)=0.1 microg/L/d. The bulk attenuation rate constant of naphthalene retrieved from the classical first order decay model was 0.0038 d(-1). The stable isotope-based biodegradation rate constant of 0.0027 d(-1) was smaller in the reduced zone, while residual naphthalene in the oxic part of the plume further downgradient was degraded at a higher rate of 0.0038 d(-1). With MM-kinetics a maximum degradation rate of k(max)=12 microg/L/d was determined. Although best fits were obtained by MM-kinetics, we consider the carbon stable isotope-based approach more appropriate as it is specific for biodegradation (not overall attenuation) and at the same time accounts for the dominant electron-accepting process. For o-xylene a field based isotope enrichment factor epsilon(field) of -1.4 could be determined using the Rayleigh model, which closely matched values from laboratory studies of o-xylene degradation under sulfate-reducing conditions.
Button, D K; Robertson, Betsy; Gustafson, Elizabeth; Zhao, Xiaoming
2004-09-01
A theory for solute uptake by whole cells was derived with a focus on the ability of oligobacteria to sequester nutrients. It provided a general relationship that was used to obtain the kinetic constants for in situ marine populations in the presence of naturally occurring substrates. In situ affinities of 0.9 to 400 liters g of cells(-1) h(-1) found were up to 10(3) times smaller than those from a "Marinobacter arcticus " isolate, but springtime values were greatly increased by warming. Affinities of the isolate for usual polar substrates but not for hydrocarbons were diminished by ionophores. A kinetic curve or Monod plot was constructed from the best available data for cytoarchitectural components of the isolate by using the theory together with concepts and calculations from first principles. The order of effect of these components on specific affinity was membrane potential > cytoplasmic enzyme concentration > cytoplasmic enzyme affinity > permease concentration > area of the permease site > translation coefficient > porin concentration. Component balance was influential as well; a small increase in cytoplasmic enzyme concentration gave a large increase in the effect of permease concentration. The effect of permease concentration on specific affinity was large, while the effect on K(m) was small. These results are in contrast to the Michaelis-Menten theory as applied by Monod that has uptake kinetics dependent on the quality of the permease molecules, with K(m) as an independent measure of affinity. Calculations demonstrated that most oligobacteria in the environment must use multiple substrates simultaneously to attain sufficient energy and material for growth, a requirement consistent with communities largely comprising few species.
André Rosa Martins
2015-01-01
.... One model was obtained, among the evaluated proposals, with performance indicating behavior similar to the classical Michaelis-Menten model, where the reaction complex is rapidly formed and, along...
Yu, Xiao-Zhang; Zhang, Xue-Hong
2016-07-01
Hydroponic experiments were conducted with different species of plants (rice, maize, soybean and willow) exposed to ferri-cyanide to investigate the half-saturation constant (K M ) and the maximal metabolic capacity (v max ) involved in phyto-assimilation. Three varieties for each testing species were collected from different origins. Measured concentrations show that the uptake rates responded biphasically to ferri-cyanide treatments by showing increases linearly at low and almost constant at high concentrations from all treatments, indicating that phyto-assimilation of ferri-cyanide followed the Michaelis-Menten kinetics. Using non-linear regression, the highest v max was by rice, followed by willows. The lowest v max was found for soybean. All plants, except maize (DY26) and rice (XJ12), had a similar K M value, suggesting the same enzyme was active in phyto-assimilation of ferri-cyanide. Transcript level, by real-time quantitative PCR, of enzymes involved in degradation of cyanides showed that the analyzed genes were differently expressed during different cyanides exposure. The expression of CAS and ST genes responded positively to KCN exposure, suggesting that β-CAS and ST pathways were two possible pathways for cyanide detoxification in rice. The transcript level of NIT and ASPNASE genes also showed a remarkable up-regulation to KCN, implying the contribution to the pool of amino acid aspartate, which is an end product of CN metabolism. Up-regulation of GS genes suggests that acquisition of ammonium released from cyanide degradation may be an additional nitrogen source for plant nutrition. Results also revealed that the expressions of these genes, except for GS, were relatively constant during iron cyanide exposure, suggesting that they are likely metabolized by plants through a non-defined pathway rather than the β-CAS pathway.
Michaelis-Menten relations for complex enzymatic networks.
Kolomeisky, Anatoly B
2011-04-21
Most biological processes are controlled by complex systems of enzymatic chemical reactions. Although the majority of enzymatic networks have very elaborate structures, there are many experimental observations indicating that some turnover rates still follow a simple Michaelis-Menten relation with a hyperbolic dependence on a substrate concentration. The original Michaelis-Menten mechanism has been derived as a steady-state approximation for a single-pathway enzymatic chain. The validity of this mechanism for many complex enzymatic systems is surprising. To determine general conditions when this relation might be observed in experiments, enzymatic networks consisting of coupled parallel pathways are investigated theoretically. It is found that the Michaelis-Menten equation is satisfied for specific relations between chemical rates, and it also corresponds to a situation with no fluxes between parallel pathways. Our results are illustrated for a simple model. The importance of the Michaelis-Menten relationship and derived criteria for single-molecule experimental studies of enzymatic processes are discussed.
Sakoda, M; Hiromi, K
1976-09-01
The best-fit values of the Michaelis constant (Km) and the maximum velocity (V) in the Michaelis-Menten equation can be obtained by the method of least squares with the Taylor expansion for the sum of squares of the absolute residual, i.e., the difference between the observed velocity and the corresponding velocity by calculation. This method makes it possible to determine the values of Km and V not in a trial-and-error manner but in a deductive and unique manner after some iterative procedures starting from arbitrary approximate values of Km and V. These values can be said to be uniquely determined for a set of data as the finally converged values are no longer dependent upon the initial approximate values of Km and V. It is also very important to obtain initial approximate values of parameters for the application of the method described above. A simple method is proposed to estimate the approximate values of parameters involved in fractional functions. The method of rearrangement after canceling of denominator of a fractional function can be utilized to obtain approximate values, not only for cases of two unknown parameters such as the Michaelis-Menten equation, but also for cases with more than two unknowns.
Longatte, Guillaume; Guille-Collignon, Manon; Lemaître, Frédéric
2017-06-15
In the past years, many strategies have been implemented to benefit from oxygenic photosynthesis to harvest photosynthetic electrons and produce a significant photocurrent. Therefore, electrochemical tools were considered and have globally relied on the electron transfer(s) between the photosynthetic chain and a collecting electrode. In this context, we recently reported the implementation of an electrochemical set-up at the preparative scale to produce photocurrents from a Chlamydomonas reinhardtii algae suspension with an appropriate mediator (2,6-DCBQ) and a carbon gauze as the working electrode. In the present work, we wish to describe a mathematical modeling of the recorded photocurrents to better understand the effects of the experimental conditions on the photosynthetic extraction of electrons. In that way, we established a general model of an electrocatalytic mechanism at the preparative scale (that is, assuming a homogenous bulk solution at any time and a constant diffusion layer, both assumptions being valid under forced convection) in which the chemical step involves a Michaelis-Menten-like behaviour. Dependences of transient and steady-state corresponding currents were analysed as a function of different parameters by means of zone diagrams. This model was tested to our experimental data related to photosynthesis. The corresponding results suggest that competitive pathways beyond photosynthetic harvesting alone should be taken into account. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Zhou, Chuanzheng; Chattopadhyaya, Jyoti
2010-04-02
In this study, 12 different native or LNA, carba-LNA-modified dinucleoside phosphates were designed as simple chemical models to study how carba-LNA modifications improve the 3'-exonuclease (SVPDE in this study) resistance of internucleotidic phosphate compared to those exhibited by LNA-modified and the native counterparts. Michaelis-Menten kinetic studies for dimers 3 - 7, in which the LNA or carba-LNA modifications are located at the 5'-end, showed that (i) increased 3'-exonuclease resistance of (5')[LNA-T](p)T (3) compared to the native (5')T(p)T (1) was mainly attributed to steric hindrance imposed by the LNA modification that retards the nuclease binding (K(M)) and (ii) digestion of (5')[carba-LNA-dT](p)T (4) and (5')[LNA-T](p)T (3), however, exhibit similar K(M)s, whereas the former shows a 100x decrease in K(cat) and is hence more stable than the latter. By studying the correlation between log k(cat) and pK(a) of the departing 3'(or 6')-OHs for 3-7, we found the pK(a) of 3'-OH of carba-LNA-T was 1.4 pK(a) units higher than that of LNA-T, and this relatively less acidic character of the 3'-OH in the former leads to the 100x decrease in the catalytic efficiency for the digestion of (5')[carba-LNA-T](p)T (4). In contrast, Michaelis-Menten kinetic studies for dimers 9-12, with the LNA or carba-LNA modifications at the 3'-end, showed that the digestion of (5')T(p)[LNA-T] (9) exhibited similar K(M) but k(cat) decreased around 40 times compared to that of the native (5')T(p)T (1). Similar k(cat) values have been observed for digestion of (5')T(p)[carba-LNA-T] (10) and (5')T(p)[LNA-T] (9). The higher stability of carba-LNA modified dimer 10 compared with LNA modified dimer 9 comes solely from the increased K(M).
Carvalho,Nakédia M. F.; Pires, Bianca M.; Antunes,Octavio A. C.; Roberto B Faria; Osório,Renata E. H. M. B.; Clovis Piovezan; Ademir Neves
2010-01-01
The Michaelis-Menten equation is used in many biochemical and bioinorganic kinetic studies involving homogeneous catalysis. Otherwise, it is known that determination of Michaelis-Menten parameters K M, Vmax, and k cat by the well-known Lineweaver-Burk double reciprocal linear equation does not produce the best values for these parameters. In this paper we present a discussion on different linear equations which can be used to calculate these parameters and we compare their results with the va...
Goličnik, Marko
2011-04-15
Various explicit reformulations of time-dependent solutions for the classical two-step irreversible Michaelis-Menten enzyme reaction model have been described recently. In the current study, I present further improvements in terms of a generalized integrated form of the Michaelis-Menten equation for computation of substrate or product concentrations as functions of time for more real-world, enzyme-catalyzed reactions affected by the product. The explicit equations presented here can be considered as a simpler and useful alternative to the exact solution for the generalized integrated Michaelis-Menten equation when fitted to time course data using standard curve-fitting software. Copyright © 2011 Elsevier Inc. All rights reserved.
Filobello-Nino, Uriel; Vazquez-Leal, Hector; Benhammouda, Brahim; Hernandez-Martinez, Luis; Khan, Yasir; Jimenez-Fernandez, Victor Manuel; Herrera-May, Agustin Leobardo; Castaneda-Sheissa, Roberto; Pereyra-Diaz, Domitilo; Cervantes-Perez, Juan; Agustin Perez-Sesma, Jose Antonio; Hernandez-Machuca, Sergio Francisco; Cuellar-Hernandez, Leticia
2014-01-01
In this article, Perturbation Method (PM) is employed to obtain a handy approximate solution to the steady state nonlinear reaction diffusion equation containing a nonlinear term related to Michaelis-Menten of the enzymatic reaction. Comparing graphics between the approximate and exact solutions, it will be shown that the PM method is quite efficient.
Filobello-Nino, Uriel; Vazquez-Leal, Hector; Benhammouda, Brahim; Hernandez-Martinez, Luis; Khan, Yasir; Jimenez-Fernandez, Victor Manuel; Herrera-May, Agustin Leobardo; Castaneda-Sheissa, Roberto; Pereyra-Diaz, Domitilo; Cervantes-Perez, Juan; Agustin Perez-Sesma, Jose Antonio; Hernandez-Machuca, Sergio Francisco; Cuellar-Hernandez, Leticia
2014-01-01
In this article, Perturbation Method (PM) is employed to obtain a handy approximate solution to the steady state nonlinear reaction diffusion equation containing a nonlinear term related to Michaelis-Menten of the enzymatic reaction. Comparing graphics between the approximate and exact solutions, it will be shown that the PM method is quite efficient.
Her, Cheenou; Alonzo, Aaron P.; Vang, Justin Y.; Torres, Ernesto; Krishnan, V. V.
2015-01-01
Enzyme kinetics is an essential part of a chemistry curriculum, especially for students interested in biomedical research or in health care fields. Though the concept is routinely performed in undergraduate chemistry/biochemistry classrooms using other spectroscopic methods, we provide an optimized approach that uses a real-time monitoring of the…
Her, Cheenou; Alonzo, Aaron P.; Vang, Justin Y.; Torres, Ernesto; Krishnan, V. V.
2015-01-01
Enzyme kinetics is an essential part of a chemistry curriculum, especially for students interested in biomedical research or in health care fields. Though the concept is routinely performed in undergraduate chemistry/biochemistry classrooms using other spectroscopic methods, we provide an optimized approach that uses a real-time monitoring of the…
Stroberg, Wylie; Schnell, Santiago
2016-12-01
The conditions under which the Michaelis-Menten equation accurately captures the steady-state kinetics of a simple enzyme-catalyzed reaction is contrasted with the conditions under which the same equation can be used to estimate parameters, KM and V, from progress curve data. Validity of the underlying assumptions leading to the Michaelis-Menten equation are shown to be necessary, but not sufficient to guarantee accurate estimation of KM and V. Detailed error analysis and numerical "experiments" show the required experimental conditions for the independent estimation of both KM and V from progress curves. A timescale, tQ, measuring the portion of the time course over which the progress curve exhibits substantial curvature provides a novel criterion for accurate estimation of KM and V from a progress curve experiment. It is found that, if the initial substrate concentration is of the same order of magnitude as KM, the estimated values of the KM and V will correspond to their true values calculated from the microscopic rate constants of the corresponding mass-action system, only so long as the initial enzyme concentration is less than KM. Copyright © 2016 Elsevier B.V. All rights reserved.
The total quasi-steady-state approximation for complex enzyme reactions
Pedersen, Morten Gram; Bersani, A. M.; Bersani, E.
2008-01-01
Biochemistry in general and enzyme kinetics in particular have been heavily influenced by the model of biochemical reactions known as Michaelis-Menten kinetics. Assuming that the complex concentration is approximately constant after a short transient phase leads to the usual Michaelis-Menten (MM...
Robustness of optimal designs for the Michaelis-Menten model under a variation of criteria
Dette, Holger; Kiss, Christine; Wong, Weng Kee
2009-01-01
The Michaelis-Menten model has and continues to be one of the most widely used models in many diverse fields. In the biomedical sciences, the model continues to be ubiquitous in biochemistry, enzyme kinetics studies, nutrition science and in the pharmaceutical sciences. Despite its wide ranging applications across disciplines, design issues for this model are given short shrift. This paper focuses on design issues and provides a variety of optimal designs of this model. In addition, we ...
Nakédia M. F. Carvalho
2010-01-01
Full Text Available The Michaelis-Menten equation is used in many biochemical and bioinorganic kinetic studies involving homogeneous catalysis. Otherwise, it is known that determination of Michaelis-Menten parameters K M, Vmax, and k cat by the well-known Lineweaver-Burk double reciprocal linear equation does not produce the best values for these parameters. In this paper we present a discussion on different linear equations which can be used to calculate these parameters and we compare their results with the values obtained by the more reliable nonlinear least-square fit.
Uso de equações lineares na determinação dos parâmetros de Michaelis-Menten
Carvalho,Nakédia M. F.; Pires, Bianca M.; Antunes,Octavio A. C.; Roberto B Faria; Osório,Renata E. H. M. B.; Piovezan, Clovis; Neves,Ademir
2010-01-01
The Michaelis-Menten equation is used in many biochemical and bioinorganic kinetic studies involving homogeneous catalysis. Otherwise, it is known that determination of Michaelis-Menten parameters K M, Vmax, and k cat by the well-known Lineweaver-Burk double reciprocal linear equation does not produce the best values for these parameters. In this paper we present a discussion on different linear equations which can be used to calculate these parameters and we compare their results with the va...
Wenzhen Gan; Canrong Tian; Qunying Zhang; Zhigui Lin
2013-01-01
This paper is concerned with the asymptotical behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition. By taking food ingestion and species' moving into account, the model is further coupled with Michaelis-Menten type functional response and nonlocal delay. Sufficient conditions are derived for the global stability of the positive steady state and the semitrivial steady state of the proposed problem by using the Lyapunov functional. Our results show...
Wenzhen Gan
2013-01-01
Full Text Available This paper is concerned with the asymptotical behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition. By taking food ingestion and species' moving into account, the model is further coupled with Michaelis-Menten type functional response and nonlocal delay. Sufficient conditions are derived for the global stability of the positive steady state and the semitrivial steady state of the proposed problem by using the Lyapunov functional. Our results show that intraspecific competition benefits the coexistence of prey and predator. Furthermore, the introduction of Michaelis-Menten type functional response positively affects the coexistence of prey and predator, and the nonlocal delay is harmless for stabilities of all nonnegative steady states of the system. Numerical simulations are carried out to illustrate the main results.
The Michaelis-Menten-Stueckelberg Theorem
Gorban, Alexander N.; Muhammad Shahzad
2011-01-01
We study chemical reactions with complex mechanisms under two assumptions: (i) intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS) and (ii) they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE). Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without mic...
Accuracy of the Michaelis-Menten approximation when analysing effects of molecular noise.
Lawson, Michael J; Petzold, Linda; Hellander, Andreas
2015-05-06
Quantitative biology relies on the construction of accurate mathematical models, yet the effectiveness of these models is often predicated on making simplifying approximations that allow for direct comparisons with available experimental data. The Michaelis-Menten (MM) approximation is widely used in both deterministic and discrete stochastic models of intracellular reaction networks, owing to the ubiquity of enzymatic activity in cellular processes and the clear biochemical interpretation of its parameters. However, it is not well understood how the approximation applies to the discrete stochastic case or how it extends to spatially inhomogeneous systems. We study the behaviour of the discrete stochastic MM approximation as a function of system size and show that significant errors can occur for small volumes, in comparison with a corresponding mass-action system. We then explore some consequences of these results for quantitative modelling. One consequence is that fluctuation-induced sensitivity, or stochastic focusing, can become highly exaggerated in models that make use of MM kinetics even if the approximations are excellent in a deterministic model. Another consequence is that spatial stochastic simulations based on the reaction-diffusion master equation can become highly inaccurate if the model contains MM terms. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
Design issues for the Michaelis-Menten model.
López-Fidalgo, J; Wong, Weng Kee
2002-03-07
We discuss design issues for the Michaelis-Menten model and use geometrical arguments to find optimal designs for estimating a subset of the model parameters, or a linear combination of the parameters. We propose multiple-objective optimal designs when the parameters have different levels of interest to the researcher. In addition, we compare six commonly used sequence designs in the biological sciences for estimating parameters and, propose optimal choices for the parameters for geometric designs using closed-form efficiency formulas.
Robust and efficient designs for the Michaelis-Menten model
Dette, Holger; Biedermann, Stefanie
2002-01-01
For the Michaelis-Menten model, we determine designs that maximize the minimum of the D-efficiencies over a certain interval for the nonlinear parameter. The best two point designs can be found explicitly, and a characterization is given when these designs are optimal within the class of all designs. In most cases of practical interest, the determined designs are highly efficient and robust with respect to misspecification of the nonlinear parameter. The results are illustrated and applied in...
Optimal designs for the Michaelis Menten model with correlated observations
Dette, Holger; Kunert, Joachim
2012-01-01
In this paper we investigate the problem of designing experiments for weighted least squares analysis in the Michaelis Menten model. We study the structure of exact D-optimal designs in a model with an autoregressive error structure. Explicit results for locally D-optimal are derived for the case where 2 observations can be taken per subject. Additionally standardized maximin D-optimal designs are obtained in this case. The results illustrate the enormous difficulties to find e...
Dutta, Annwesha; Chowdhury, Debashish
2017-05-01
The sequence of amino acid monomers in the primary structure of a protein is decided by the corresponding sequence of codons (triplets of nucleic acid monomers) on the template messenger RNA (mRNA). The polymerization of a protein, by incorporation of the successive amino acid monomers, is carried out by a molecular machine called ribosome. We develop a stochastic kinetic model that captures the possibilities of mis-reading of mRNA codon and prior mis-charging of a tRNA. By a combination of analytical and numerical methods, we obtain the distribution of the times taken for incorporation of the successive amino acids in the growing protein in this mathematical model. The corresponding exact analytical expression for the average rate of elongation of a nascent protein is a 'biologically motivated' generalization of the Michaelis-Menten formula for the average rate of enzymatic reactions. This generalized Michaelis-Menten-like formula (and the exact analytical expressions for a few other quantities) that we report here display the interplay of four different branched pathways corresponding to selection of four different types of tRNA.
Determination of individual cell Michaelis-Menten constants.
Sunray, Merav; Zurgil, Naomi; Shafran, Yana; Deutsch, Mordechai
2002-01-01
A novel methodology for the measurement and analysis of apparent K(M) (Michaelis-Menten constant) and V(MAX) values of individual cells is suggested. It is based on a mathematical model that considers substrate influx into the cell, its intracellular enzymatic hydrolysis, and the product efflux. The mathematical formulation was approximated linearly in order to analyze intracellular substrate conversion characteristics via Michaelis-Menten theory. Utilizing static cytometry, the time dependence of the fluorescence intensity [FI(t)] emitted from prelocalized and defined FDA stained cells was recorded. This required frequent periodical measurements of the same cells, which are sequentially exposed to various fluorogenic substrate concentrations. Model simulations correlated with experimental results. Differences in distributions of individual K(M) and V(MAX) values of cells incubated with and without PHA were evident. Average K(M) and V(MAX) values of PHA-stimulated cells increased by 99% and 540%, respectively. This study may provide a tool for assessing intracellular enzymatic activity in individual intact cells under defined physiologic conditions. This may open new vistas in various areas, giving answers to critical questions arising in the field of cell and developmental biology, immunology, oncology, and pharmacology. Copyright 2001 Wiley-Liss, Inc.
Golicnik, Marko
2011-01-01
The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate "V", and the Michaelis constant "K"[subscript M]) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to…
Golicnik, Marko
2011-01-01
The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate "V", and the Michaelis constant "K"[subscript M]) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to…
廖飞; 杨晓; 周岐新; 曾昭淳; 左渝萍
2003-01-01
Objective: To investigate the reliability for fast estimation of Michaelis-Menten constant (Km) with calibrated specific activity at only two medium concentrations of substrate by both simulation and experimentation with arylesterase (ArE)as model. Methods: Initial rates were simulated by randomly inserting uniform absolute error, and the experimental initial rates of ArE were determined by measuring the increaser of product absorbance. Calibrated specific activities at two substrate concentrations were obtained by regression analysis, and Km was calculated according to Michaelis-Menten equation. Results: By simulation with calibrated specific activities at two medium substrate concentrations, Km could be calculated according to Michaelis-Menten equation with reasonable precision and accuracy. By experimentation with substrates of 2-naphthyl acetate, phenyl acetate, and p-nitrophenyl acetate, there were no differences between the mean and SD of Km of ArE for either substrate by this linear kinetic method and the Lineweaver-Burk plot. Conclusion: This linear kinetic method was reliable for fast estimation of the Km of some specified enzyme on its substrate of lower solubility or lower sensitivity for quantification by common methods.
Ever-fluctuating single enzyme molecules : Michaelis-Menten equation revisited
English, Brian P.; Min, Wei; Oijen, Antoine M. van; Lee, Kang Taek; Luo, Guobin; Sun, Hongye; Cherayil, Binny J.; Kou, S.C.; Xie, X. Sunney
2006-01-01
Enzymes are biological catalysts vital to life processes and have attracted century-long investigation. The classic Michaelis-Menten mechanism provides a highly satisfactory description of catalytic activities for large ensembles of enzyme molecules. Here we tested the Michaelis-Menten equation at
Stochastic Total Quasi-Steady-State Approximation for the Michaelis-Menten Scheme
Galstyan, Vahe
2015-01-01
In biochemical systems the Michaelis-Menten (MM) scheme is one of the best-known models of the enzyme- catalyzed kinetics. In the academic literature the MM approximation has been thoroughly studied in the context of differential equation models. At the level of the cell, however, molecular fluctuations have many important consequences, and thus, a stochastic investigation of the MM scheme is often necessary. In their work Barik et al. [Biophysical Journal, 95, 3563-3574, (2008)] presented a stochastic approximation of the MM scheme. They suggested a substitution of the propensity function in the reduced master equation with the total quasi-steady- state approximation (tQSSA) rate. The justification of the substitution, however, was provided for a special case only and did not cover the whole parameter domain of the tQSSA. In this manuscript we present a derivation of the stochastic tQSSA that is valid for the entire tQSSA parameter domain.
Analysis of noise-induced bistability in Michaelis Menten single-step enzymatic cycle
Remondini, Daniel; Bazzani, Armando; Castellani, Gastone; Maritan, Amos
2011-01-01
In this paper we study noise-induced bistability in a specific circuit with many biological implications, namely a single-step enzymatic cycle described by Michaelis Menten equations with quasi-steady state assumption. We study the system both with a Master Equation formalism, and with the Fokker-Planck continuous approximation, characterizing the conditions in which the continuous approach is a good approximation of the exact discrete model. An analysis of the stationary distribution in both cases shows that bimodality can not occur in such a system. We discuss which additional requirements can generate stochastic bimodality, by coupling the system with a chemical reaction involving enzyme production and turnover. This extended system shows a bistable behaviour only in specific parameter windows depending on the number of molecules involved, providing hints about which should be a feasible system size in order that such a phenomenon could be exploited in real biological systems.
Goličnik, Marko
2011-06-01
Many pharmacodynamic processes can be described by the nonlinear saturation kinetics that are most frequently based on the hyperbolic Michaelis-Menten equation. Thus, various time-dependent solutions for drugs obeying such kinetics can be expressed in terms of the Lambert W(x)-omega function. However, unfortunately, computer programs that can perform the calculations for W(x) are not widely available. To avoid this problem, the replacement of the integrated Michaelis-Menten equation with an empiric integrated 1--exp alternative model equation was proposed recently by Keller et al. (Ther Drug Monit. 2009;31:783-785), although, as shown here, it was not necessary. Simulated concentrations of model drugs obeying Michaelis-Menten elimination kinetics were generated by two approaches: 1) calculation of time-course data based on an approximation equation W2*(x) performed using Microsoft Excel; and 2) calculation of reference time-course data based on an exact W(x) function built in to the Wolfram Mathematica. I show here that the W2*(x) function approximates the actual W(x) accurately. W2*(x) is expressed in terms of elementary mathematical functions and, consequently, it can be easily implemented using any of the widely available software. Hence, with the example of a hypothetical drug, I demonstrate here that an equation based on this approximation is far better, because it is nearly equivalent to the original solution, whereas the same characteristics cannot be fully confirmed for the 1--exp model equation. The W2*(x) equation proposed here might have an important role as a useful shortcut in optional software to estimate kinetic parameters from experimental data for drugs, and it might represent an easy and universal analytical tool for simulating and designing dosing regimens.
Hum, Ryan J; Jha, Prabhat; McGahan, Anita M; Cheng, Yu-Ling
2012-12-13
Life expectancy has risen sharply in the last 50 years. We applied the classic Michaelis-Menten enzyme kinetics to demonstrate a novel mathematical relationship of income to childhood (aged 0-5 years) and adult (aged 15-60 years) survival. We treat income as a substrate that is catalyzed to increase survival (from technologies that income buys) for 180 countries from 1970 and 2007. Michaelis-Menten kinetics permit estimates of maximal survival and, uniquely, the critical income needed to achieve half of the period-specific maximum. Maximum child and adult survival rose by about 1% per year. Critical incomes fell by half for children, but doubled for men. HIV infection and smoking account for some, but not all, of the rising critical incomes for adult survival. Altering the future cost curve for adult survival will require more widespread use of current interventions, most notably tobacco control, but also research to identify practicable low-cost drugs, diagnostics, and strategies.DOI:http://dx.doi.org/10.7554/eLife.00051.001.
More Nuts and Bolts of Michaelis-Menten Enzyme Kinetics
Lechner, Joseph H.
2011-01-01
Several additions to a classroom activity are proposed in which an "enzyme" (the student) converts "substrates" (nut-bolt assemblies) into "products" (separated nuts and bolts) by unscrewing them. (Contains 1 table.)
More Nuts and Bolts of Michaelis-Menten Enzyme Kinetics
Lechner, Joseph H.
2011-01-01
Several additions to a classroom activity are proposed in which an "enzyme" (the student) converts "substrates" (nut-bolt assemblies) into "products" (separated nuts and bolts) by unscrewing them. (Contains 1 table.)
Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revisited.
English, Brian P; Min, Wei; van Oijen, Antoine M; Lee, Kang Taek; Luo, Guobin; Sun, Hongye; Cherayil, Binny J; Kou, S C; Xie, X Sunney
2006-02-01
Enzymes are biological catalysts vital to life processes and have attracted century-long investigation. The classic Michaelis-Menten mechanism provides a highly satisfactory description of catalytic activities for large ensembles of enzyme molecules. Here we tested the Michaelis-Menten equation at the single-molecule level. We monitored long time traces of enzymatic turnovers for individual beta-galactosidase molecules by detecting one fluorescent product at a time. A molecular memory phenomenon arises at high substrate concentrations, characterized by clusters of turnover events separated by periods of low activity. Such memory lasts for decades of timescales ranging from milliseconds to seconds owing to the presence of interconverting conformers with broadly distributed lifetimes. We proved that the Michaelis-Menten equation still holds even for a fluctuating single enzyme, but bears a different microscopic interpretation.
The original Michaelis constant: translation of the 1913 Michaelis-Menten paper.
Michaelis, Leonor; Menten, Maud Leonora; Johnson, Kenneth A; Goody, Roger S
2011-10-04
Nearly 100 years ago Michaelis and Menten published their now classic paper [Michaelis, L., and Menten, M. L. (1913) Die Kinetik der Invertinwirkung. Biochem. Z. 49, 333-369] in which they showed that the rate of an enzyme-catalyzed reaction is proportional to the concentration of the enzyme-substrate complex predicted by the Michaelis-Menten equation. Because the original text was written in German yet is often quoted by English-speaking authors, we undertook a complete translation of the 1913 publication, which we provide as Supporting Information . Here we introduce the translation, describe the historical context of the work, and show a new analysis of the original data. In doing so, we uncovered several surprises that reveal an interesting glimpse into the early history of enzymology. In particular, our reanalysis of Michaelis and Menten's data using modern computational methods revealed an unanticipated rigor and precision in the original publication and uncovered a sophisticated, comprehensive analysis that has been overlooked in the century since their work was published. Michaelis and Menten not only analyzed initial velocity measurements but also fit their full time course data to the integrated form of the rate equations, including product inhibition, and derived a single global constant to represent all of their data. That constant was not the Michaelis constant, but rather V(max)/K(m), the specificity constant times the enzyme concentration (k(cat)/K(m) × E(0)).
Choi, I Y; Lee, S P; Kim, S G; Gruetter, R
2001-06-01
Glucose is the major substrate that sustains normal brain function. When the brain glucose concentration approaches zero, glucose transport across the blood-brain barrier becomes rate limiting for metabolism during, for example, increased metabolic activity and hypoglycemia. Steady-state brain glucose concentrations in alpha-chloralose anesthetized rats were measured noninvasively as a function of plasma glucose. The relation between brain and plasma glucose was linear at 4.5 to 30 mmol/L plasma glucose, which is consistent with the reversible Michaelis-Menten model. When the model was fitted to the brain glucose measurements, the apparent Michaelis-Menten constant, Kt, was 3.3 +/- 1.0 mmol/L, and the ratio of the maximal transport rate relative to CMRglc, Tmax/CMRglc, was 2.7 +/- 0.1. This Kt is comparable to the authors' previous human data, suggesting that glucose transport kinetics in humans and rats are similar. Cerebral blood flow (CBF) was simultaneously assessed and constant above 2 mmol/L plasma glucose at 73 +/- 6 mL 100 g(-1) min(-1). Extrapolation of the reversible Michaelis-Menten model to hypoglycemia correctly predicted the plasma glucose concentration (2.1 +/- 0.6 mmol/L) at which brain glucose concentrations approached zero. At this point, CBF increased sharply by 57% +/- 22%, suggesting that brain glucose concentration is the signal that triggers defense mechanisms aimed at improving glucose delivery to the brain during hypoglycemia.
KINETICS OF QUERCETIN NITRATIO N BY HORSERADISH PEROXIDASE
Andrija Šmelcerović
2013-03-01
Full Text Available In this study we investigated the kinetics of the nitration of quercetin by horseradish peroxidase. Quercetin nitration reaction was followed by recording the spectral changes over the time at 380 nm. The reaction rate increases with increasing of the quercetin concentration and follows the Michaelis-Menten type kinetics. Kinetic parameters of the studied enzymatic reaction were determined.
Single-molecule enzymology à la Michaelis-Menten.
Grima, Ramon; Walter, Nils G; Schnell, Santiago
2014-01-01
Over the past 100 years, deterministic rate equations have been successfully used to infer enzyme-catalysed reaction mechanisms and to estimate rate constants from reaction kinetics experiments conducted in vitro. In recent years, sophisticated experimental techniques have been developed that begin to allow the measurement of enzyme-catalysed and other biopolymer-mediated reactions inside single cells at the single-molecule level. Time-course data obtained using these methods are considerably noisy because molecule numbers within cells are typically quite small. As a consequence, the interpretation and analysis of single-cell data requires stochastic methods, rather than deterministic rate equations. Here, we concisely review both experimental and theoretical techniques that enable single-molecule analysis, with particular emphasis on the major developments in the field of theoretical stochastic enzyme kinetics, from its inception in the mid-20th century to its modern-day status. We discuss the differences between stochastic and deterministic rate equation models, how these depend on enzyme molecule numbers and substrate inflow into the reaction compartment, and how estimation of rate constants from single-cell data is possible using recently developed stochastic approaches. © 2013 FEBS.
A generalized Michaelis-Menten type equation for the analysis of growth
Lopez, S.; France, J.; Gerrits, W.J.J.; Dhanoa, M.S.; Humphries, D.J.; Dijkstra, J.
2000-01-01
The functional form W = (W0Kc Wf t(c)) /(Kc t(c)), where W is body size at age t, W0 and Wf are the zero- and infinite-time values of W, respectively, and K and c are constants, is derived. This new generalized Michaelis-Menten-type equation provides a flexible model for animal growth capable of
A two-substrate Michaelis-Menten model for the growth of self-replicating polymers.
Ferreira, R
1987-10-07
A two-substrate Michaelis-Menten model is proposed for the growth of autocatalytic self-replicating polymers. Selective growth depends on the existence of two complementary pairs of monomers. Discrimination among sequences results from different products of binding constants, KCGnKAUm. The results support an earlier renormalization group treatment (Ferreira & Tsallis, 1985).
Kinetic modelling of coupled transport across biological membranes.
Korla, Kalyani; Mitra, Chanchal K
2014-04-01
In this report, we have modelled a secondary active co-transporter (symport and antiport), based on the classical kinetics model. Michaelis-Menten model of enzyme kinetics for a single substrate, single intermediate enzyme catalyzed reaction was proposed more than a hundred years ago. However, no single model for the kinetics of co-transport of molecules across a membrane is available in the literature We have made several simplifying assumptions and have followed the basic Michaelis-Menten approach. The results have been simulated using GNU Octave. The results will be useful in general kinetic simulations and modelling.
Yan, Shaomin; Wu, Guang
2011-10-01
In this study, we attempted to use the neural network to model a quantitative structure-K(m) (Michaelis-Menten constant) relationship for beta-glucosidase, which is an important enzyme to cut the beta-bond linkage in glucose while K(m) is a very important parameter in enzymatic reactions. Eight feedforward backpropagation neural networks with different layers and neurons were applied for the development of predictive model, and twenty-five different features of amino acids were chosen as predictors one by one. The results show that the 20-1 feedforward backpropagation neural network can serve as a predictive model while the normalized polarizability index as well as the amino-acid distribution probability can serve as the predictors. This study threw lights on the possibility of predicting the K(m) in beta-glucosidases based on their amino-acid features.
A Squared Michaelis-Menten Function of Substrate Concentration for Plant Mitochondrial Respiration 1
James, Alan T.; Wiskich, Joseph T.; Dry, Ian B.
1990-01-01
Dry and Wiskich ([1987] Arch Biochem Biophys 257: 92-99) have published data showing the response of plant mitochondrial respiration to increasing additions of oxaloacetate or malate when these substrates have been depleted by inhibition of succinate dehydrogenase by malonate, and coenzyme A (CoA) has been sequestered as acetyl-CoA by pyruvate dehydrogenase. In the presence of 2-oxoglutarate, it is shown that the response is given by a Michaelis-Menten curve, but in its absence, when malate has to supply substrate for dehydrogenation as well as to liberate CoA via malate dehydrogenase and citrate synthase, the response is presumably the product of two Michaelis-Menten functions, which can be approximated by the square of a single function. PMID:16667257
Optimal Designs for Discriminating Between some Extensions of the Michaelis-Menten Model
Jesus Lopez Fidalgo; Chiara Tommasi; Camelia Trandafir
2005-01-01
In this paper some results on the problem of computing optimal designs for discriminating between rival models are provided. Using T-optimality for two rival models a compound criterion is developed to discriminate between more than two models. Surprising results arise when T-optimal designs are compared with classical c-optimal designs for nonlinear models. In particular, some practical deviations of the Michaelis-Menten model are considered in order to measure and compare efficiencies of di...
Solution of the Michaelis-Menten equation using the decomposition method.
Sonnad, Jagadeesh R; Goudar, Chetan T
2009-01-01
We present a low-order recursive solution to the Michaelis-Menten equation using the decomposition method. This solution is algebraic in nature and provides a simpler alternative to numerical approaches such as differential equation evaluation and root-solving techniques that are currently used to compute substrate concentration in the Michaelis-Menten equation. A detailed characterization of the errors in substrate concentrations computed from decomposition, Runge-Kutta, and bisection methods over a wide range of s(0) : K(m) values was made by comparing them with highly accurate solutions obtained using the Lambert W function. Our results indicated that solutions obtained from the decomposition method were usually more accurate than those from the corresponding classical Runge-Kutta methods. Moreover, these solutions required significantly fewer computations than the root-solving method. Specifically, when the stepsize was 0.1% of the total time interval, the computed substrate concentrations using the decomposition method were characterized by accuracies on the order of 10(-8) or better. The algebraic nature of the decomposition solution and its relatively high accuracy make this approach an attractive candidate for computing substrate concentration in the Michaelis-Menten equation.
Widmer, L A; Stelling, J; Doyle, F J
2013-10-28
Using the (slow-scale) linear noise approximation, we give parameter-independent bounds to the substrate and product intrinsic noise variance for the stochastic Michaelis-Menten approximation at steady state.
无
2012-01-01
In this paper,the existence of eight periodic solutions to a Michaelis-Menten-type predator-prey system with delay and harvesting in patch environment is established using the analytical techniques and Mawhin's coincidence degree theory.
Bentz, Joe; Tran, Thuy Thanh; Polli, Joseph W; Ayrton, Andrew; Ellens, Harma
2005-10-01
Typically, the kinetics of membrane transport is analyzed using the steady-state Michaelis-Menten (or Eadie-Hofstee or Hanes) equations. This approach has been successful when the substrate is picked up from the aqueous phase, like a water-soluble enzyme, for which the Michaelis-Menten steady-state analysis was developed. For membrane transporters whose substrate resides in the lipid bilayer of the plasma membrane, like P-glycoprotein (P-gp), there has been no validation of the accuracy of the steady-state analysis because the elementary rate constants for transport were not known. Recently, we fitted the mass action elementary kinetic rate constants of P-gp transport of three different drugs through a confluent monolayer of MDCKII-hMDR1 cells. With these elementary rate constants in hand, we use computer simulations to assess the accuracy of the steady-state Michaelis-Menten parameters. This limits the simulation to parameter ranges known to be physiologically relevant. Using over 2,300 different vectors of initial elementary parameters spanning the space bounded by the three drugs, which defines 2,300 "virtual substrates", the concentrations of substrate transported were calculated and fitted to Eadie-Hofstee plots. Acceptable plots were obtained for 1,338 cases. The fitted steady-state Vmax values from the analysis correlated to within a factor of 2-3 with the values predicted from the elementary parameters. However, the fitted Km value could be generated by a wide range of underlying "molecular" Km values. This is because of the convolution of the drug passive permeability kinetics into the fitted Km. This implies that Km values measured in simpler systems, e.g., microsomes or proteoliposomes, even if accurate, would not predict the Km values for the confluent monolayer system or, by logical extension, in vivo. Reliable in vitro-in vivo extrapolation seems to require using the elementary rate constants rather than the Michaelis-Menten steady-state parameters.
Gejl, Michael; Rungby, Jørgen; Brock, Birgitte; Gjedde, Albert
2014-08-01
Glucagon-like peptide-1 (GLP-1) is a potent insulinotropic incretin hormone with both pancreatic and extrapancreatic effects. Studies of GLP-1 reveal significant effects in regions of brain tissue that regulate appetite and satiety. GLP-1 mimetics are used for the treatment of type 2 diabetes mellitus. GLP-1 interacts with peripheral functions in which the autonomic nervous system plays an important role, and emerging pre-clinical findings indicate a potential neuroprotective role of the peptide, for example in models of stroke and in neurodegenerative disorders. A century ago, Leonor Michaelis and Maud Menten described the steady-state enzyme kinetics that still apply to the multiple receptors, transporters and enzymes that define the biochemical reactions of the brain, including the glucose-dependent impact of GLP-1 on blood-brain glucose transfer and metabolism. This MiniReview examines the potential of GLP-1 as a molecule of interest for the understanding of brain energy metabolism and with reference to the impact on brain metabolism related to appetite and satiety regulation, stroke and neurodegenerative disorders. These effects can be understood only by reference to the original formulation of the Michaelis-Menten equation as applied to a chain of kinetically controlled steps. Indeed, the effects of GLP-1 receptor activation on blood-brain glucose transfer and brain metabolism of glucose depend on the glucose concentration and relative affinities of the steps both in vitro and in vivo, as in the pancreas. © 2014 Nordic Association for the Publication of BCPT (former Nordic Pharmacological Society).
Igamberdiev, Abir U; Roussel, Marc R
2012-03-01
Rubisco, the most abundant protein serving as the primary engine generating organic biomass on Earth, is characterized by a low catalytic constant (in higher plants approx. 3s(-1)) and low specificity for CO(2) leading to photorespiration. We analyze here why this enzyme evolved as the main carbon fixation engine. The high concentration of Rubisco exceeding the concentration of its substrate CO(2) by 2-3 orders of magnitude makes application of Michaelis-Menten kinetics invalid and requires alternative kinetic approaches to describe photosynthetic CO(2) assimilation. Efficient operation of Rubisco is supported by a strong flux of CO(2) to the chloroplast stroma provided by fast equilibration of bicarbonate and CO(2) and forwarding the latter to Rubisco reaction centers. The main part of this feedforward mechanism is a thylakoidal carbonic anhydrase associated with photosystem II and pumping CO(2) from the thylakoid lumen in coordination with the rate of electron transport, water splitting and proton gradient across the thylakoid membrane. This steady flux of CO(2) limits photosynthesis at saturating CO(2) concentrations. At low ambient CO(2) and correspondingly limited capacity of the bicarbonate pool in the stroma, its depletion at the sites of Rubisco is relieved by utilizing O(2) instead of CO(2), i.e. by photorespiration, a process which supplies CO(2) back to Rubisco and buffers the redox state and energy level in the chloroplast. Thus, the regulation of Rubisco function aims to keep steady non-equilibrium levels of CO(2), NADPH/NADP and ATP/ADP in the chloroplast stroma and to optimize the condition of homeostatic photosynthetic flux of matter and energy. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.
Model-order reduction of biochemical reaction networks
Rao, Shodhan; Schaft, Arjan van der; Eunen, Karen van; Bakker, Barbara M.; Jayawardhana, Bayu
2013-01-01
In this paper we propose a model-order reduction method for chemical reaction networks governed by general enzyme kinetics, including the mass-action and Michaelis-Menten kinetics. The model-order reduction method is based on the Kron reduction of the weighted Laplacian matrix which describes the gr
Michaelis-Menten speeds up tau-leaping under a wide range of conditions.
Wu, Sheng; Fu, Jin; Cao, Yang; Petzold, Linda
2011-04-07
This paper examines the benefits of Michaelis-Menten model reduction techniques in stochastic tau-leaping simulations. Results show that although the conditions for the validity of the reductions for tau-leaping remain the same as those for the stochastic simulation algorithm (SSA), the reductions result in a substantial speed-up for tau-leaping under a different range of conditions than they do for SSA. The reason of this discrepancy is that the time steps for SSA and for tau-leaping are determined by different properties of system dynamics.
Michaelis-Menten speeds up tau-leaping under a wide range of conditions
Wu, Sheng; Fu, Jin; Cao, Yang; Petzold, Linda
2011-04-01
This paper examines the benefits of Michaelis-Menten model reduction techniques in stochastic tau-leaping simulations. Results show that although the conditions for the validity of the reductions for tau-leaping remain the same as those for the stochastic simulation algorithm (SSA), the reductions result in a substantial speed-up for tau-leaping under a different range of conditions than they do for SSA. The reason of this discrepancy is that the time steps for SSA and for tau-leaping are determined by different properties of system dynamics.
A comparison of the parameter estimating procedures for the Michaelis-Menten model.
Tseng, S J; Hsu, J P
1990-08-23
The performance of four parameter estimating procedures for the estimation of the adjustable parameters in the Michaelis-Menten model, the maximum initial rate Vmax, and the Michaelis-Menten constant Km, including Lineweaver & Burk transformation (L-B), Eadie & Hofstee transformation (E-H), Eisenthal & Cornish-Bowden transformation (ECB), and Hsu & Tseng random search (H-T) is compared. The analysis of the simulated data reveals the followings: (i) Vmax can be estimated more precisely than Km. (ii) The sum of square errors, from the smallest to the largest, follows the sequence H-T, E-H, ECB, L-B. (iii) Considering the sum of square errors, relative error, and computing time, the overall performance follows the sequence H-T, L-B, E-H, ECB, from the best to the worst. (iv) The performance of E-H and ECB are on the same level. (v) L-B and E-H are appropriate for pricesly measured data. H-T should be adopted for data whose error level are high. (vi) Increasing the number of data points has a positive effect on the performance of H-T, and a negative effect on the performance of L-B, E-H, and ECB.
The integrated Michaelis-Menten rate equation: déjà vu or vu jàdé?
Goličnik, Marko
2013-08-01
A recent article of Johnson and Goody (Biochemistry, 2011;50:8264-8269) described the almost-100-years-old paper of Michaelis and Menten. Johnson and Goody translated this classic article and presented the historical perspective to one of incipient enzyme-reaction data analysis, including a pioneering global fit of the integrated rate equation in its implicit form to the experimental time-course data. They reanalyzed these data, although only numerical techniques were used to solve the model equations. However, there is also the still little known algebraic rate-integration equation in a closed form that enables direct fitting of the data. Therefore, in this commentary, I briefly present the integral solution of the Michaelis-Menten rate equation, which has been largely overlooked for three decades. This solution is expressed in terms of the Lambert W function, and I demonstrate here its use for global nonlinear regression curve fitting, as carried out with the original time-course dataset of Michaelis and Menten.
Baesjou, PJ; Driessen, WL; Challa, G; Reedijk, J
1999-01-01
The kinetics of the copper/N-methylimidazole catalysed oxidative coupling reaction with the C-O coupled dimer of 2,6-dimethylphenol (DMP or monomer), viz. 4-(2',6'-dimethylphenoxy)-2,6-dimethylphenol (dimer), as the substrate have been studied. The reaction was found to obey Michaelis-Menten
Maggi, F.M.; Riley, W.J.
2009-06-01
The theoretical formulation of biological kinetic reactions in isotopic applications often assume first-order or Michaelis-Menten-Monod kinetics under the quasi-steady-state assumption to simplify the system kinetics. However, isotopic e ects have the same order of magnitude as the potential error introduced by these simpli cations. Both formulations lead to a constant fractionation factor which may yield incorrect estimations of the isotopic effect and a misleading interpretation of the isotopic signature of a reaction. We have analyzed the isotopic signature of denitri cation in biogeochemical soil systems by Menyailo and Hungate [2006], where high {sup 15}N{sub 2}O enrichment during N{sub 2}O production and inverse isotope fractionation during N{sub 2}O consumption could not be explained with first-order kinetics and the Rayleigh equation, or with the quasi-steady-state Michaelis-Menten-Monod kinetics. When the quasi-steady-state assumption was relaxed, transient Michaelis-Menten-Monod kinetics accurately reproduced the observations and aided in interpretation of experimental isotopic signatures. These results may imply a substantial revision in using the Rayleigh equation for interpretation of isotopic signatures and in modeling biological kinetic isotope fractionation with first-order kinetics or quasi-steady-state Michaelis-Menten-Monod kinetics.
Baesjou, PJ; Driessen, WL; Challa, G; Reedijk, J
1998-01-01
The influence of varying concentrations and ratios of phenol, base and copper on the copper/N-methylimidazole catalysed oxidative coupling of 2,6-dimethylphenol (DMP) has been studied. The reaction obeys simple Michaelis-Menten kinetics with respect to the phenol. The amount of DPQ formed during the
Baesjou, PJ; Driessen, WL; Challa, G; Reedijk, J
1998-01-01
The influence of varying concentrations and ratios of phenol, base and copper on the copper/N-methylimidazole catalysed oxidative coupling of 2,6-dimethylphenol (DMP) has been studied. The reaction obeys simple Michaelis-Menten kinetics with respect to the phenol. The amount of DPQ formed during the
Mechanistic interpretation of conventional Michaelis-Menten parameters in a transporter system.
Vivian, Diana; Polli, James E
2014-11-20
The aim was to elucidate how steps in drug translocation by a solute carrier transporter impact Michaelis-Menten parameters Km, Ki, and Vmax. The first objective was to derive a model for carrier-mediated substrate translocation and perform sensitivity analysis with regard to the impact of individual microrate constants on Km, Ki, and Vmax. The second objective was to compare underpinning microrate constants between compounds translocated by the same transporter. Equations for Km, Ki, and Vmax were derived from a six-state model involving unidirectional transporter flipping and reconfiguration. This unidirectional model is applicable to co-transporter type solute carriers, like the apical sodium-dependent bile acid transporter (ASBT) and the proton-coupled peptide cotransporter (PEPT1). Sensitivity analysis identified the microrate constants that impacted Km, Ki, and Vmax. Compound comparison using the six-state model employed regression to identify microrate constant values that can explain observed Km and Vmax values. Results yielded some expected findings, as well as some unanticipated effects of microrate constants on Km, Ki, and Vmax. Km and Ki were found to be equal for inhibitors that are also substrates. Additionally, microrate constant values for certain steps in transporter functioning influenced Km and Vmax to be low or high. Copyright © 2014 Elsevier B.V. All rights reserved.
Yan, Xiaoyu; Krzyzanski, Wojciech
2012-04-01
The Michaelis-Menten (M-M) approximation of the target-mediated drug disposition (TMDD) pharmacokinetic (PK) model was derived based on the rapid binding (RB) or quasi steady-state (QSS) assumptions that implied that the target and drug binding and dissociation were in equilibrium. However, the initial dose for an IV bolus injection for the M-M model did not account for a fraction bound to the target. We postulated a correction to an initial condition that was consistent with the assumptions underlying the M-M approximation. We determined that the difference between the injected dose and one that should be used for the initial condition is equal to the amount of drug bound to the target upon reaching the equilibrium. We also observed that the corrected initial condition made the internalization rate constant an identifiable parameter that was not for the original M-M model. Finally, we performed a simulation exercise to check if the correction will impact the model performance and the bias of the M-M parameter estimates. We used literature data to simulate plasma drug concentrations described by the RB/QSS TMDD model. The simulated data were refitted by both models. All the parameters estimated from the original M-M model were substantially biased. On the other hand, the corrected M-M is able to accurately estimate these parameters except for equilibrium constant K(m). Weighted sum of square residual and Akaike information criterion suggested a better performance of the corrected M-M model compared with the original M-M model. Further studies are necessary to determine the importance of this correction for the M-M model applications to analysis of TMDD driven PK data.
Selection between Michaelis-Menten and target-mediated drug disposition pharmacokinetic models.
Yan, Xiaoyu; Mager, Donald E; Krzyzanski, Wojciech
2010-02-01
Target-mediated drug disposition (TMDD) models have been applied to describe the pharmacokinetics of drugs whose distribution and/or clearance are affected by its target due to high binding affinity and limited capacity. The Michaelis-Menten (M-M) model has also been frequently used to describe the pharmacokinetics of such drugs. The purpose of this study is to investigate conditions for equivalence between M-M and TMDD pharmacokinetic models and provide guidelines for selection between these two approaches. Theoretical derivations were used to determine conditions under which M-M and TMDD pharmacokinetic models are equivalent. Computer simulations and model fitting were conducted to demonstrate these conditions. Typical M-M and TMDD profiles were simulated based on literature data for an anti-CD4 monoclonal antibody (TRX1) and phenytoin administered intravenously. Both models were fitted to data and goodness of fit criteria were evaluated for model selection. A case study of recombinant human erythropoietin was conducted to qualify results. A rapid binding TMDD model is equivalent to the M-M model if total target density R ( tot ) is constant, and R ( tot ) K ( D ) /(K ( D ) + C) ( 2 ) < 1 where K ( D ) represents the dissociation constant and C is the free drug concentration. Under these conditions, M-M parameters are defined as: V ( max ) = k ( int ) R ( tot ) V ( c ) and K ( m ) = K ( D ) where k ( int ) represents an internalization rate constant, and V ( c ) is the volume of the central compartment. R ( tot ) is constant if and only if k ( int ) = k ( deg,) where k ( deg ) is a degradation rate constant. If the TMDD model predictions are not sensitive to k ( int ) or k ( deg ) parameters, the condition of R ( tot ) K ( D ) /(K ( D ) + C) ( 2 ) < 1 alone can preserve the equivalence between rapid binding TMDD and M-M models. The model selection process for drugs that exhibit TMDD should involve a full mechanistic model as well as reduced models. The best model
Padayachee, Letrisha; Pillay, Ché S
2016-07-01
The thioredoxin system, consisting of thioredoxin reductase, thioredoxin and NADPH, is present in most living organisms and reduces a large array of target protein disulfides. The insulin reduction assay is commonly used to characterise thioredoxin activity in vitro, but it is not clear whether substrate saturation datasets from this assay should be fitted and modeled with the Michaelis-Menten equation (thioredoxin enzyme model), or fitted to the thioredoxin system with insulin reduction described by mass-action kinetics (redox couple model). We utilized computational modeling and in vitro assays to determine which of these approaches yield consistent and accurate kinetic parameter sets for insulin reduction. Using computational modeling, we found that fitting to the redox couple model, rather than to the thioredoxin enzyme model, resulted in consistent parameter sets over a range of thioredoxin reductase concentrations. Furthermore, we established that substrate saturation in this assay was due to the progressive redistribution of the thioredoxin moiety into its oxidised form. We then confirmed these results in vitro using the yeast thioredoxin system. This study shows how consistent parameter sets for thioredoxin activity can be obtained regardless of the thioredoxin reductase concentration used in the insulin reduction assay, and validates computational systems biology modeling studies that have described the thioredoxin system with the redox couple modeling approach.
Lu, Jian; Dong, Yuxia; Ng, Emily C; Siehl, Daniel L
2017-05-01
One of applications of directed evolution is to desensitize an enzyme to an inhibitor. kcat,1/KM and KI are three dimensions that when multiplied measure an enzyme's intrinsic capacity for catalysis in the presence of an inhibitor. The ideal values for the individual dimensions depend on substrate and inhibitor concentrations under the conditions of the application. When attempting to optimize those values by directed evolution, (kcat/KM)*KI can be an informative parameter for evaluating libraries of variants, but throughput is limited. We describe a manipulation of the Michaelis-Menten equation for competitive inhibition that isolates (kcat/KM)*KI on one side of the equation. If velocity is measured at constant enzyme and substrate concentrations with two different inhibitor concentrations (one of which can be 0), the data are sufficient to calculate (kcat/KM)*KI with just two rate measurements. The procedure is validated by correlating values obtained by the rapid method with those obtained by substrate saturation kinetics. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
Modeling of Bacillus spores: Inactivation and Outgrowth
2011-03-01
52 Michaelis - Menten Kinetics ...of repair mechanism [36]. These models were based on Michaelis - Menten kinetics , which is also the foundation of the work in this research Michaelis ...catalyzed reactions. Michaelis - Menten kinetics is a model of enzyme kinetics . The Michaelis - Menten equation describes the rates of enzymatic reactions by
Emergence of Dynamic Cooperativity in the Stochastic Kinetics of Fluctuating Enzymes
Kumar, Ashutosh; Nandi, Mintu; Dua, Arti
2016-01-01
Dynamic cooperativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic cooperativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative cooperativity. For fewer enzymes, dynamic cooperativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, how...
Evaluation of rate law approximations in bottom-up kinetic models of metabolism
Du, Bin; Zielinski, Daniel C.; Kavvas, Erol S.
2016-01-01
. These approximate rate laws were: 1) a Michaelis-Menten rate law with measured enzyme parameters, 2) a Michaelis-Menten rate law with approximated parameters, using the convenience kinetics convention, 3) a thermodynamic rate law resulting from a metabolite saturation assumption, and 4) a pure chemical reaction......Background: The mechanistic description of enzyme kinetics in a dynamic model of metabolism requires specifying the numerical values of a large number of kinetic parameters. The parameterization challenge is often addressed through the use of simplifying approximations to form reaction rate laws...... with reduced numbers of parameters. Whether such simplified models can reproduce dynamic characteristics of the full system is an important question. Results: In this work, we compared the local transient response properties of dynamic models constructed using rate laws with varying levels of approximation...
Kim, Seung-Hyun; Chung, Jong-Bae; Jeong, Byeong-Ryong; Lee, Young-Deuk; Prasher, Shiv O
2003-01-01
During the dry season in Korea, rivers become more vulnerable to contamination by biochemical oxygen demand (BOD) and nitrogen. It is hypothesized that the natural characteristics of the streams in Korea allow the contaminated water to be treated at the tributaries. Down-stream river water quality in Korea may be improved by spraying the contaminated stream water from the tributaries over the surrounding floodplains. The consequent water filtration through the soil could remove the contaminants through aerobic and denitrifying reactions. In this study, the kinetics parameters of the denitrifying reaction in floodplain filtration were determined using contaminated stream water. For the electron donor the Monod kinetics was used, while the competitive Michaelis-Menten model was employed for the electron acceptors. The parameters to the competitive Michaelis-Menten model were found using continuous denitrifying reactions, instead of the batch reactions employed in previous studies, to match the conditions needed to apply the competitive Michaelis-Menten kinetics. From the result, it was found that continuous reactions as well as batch reactions could be used to determine the affinity coefficients in denitrification. The results of this study also showed that the affinity coefficient of NO2, using continuous reactions, was similar to that of other studies in the literature found via batch reactions, whereas the affinity coefficient of N2O was much larger than that acquired with batch reactions. The parameters obtained in this study will be used in future work to simulate the contaminant behaviors during floodplain filtration using a mathematical model.
Extended kinetic model of real-time polymerase chain reaction process
Fedorov, A. A.; Sochivko, D. G.; Varlamov, D. A.; Kurochkin, V. E.
2016-11-01
Real-time polymerase chain reaction (real-time PCR) is the main molecular genetic method used for qualitative and quantitative analysis of specific nucleic acid sequences in many areas of biomedical research. Theoretical study of pCr models allows to estimate the influence of various reaction components and parameters, and to determine the unknown parameter values by approximating the experimental real-time PCR curves. An extended kinetic model of real-time PCR is presented. The model takes into account the enzyme activity based on Michaelis-Menten kinetics, the hybridization of complementary DNA fragments, the presence of a fluorescent probe used for detection of the reaction products, and the temperature dependence of primers and probe hybridization.
Reeve, Russell; Turner, J Rick
2013-05-01
The Hill equation is often used in dose-response or exposure-response modeling. Aliases for the Hill model include the Emax model, and the Michaelis-Menten model. There is confusion about the appropriate parameterization, how to interpret the parameters, what the meaning is of the various parameterizations found in the literature, and which parameterization best approximates the statistical inferences produced when fitting the Hill equation to data. In this paper, we present several equivalent versions of the Hill model; show that they are equivalent in terms of yielding the same prediction for a given dose, and are equivalent to the four-parameter logistic model in this same sense; and deduce which parameterization is optimal in the sense of having the least statistical curvature and preferable multicollinearity.
Sudhamalla, Babu; Kumar, Mahesh; Roy, Karnati R; Kumar, R Sunil; Bhuyan, Abani K
2013-11-01
It is known that tandem domains of enzymes can carry out catalysis independently or by collaboration. In the case of cysteine proteases, domain sequestration abolishes catalysis because the active site residues are distributed in both domains. The validity of this argument is tested here by using isolated human ribosomal protein S4, which has been recently identified as an unorthodox cysteine protease. Cleavage of the peptide substrate Z-FR↓-AMC catalyzed by recombinant C-terminal domain of human S4 (CHS4) is studied by fluorescence-monitored steady-state and stopped-flow kinetic methods. Proteolysis and autoproteolysis were analyzed by electrophoresis. The CHS4 domain comprised of sequence residues 116-263 has been cloned and ovreexpressed in Escherichia coli. The purified domain is enzymatically active. Barring minor differences, steady-state kinetic parameters for catalysis by CHS4 are very similar to those for full-length human S4. Further, stopped-flow transient kinetics of pre-steady-state substrate binding shows that the catalytic mechanism for both full-length S4 and CHS4 obeys the Michaelis-Menten model adequately. Consideration of the evolutionary domain organization of the S4e family of ribosomal proteins indicates that the central domain (residues 94-170) within CHS4 is indispensable. The C-terminal domain can carry out catalysis independently and as efficiently as the full-length human S4 does. Localization of the enzyme function in the C-terminal domain of human S4 provides the only example of a cysteine endoprotease where substrate-mediated intramolecular domain interaction is irrelevant for catalytic activity. Copyright © 2013 Elsevier B.V. All rights reserved.
New types of experimental data shape the use of enzyme kinetics for dynamic network modeling.
Tummler, Katja; Lubitz, Timo; Schelker, Max; Klipp, Edda
2014-01-01
Since the publication of Leonor Michaelis and Maude Menten's paper on the reaction kinetics of the enzyme invertase in 1913, molecular biology has evolved tremendously. New measurement techniques allow in vivo characterization of the whole genome, proteome or transcriptome of cells, whereas the classical enzyme essay only allows determination of the two Michaelis-Menten parameters V and K(m). Nevertheless, Michaelis-Menten kinetics are still commonly used, not only in the in vitro context of enzyme characterization but also as a rate law for enzymatic reactions in larger biochemical reaction networks. In this review, we give an overview of the historical development of kinetic rate laws originating from Michaelis-Menten kinetics over the past 100 years. Furthermore, we briefly summarize the experimental techniques used for the characterization of enzymes, and discuss web resources that systematically store kinetic parameters and related information. Finally, describe the novel opportunities that arise from using these data in dynamic mathematical modeling. In this framework, traditional in vitro approaches may be combined with modern genome-scale measurements to foster thorough understanding of the underlying complex mechanisms.
Commemorating the 1913 Michaelis-Menten paper Die Kinetik der Invertinwirkung: three perspectives.
Deichmann, Ute; Schuster, Stefan; Mazat, Jean-Pierre; Cornish-Bowden, Athel
2014-01-01
Methods and equations for analysing the kinetics of enzyme-catalysed reactions were developed at the beginning of the 20th century in two centres in particular; in Paris, by Victor Henri, and, in Berlin, by Leonor Michaelis and Maud Menten. Henri made a detailed analysis of the work in this area that had preceded him, and arrived at a correct equation for the initial rate of reaction. However, his approach was open to the important objection that he took no account of the hydrogen-ion concentration (a subject largely undeveloped in his time). In addition, although he wrote down an expression for the initial rate of reaction and described the hyperbolic form of its dependence on the substrate concentration, he did not appreciate the great advantages that would come from analysis in terms of initial rates rather than time courses. Michaelis and Menten not only placed Henri's analysis on a firm experimental foundation, but also defined the experimental protocol that remains standard today. Here, we review this development, and discuss other scientific contributions of these individuals. The three parts have different authors, as indicated, and do not necessarily agree on all details, in particular about the relative importance of the contributions of Michaelis and Menten on the one hand and of Henri on the other. Rather than force the review into an unrealistic consensus, we consider it appropriate to leave the disagreements visible. © 2013 FEBS.
Sousa Jr R.
2004-01-01
Full Text Available Partial hydrolysis of whey proteins by enzymes immobilized on an inert support can either change or evidence functional properties of the produced peptides, thereby increasing their applications. The hydrolysis of sweet cheese whey proteins by alcalase, which is multipoint-immobilized on agarose gel, is studied here. A Michaelis-Menten model that takes into account competitive inhibition by the product was fitted to experimental data. The influence of pH on the kinetic parameters in the range 6.0 to 11.0 was assessed, at 50ºC. Initial reaction-rate assays in a pHstat at different concentrations of substrate were used to estimate kinetic and Michaelis-Menten parameters, k and K M. Experimental data from long-term batch assays were used to quantify the inhibition parameter, K I. The fitting of the model to the experimental data was accurate in the entire pH range.
Verlindo de Araujo, Bibiana; Farias da Silva, Cristófer; Costa, Teresa Dalla
2010-01-01
the determination of oral bioavailability of drugs which follow nonlinear pharmacokinetics is difficult and few methods are available. In this work, an alternative approach to determine oral bioavailability of voriconazole (VRC), used as a model drug, is presented. VRC pharmacokinetics was investigated in Wistar rats after p.o. (40 mg/kg) and i.v. administration (2.5, 5 and 10 mg/kg). VRC elimination showed saturation in all doses investigated, except the lower i.v. dose in which case a 3-compartment model with linear elimination adequately fitted the data. Data for the 2 higher i.v. doses were best described by a 3-compartment model with Michaelis-Menten elimination. A 1-compartment disposition with a saturable metabolic elimination model described the oral profile. VRC absolute oral bioavailability was determined by simultaneous fitting of the i.v. and oral profiles. the Michaelis constant and the maximum velocity estimated after 5 and 10 mg/kg i.v. dosing were 0.54 +/- 0.25 microg/ml and 2.53 +/- 0.54 microg/h, and 0.62 +/- 0.12 microg/ml and 2.74 +/- 0.84 microg/h, respectively. VRC oral bioavailability was determined to be 82.8%. the approach presented is an alternative for determining the bioavailability of drugs with similar nonlinear behavior. 2010 S. Karger AG, Basel.
Kinetic Measurements for Enzyme Immobilization.
Cooney, Michael J
2017-01-01
Enzyme kinetics is the study of the chemical reactions that are catalyzed by enzymes, with a focus on their reaction rates. The study of an enzyme's kinetics considers the various stages of activity, reveals the catalytic mechanism of this enzyme, correlates its value to assay conditions, and describes how a drug or a poison might inhibit the enzyme. Victor Henri initially reported that enzyme reactions were initiated by a bond between the enzyme and the substrate. By 1910, Michaelis and Menten were advancing their work by studying the kinetics of an enzyme saccharase which catalyzes the hydrolysis of sucrose into glucose and fructose. They published their analysis and ever since the Michaelis-Menten equation has been used as the standard to describe the kinetics of many enzymes. Unfortunately, soluble enzymes must generally be immobilized to be reused for long times in industrial reactors. In addition, other critical enzyme properties have to be improved like stability, activity, inhibition by reaction products, and selectivity towards nonnatural substrates. Immobilization is by far the chosen process to achieve these goals.Although the Michaelis-Menten approach has been regularly adapted to the analysis of immobilized enzyme activity, its applicability to the immobilized state is limited by the barriers the immobilization matrix places upon the measurement of compounds that are used to model enzyme kinetics. That being said, the estimated value of the Michaelis-Menten coefficients (e.g., V max, K M) can be used to evaluate effects of immobilization on enzyme activity in the immobilized state when applied in a controlled manner. In this review enzyme activity and kinetics are discussed in the context of the immobilized state, and a few novel protocols are presented that address some of the unique constraints imposed by the immobilization barrier.
李华; 霍瑞贞
2000-01-01
In experiment,the polyphenoloxidase was extracted from mushroom by using acetone precipitating method threetimes. And then, it was immobilized by using the absorbentdeposition method with porous glass powder as carriers,It wasstudied to catalize p-chlorophenol oxidizing reaction inchloroform, complys with Michaelis-Menten dynamicmodel.And themoisture content in organic solvent directly affected thecatalytic activity of mushroom polyphenoloxidase. Theoptimum reaction condition for the catalyrtic oxidation of p-chlorophenol in chloroform was determined: pH:7, temperature:25°C, moisture content: 0.5%(v/v).The measured value of dynamic parameters was 29.45kJ. mol-1 for apparent activationenergy,1.058mol. L-1 for Michaelis-Menten kinetics and 9.074×10-2 min-1 for the maximum reaction rate.% 本文用丙酮沉淀法从蘑菇中提取多酚氧化酶,以多孔玻璃粉为载体,用吸附沉积法将酶固定,研究了该酶在氯仿介质中催化对氯苯酚氧化反应的机理遵循米氏(Michaelis-Menten)动力学方程；而且,在有机介质中含水率大小直接影响酶的催化活性.实验测得反应的最佳条件为pH=7.0,温度为25°C,含水率为0.5%(v/v)；表观活化能Ea=29.54kJ . mol-1,米氏常数Km=1.058mol . dm-3,最大反应速率rmax=90.74×10-3min-1.
A. Adetoro
2011-10-01
Full Text Available The kinetics of the oxidation of Pyrocatechol violet (PCVH by nitrite ion (NO2- in aqueous acidic medium has been studied at 24±1ºC, I = 0.50 mol/dm3(NaCl, [H+] = 1.0×10-3 mol/dm3. The reaction is first order to [PCVH] and half order to [NO2-]. The redox reaction displayed a 1:1 stoichiometry and obeys the rate law: d[PCVH]/dt = (a + b[H+] [PCVH][NO2-]½. The second-order rate constant increases with increase in acid concentration and ionic strength. This system displayed positive salt effect while spectroscopic investigation and Michaelis-Menten plot showed evidence of intermediate complex formation in the course of the reaction. A plausible mechanism has been proposed for the reaction.
A Century of Enzyme Kinetic Analysis, 1913 to 2013
Johnson, Kenneth A.
2013-01-01
This review traces the history and logical progression of methods for quantitative analysis of enzyme kinetics from the 1913 Michaelis and Menten paper to the application of modern computational methods today. Following a brief review of methods for fitting steady state kinetic data, modern methods are highlighted for fitting full progress curve kinetics based upon numerical integration of rate equations, including a re-analysis of the original Michaelis-Menten full time course kinetic data. Finally, several illustrations of modern transient state kinetic methods of analysis are shown which enable the elucidation of reactions occurring at the active sites of enzymes in order to relate structure and function. PMID:23850893
A century of enzyme kinetic analysis, 1913 to 2013.
Johnson, Kenneth A
2013-09-02
This review traces the history and logical progression of methods for quantitative analysis of enzyme kinetics from the 1913 Michaelis and Menten paper to the application of modern computational methods today. Following a brief review of methods for fitting steady state kinetic data, modern methods are highlighted for fitting full progress curve kinetics based upon numerical integration of rate equations, including a re-analysis of the original Michaelis-Menten full time course kinetic data. Finally, several illustrations of modern transient state kinetic methods of analysis are shown which enable the elucidation of reactions occurring at the active sites of enzymes in order to relate structure and function.
Multi-system Nernst-Michaelis-Menten model applied to bioanodes formed from sewage sludge.
Rimboud, Mickaël; Desmond-Le Quemener, Elie; Erable, Benjamin; Bouchez, Théodore; Bergel, Alain
2015-11-01
Bioanodes were formed under constant polarization at -0.2 V/SCE from fermented sewage sludge. Current densities reached were 9.3±1.2 A m(-2) with the whole fermented sludge and 6.2±0.9 A m(-2) with the fermented sludge supernatant. The bioanode kinetics was analysed by differentiating among the contributions of the three redox systems identified by voltammetry. Each system ensured reversible Nernstian electron transfer but around a different central potential. The global overpotential required to reach the maximum current plateau was not imposed by slow electron transfer rates but was due to the potential range covered by the different redox systems. The microbial communities of the three bioanodes were analysed by 16S rRNA gene pyrosequencing. They showed a significant microbial diversity around a core of Desulfuromonadales, the proportion of which was correlated with the electrochemical performance of the bioanodes. Copyright © 2015 Elsevier Ltd. All rights reserved.
Leonard, Erin M; Marentette, Julie R; Balshine, Sigal; Wood, Chris M
2014-03-01
Traditionally, water quality guidelines/criteria are based on lethality tests where results are expressed as a function of waterborne concentrations (e.g. LC50). However, there is growing interest in the use of uptake and binding relationships, such as biotic ligand models (BLM), and in bioaccumulation parameters, such as critical body residue values (e.g. CBR50), to predict metal toxicity in aquatic organisms. Nevertheless, all these approaches only protect species against physiological death (e.g. mortality, failed recruitment), and do not consider ecological death which can occur at much lower concentrations when the animal cannot perform normal behaviours essential for survival. Therefore, we investigated acute (96 h) Ni toxicity in two freshwater fish species, the round goby (Neogobius melanostomus) and rainbow trout (Oncorhynchus mykiss) and compared LC, BLM, and CBR parameters for various organs, as well as behavioural responses (spontaneous activity). In general, round goby were more sensitive. Ni bioaccumulation displayed Michaelis-Menten kinetics in most tissues, and round goby gills had lower Kd (higher binding affinity) but similar Bmax (binding site density) values relative to rainbow trout gills. Round goby also accumulated more Ni than did trout in most tissues at a given exposure concentration. Organ-specific 96 h acute CBR values tended to be higher in round goby but 96 h acute CBR50 and CBR10 values in the gills were very similar in the two species. In contrast, LC50 and LC10 values were significantly higher in rainbow trout. With respect to BLM parameters, gill log KNiBL values for bioaccumulation were higher by 0.4-0.8 log units than the log KNiBL values for toxicity in both species, and both values were higher in goby (more sensitive). Round goby were also more sensitive with respect to the behavioural response, exhibiting a significant decline of 63-75 % in movements per minute at Ni concentrations at and above only 8 % of the LC50 value
Stability in a diffusive food chain model with Michaelis-Menten functional response
Lin, Zhigui; Pedersen, Michael
2004-01-01
This paper deals with the behavior of positive solutions to a reaction-diffusion system with homogeneous Neumann boundary conditions describing a three species food chain. A sufficient condition for the local asymptotical stability is given by linearization and also a sufficient condition...... for the global asymptotical stability is given by a Lyapunov function. Our result shows that the equilibrium solution is globally asymptotically stable if the net birth rate of the first species is big enough and the net death rate of the third species is neither too big nor too small. (C) 2004 Elsevier Ltd. All...
Specificity of non-Michaelis-Menten enzymes: necessary information for analyzing metabolic pathways.
Cornish-Bowden, Athel; Cárdenas, María Luz
2010-12-16
The specificity of an enzyme obeying the Michaelis−Menten equation is normally measured by comparing the kcat/Km for different substrates, but this is inappropriate for enzymes with a Hill coefficient h different from 1. The obvious alternative of generalizing Km in the expression as K0.5, the substrate concentration for half-saturation, is better, but it is not entirely satisfactory either, and here we show that kcat/K0.5(h) gives satisfactory results for analyzing the kinetic behavior of metabolic pathways. The importance of using kcat/K0.5(h) increases with the value of h, but even when h is small, it makes an appreciable difference, as illustrated for the mammalian hexokinases. Reinterpretation of data for the specificity of these enzymes in terms of the proposed definition indicates that hexokinase D, often believed highly specific for glucose, and accordingly called “glucokinase”, actually has the lowest preference for glucose over fructose of the four isoenzymes found in mammals.
Mafrica, Stefano; Godiot, Stéphanie; Menouni, Mohsine; Boyron, Marc; Expert, Fabien; Juston, Raphaël; Marchand, Nicolas; Ruffier, Franck; Viollet, Stéphane
2015-03-09
In this paper, we present: (i) a novel analog silicon retina featuring auto-adaptive pixels that obey the Michaelis-Menten law, i.e. V=V(m) I(n)/I(n)+σ(n); (ii) a method of characterizing silicon retinas, which makes it possible to accurately assess the pixels' response to transient luminous changes in a ±3-decade range, as well as changes in the initial steady-state intensity in a 7-decade range. The novel pixel, called M(2)APix, which stands for Michaelis-Menten Auto-Adaptive Pixel, can auto-adapt in a 7-decade range and responds appropriately to step changes up to ±3 decades in size without causing any saturation of the Very Large Scale Integration (VLSI) transistors. Thanks to the intrinsic properties of the Michaelis-Menten equation, the pixel output always remains within a constant limited voltage range. The range of the Analog to Digital Converter (ADC) was therefore adjusted so as to obtain a Least Significant Bit (LSB) voltage of 2.35mV and an effective resolution of about 9 bits. The results presented here show that the M(2)APix produced a quasi-linear contrast response once it had adapted to the average luminosity. Differently to what occurs in its biological counterparts, neither the sensitivity to changes in light nor the contrast response of the M(2)APix depend on the mean luminosity (i.e. the ambient lighting conditions). Lastly, a full comparison between the M(2)APix and the Delbrück auto-adaptive pixel is provided.
Yunxian Dai; Yiping Lin; Huitao Zhao
2014-01-01
We consider a predator-prey system with Michaelis-Menten type functional response and two delays. We focus on the case with two unequal and non-zero delays present in the model, study the local stability of the equilibria and the existence of Hopf bifurcation, and then obtain explicit formulas to determine the properties of Hopf bifurcation by using the normal form method and center manifold theorem. Special attention is paid to the global continuation of local Hopf bifurcation when the delay...
Machado, Eustáquio José
2014-01-01
A equação hiperbólica, conhecida no contexto bioquímico como o modelo de Michaelis-Menten, é utilizada para descrever a velocidade de reações químicas envolvendo enzimas (cinética enzimática). Este estudo teve como objetivo comparar os ajustes do modelo de Michaelis-Menten (1913) que fez uso de dois modelos não-lineares e quatro modelos linearizados. Os dois modelos não-lineares (um utilizou o método clássico assintotico usual e o outro fez uso da abordagem "bootstrap"). Os modelos linearizad...
Huang, Hsuan-Ming; Ismail-Beigi, Faramarz; Muzic, Raymond F
2011-08-01
A new model is introduced that individually resolves the delivery, transport, and phosphorylation steps of metabolism of glucose and its analogs in skeletal muscle by interpreting dynamic positron emission tomography (PET) data. The model uniquely utilizes information obtained from the competition between glucose and its radiolabeled analogs. Importantly, the model avoids use of a lumped constant which may depend on physiological state. Four basic physiologic quantities constitute our model parameters, including the fraction of total tissue space occupied by interstitial space (f(IS)), a flow-extraction product and interstitial (IS(g)) and intracellular (IC(g)) glucose concentrations. Using the values of these parameters, cellular influx (CI) and efflux (CE) of glucose, glucose phosphorylation rate (PR), and maximal transport (V(G)) and phosphorylation capacities (V(H)) can all be determined. Herein, the theoretical derivation of our model is addressed and characterizes its properties via simulation. Specifically, the model performance is evaluated by simulation of basal and euglycemic hyperinsulinemic (EH) conditions. In fitting the model-generated, synthetic data (including noise), mean estimates of all but IC(g) of the parameter values are within 5% of their values for both conditions. In addition, mean errors of CI, PR, and V(G) are less than 5% whereas those of VH and CE are not. It is concluded that under the conditions tested, the novel model can provide accurate parameter estimates and physiological quantities, except IC(g) and two quantities that are dependent on IC(g), namely CE and VH. However, the ability to estimate IC(g) seems to improve with increases in intracellular glucose concentrations as evidenced by comparing IC(g) estimates under basal vs EH conditions.
Strompen, Simon; Weiss, Markus; Ingram, Thomas; Smirnova, Irina; Gröger, Harald; Hilterhaus, Lutz; Liese, Andreas
2012-06-01
A solvent-free, chemoenzymatic reaction sequence for the enantioselective synthesis of β-amino acid esters has been kinetically and thermodynamically characterized. The coupled sequence comprises a thermal aza-Michael addition of cheap starting materials and a lipase catalyzed aminolysis for the kinetic resolution of the racemic ester. Excellent ee values of >99% were obtained for the β-amino acid ester at 60% conversion. Kinetic constants for the aza-Michael addition were obtained by straightforward numerical integration of second-order rate equations and nonlinear fitting of the progress curves. A different strategy had to be devised for the biocatalytic reaction. Initially, a simplified Michaelis-Menten model including product inhibition was developed for the reaction running in THF as an organic solvent. Activity based parameters were used instead of concentrations in order to facilitate the transfer of the kinetic model to the solvent-free system. Observed solvent effects not accounted for by the use of thermodynamic activities were incorporated into the kinetic model. Enzyme deactivation was observed to depend on the ratio of the applied substrates and also included in the kinetic model. The developed simple model is in very good agreement with the experimental data and allows the simulation and optimization of the solvent-free process.
Mass action realizations of reaction kinetic system models on various time scales
Hangos, K M; Szederkenyi, G, E-mail: hangos@scl.sztaki.hu, E-mail: szeder@scl.sztaki.hu [Process Control Research Group, Computer and Automation Reseach Institute, Kende u. 13-17, H-1111 Budapest (Hungary)
2011-01-01
Complex chemical reaction networks often exhibit different dynamic behaviour on different time scales. A combined approach is proposed in this work for determining physically meaningful mass action realizations of complex chemical reaction networks that describe its dynamic behaviour on different time scales. This is achieved by appropriately reducing the detailed overall mass action kinetic scheme using quasi steady state assumptions fit to the particular time scale, and then searching for an optimal realization using mixed integer linear programing. Furthermore, the relationship between the properties (reversibility, deficiency, stability) of the obtained realizations of the same system on different time scales are also investigated and related to the same properties of the detailed overall model. It is shown that the reduced models obtained by quasi steady state assumptions may show exotic nonlinear behaviour, such as oscillations, when the original detailed is globally asymptotically stable. The proposed methods are illustrated by using a simple Michaelis-Menten type reaction kinetic example. The simplified versions of the well known Brusselator model have also been investigated and presented as a case study.
Yusof, Siti R; Abbott, N Joan; Avdeef, Alex
2017-08-30
Most studies of blood-brain barrier (BBB) permeability and transport are conducted at a single pH, but more detailed information can be revealed by using multiple pH values. A pH-dependent biophysical model was applied to the mechanistic analysis of published pH-dependent BBB luminal uptake data from three opioid derivatives in rat: pentazocine (Suzuki et al., 2002a, 2002b), naloxone (Suzuki et al., 2010a), and oxycodone (Okura et al., 2008). Two types of data were processed: in situ brain perfusion (ISBP) and brain uptake index (BUI). The published perfusion data were converted to apparent luminal permeability values, Papp, and analyzed by the pCEL-X program (Yusof et al., 2014), using the pH-dependent Crone-Renkin equation (pH-CRE) to determine the impact of cerebrovascular flow on the Michaelis-Menten transport parameters (Avdeef and Sun, 2011). For oxycodone, the ISBP data had been measured at pH7.4 and 8.4. The present analysis indicates a 7-fold lower value of the cerebrovascular flow velocity, Fpf, than that expected in the original study. From the pyrilamine-inhibited data, the flow-corrected passive intrinsic permeability value was determined to be P0=398×10(-6)cm·s(-1). The uptake data indicate that the neutral form of oxycodone is affected by a transporter at pH8.4. The extent of the cation uptake was less certain from the available data. For pentazocine, the brain uptake by the BUI method had been measured at pH5.5, 6.5, and 7.4, in a concentration range 0.1-40mM. Under similar conditions, ISBP data were also available. The pH-CRE determined values of Fpf from both methods were nearly the same, and were smaller than the expected value in the original publication. The transport of the cationic pentazocine was not fully saturated at pH5.5 at 40mM. The transport of the neutral species at pH7.4 appeared to reach saturation at 40mM pentazocine concentration, but not at 12mM. In the case of naloxone, a pH-dependent Michaelis-Menten equation (p
Youdim, K; Dodia, R
2010-04-01
Non-linear dose-exposure (supra-proportionality) occurs when plasma drug concentrations increase in a non-linear fashion with increasing dose. To predict the likelihood of this, an understanding is required of the K(M), which reflects a drug ability to saturate a specific enzyme involved in its metabolism. This study assessed the accuracy of K(M) and V(max) determinations for compounds using a substrate-depletion approach with those determined using the product-formation approach, using both recombinant human cytochrome P450 (CYP) enzymes and human liver microsomes. For the vast majority of the compounds studied, the K(M)'s using recombinant CYPs and human liver microsomes in the two approaches predicted within two-fold. Further comparisons between the K(M) and V(max)-values were made between those measured using the product-formation approach and those estimated following simultaneous fitting of the Michaelis-Menten equation to all substrate depletion plots. In each case values were comparable. In conclusion, the current study showed the substrate-depletion approach can be used to estimate K(M) and V(max) using both human liver microsomes and recombinant P450s. Estimation of these parameters during early discovery will aid in the understanding of dosages at which non-linearity may occur, but potentially aid predictions of likely clinical drug-drug interactions.
磁流变阻尼器的米氏模型及试验验证%MICHAELIS-MENTEN MODEL OF MAGNETORHEOLOGICAL DAMPER AND TEST VERIFICATION
张香成; 徐赵东; 王绍安; 沙凌峰
2013-01-01
为研究磁流变阻尼器(MRD)非线性滞回性能的影响因素,建立精确的MRD力学模型,对MRD进行力学性能试验,并基于米氏方程提出一个综合考虑电流、位移和频率影响的力学模型——米氏模型.对所提模型和传统经典力学模型进行数值模拟,并与试验结果进行对比分析,结果表明:该模型可以模拟MRD的非线性滞回性能、体现位移和频率对阻尼力及非线性滞回性能的影响.%To find the effect factors of the nonlinear hysteresis capability of a magnetorheological damper (MRD) and establish a precise mathematical model, a Michaelis-Menten (MM) Model was presented based on the MM equation which considers the effects of current, amplitude and frequency. Numerical simulations of the MM Model and traditional classical mathematic model were carried out to compare with the test results. Comparison results indicate that the MM Model could simulate the hysteresis capability of MRD and reflect the effects of current, amplitude and frequency on damping force and nonlinear hysteresis capability.
Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes.
Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu; Dua, Arti
2016-08-28
Dynamic co-operativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic co-operativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative co-operativity. For fewer enzymes, dynamic co-operativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, however, suppresses the effect of enzymatic conformational fluctuations such that dynamic co-operativity emerges solely due to the discrete changes in the number of reacting species. These results confirm that the turnover kinetics of fluctuating enzyme based on the parallel-pathway MM mechanism switches over to the single-pathway MM mechanism with the increase in the number of enzymes. For large enzyme numbers, convergence to the exact MM equation occurs in the limit of very high substrate concentration as the stochastic kinetics approaches the deterministic behaviour.
Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes
Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu; Dua, Arti
2016-08-01
Dynamic co-operativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic co-operativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative co-operativity. For fewer enzymes, dynamic co-operativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, however, suppresses the effect of enzymatic conformational fluctuations such that dynamic co-operativity emerges solely due to the discrete changes in the number of reacting species. These results confirm that the turnover kinetics of fluctuating enzyme based on the parallel-pathway MM mechanism switches over to the single-pathway MM mechanism with the increase in the number of enzymes. For large enzyme numbers, convergence to the exact MM equation occurs in the limit of very high substrate concentration as the stochastic kinetics approaches the deterministic behaviour.
A.L.O. Ferreira
2000-12-01
Full Text Available This work presents a kinetic study of the side reactions of the ampicillin enzymatic synthesis, from phenylglycine methyl ester and 6-aminopenicillanic acid using penicillin G acylase immobilized on agarose. A Michaelis-Menten model with competitive inhibition was fitted to initial rates of ester and antibiotic hydrolysis, at pH 6.5 and 25ºC. Inherent kinetic parameters were estimated for low enzymatic loads, to assure that diffusional resistance was not important. It was observed that ampicillin inhibits the hydrolysis of PGME, but the inhibitory effect of the ester on ampicillin hydrolysis was almost negligible. The obtained parameters were: k cat1= 0.025 mM/UI min, Km1 = 155.4mM, K AE = 16.18mM, k cat2= 4.67x10-3 mM/UI min, Km2 = 11.47, K EA = 0.68 mM. Parameter values are in the range reported in the literature, except for Km1, which is much higher. The large confidence interval for this parameter denotes that the model presents low sensitivity with respect to it.
Syahinaz Shahrazi
2013-01-01
Full Text Available This study relates to the mathematical modelling of enzymatic production of Cyclodextrins (CDs by Cyclodextrin Glucanotransferase (CGTase from Bacillus macerans. The experiments were carried out in batch mode using different starch sources and the results were used to estimate unknown parameters using linearization and dynamic simulation methods. Î±- and Î²-CD produced from tapioca were found to give the highest Michaelis-Menten constant, KM,i of 58.23 and 54.07 g L-1, respectively and maximum velocity, Vmax,i of 3.45 and 2.76 g L-1.min, respectively, while sago resulted in the highest KM,i and Vmax,i values of 342.35 g L-1 and 5.97 g L-1.min, respectively, for Î³-CD obtained by the linearization method. Value of product inhibition, K1,i and CD degradation coefficient rate, Î´CD,i, were estimated using dynamic simulation, indicating that exponential reaction kinetics could be fitted better with the experimental data. Sensitivity analysis revealed that the product inhibition parameter in the exponential reaction kinetic equation is more significant in the process. For validation, the production of CDs by fed batch method was undertaken and starch and enzyme were added into the reaction medium. Then, the predicted profiles generated by simulation were compared with the experimental values. The proposed exponential reaction kinetics shows good fitting with the experimental data.
Sheiner, L B; Beal, S L
1980-12-01
Individual pharmacokinetic par parameters quantify the pharmacokinetics of an individual, while population pharmacokinetic parameters quantify population mean kinetics, interindividual variability, and residual intraindividual variability plus measurement error. Individual pharmacokinetics are estimated by fitting individual data to a pharmacokinetic model. Population pharmacokinetic parameters are estimated either by fitting all individual's data together as though there was no individual kinetic differences (the naive pooled data approach), or by fitting each individual's data separately, and then combining the individual parameter estimates (the two-stage approach). A third approach, NONMEM, takes a middle course between these, and avoids shortcomings of each of them. A data set consisting of 124 steady-state phenytoin concentration-dosage pairs from 49 patients, obtained in the routine course of their therapy, was analyzed by each method. The resulting population parameter estimates differ considerably (population mean Km, for example, is estimated as 1.57, 5.36, and 4.44 micrograms/ml by the naive pooled data, two-stage, and NONMEN approaches, respectively). Simulations of the data were analyzed to investigate these differences. The simulations indicate that the pooled data approach fails to estimate variabilities and produces imprecise estimates of mean kinetics. The two-stage approach produces good estimates of mean kinetics, but biased and imprecise estimates of interindividual variability. NONMEN produces accurate and precise estimates of all parameters, and also reasonable confidence intervals for them. This performance is exactly what is expected from theoretical considerations and provides empirical support for the use of NONMEM when estimating population pharmacokinetics from routine type patient data.
Modeling networks of coupled enzymatic reactions using the total quasi-steady state approximation.
Andrea Ciliberto
2007-03-01
Full Text Available In metabolic networks, metabolites are usually present in great excess over the enzymes that catalyze their interconversion, and describing the rates of these reactions by using the Michaelis-Menten rate law is perfectly valid. This rate law assumes that the concentration of enzyme-substrate complex (C is much less than the free substrate concentration (S0. However, in protein interaction networks, the enzymes and substrates are all proteins in comparable concentrations, and neglecting C with respect to S0 is not valid. Borghans, DeBoer, and Segel developed an alternative description of enzyme kinetics that is valid when C is comparable to S0. We extend this description, which Borghans et al. call the total quasi-steady state approximation, to networks of coupled enzymatic reactions. First, we analyze an isolated Goldbeter-Koshland switch when enzymes and substrates are present in comparable concentrations. Then, on the basis of a real example of the molecular network governing cell cycle progression, we couple two and three Goldbeter-Koshland switches together to study the effects of feedback in networks of protein kinases and phosphatases. Our analysis shows that the total quasi-steady state approximation provides an excellent kinetic formalism for protein interaction networks, because (1 it unveils the modular structure of the enzymatic reactions, (2 it suggests a simple algorithm to formulate correct kinetic equations, and (3 contrary to classical Michaelis-Menten kinetics, it succeeds in faithfully reproducing the dynamics of the network both qualitatively and quantitatively.
Heering, Hendrik A
2012-10-01
Deconvolution of protein film voltammetric data by fitting multiple components (sigmoids, derivative peaks) often is ambiguous when features are partially overlapping, due to exchangeability between the width and the number of components. Here, a new method is presented to obtain the width of the components. This is based on the equivalence between the sigmoidal catalytic response as function of electrode potential, and the classical saturation curve obtained for the enzyme activity as function of the soluble substrate concentration, which is also sigmoidal when plotted versus log[S]. Thus, analysis of the catalytic voltammogram with Lineweaver-Burk, Eadie-Hofstee, and Hanes-Woolf plots is feasible. This provides a very sensitive measure of the cooperativity number (Hill coefficient), which for electrons equals the apparent (fractional) number of electrons that determine the width, and thereby the number of components (kinetic phases). This analysis is applied to the electrocatalytic oxygen reduction by Paracoccus denitrificans cytochrome aa(3) (cytochrome c oxidase). Four partially overlapping kinetic phases are observed that (stepwise) increase the catalytic efficiency with increasingly reductive potential. Translated to cell biology, the activity of the terminal oxidase stepwise adapts to metabolic demand for oxidative phosphorylation. Copyright © 2011 Elsevier B.V. All rights reserved.
Gattu, Srikanth; Crihfield, Cassandra L; Holland, Lisa A
2017-01-03
Phospholipid nanogels enhance the stability and performance of the exoglycosidase enzyme neuraminidase and are used to create a fixed zone of enzyme within a capillary. With nanogels, there is no need to covalently immobilize the enzyme, as it is physically constrained. This enables rapid quantification of Michaelis-Menten constants (KM) for different substrates and ultimately provides a means to quantify the linkage (i.e., 2-3 versus 2-6) of sialic acids. The fixed zone of enzyme is inexpensive and easily positioned in the capillary to support electrophoresis mediated microanalysis using neuraminidase to analyze sialic acid linkages. To circumvent the limitations of diffusion during static incubation, the incubation period is reproducibly achieved by varying the number of forward and reverse passes the substrate makes through the stationary fixed zone using in-capillary electrophoretic mixing. A KM value of 3.3 ± 0.8 mM (Vmax, 2100 ± 200 μM/min) was obtained for 3'-sialyllactose labeled with 2-aminobenzoic acid using neuraminidase from Clostridium perfringens that cleaves sialic acid monomers with an α2-3,6,8,9 linkage, which is similar to values reported in the literature that required benchtop analyses. The enzyme cleaves the 2-3 linkage faster than the 2-6, and a KM of 2 ± 1 mM (Vmax, 400 ± 100 μM/min) was obtained for the 6'-sialyllactose substrate. An alternative neuraminidase selective for 2-3 sialic acid linkages generated a KM value of 3 ± 2 mM (Vmax, 900 ± 300 μM/min) for 3'-sialyllactose. With a knowledge of Vmax, the method was applied to a mixture of 2-3 and 2-6 sialyllactose as well as 2-3 and 2-6 sialylated triantennary glycan. Nanogel electrophoresis is an inexpensive, rapid, and simple alternative to current technologies used to distinguish the composition of 3' and 6' sialic acid linkages.
Leonard, Erin M; Wood, Chris M
2013-06-01
We investigated the bioaccumulation and acute toxicity (48 h or 96 h) of Ni in four freshwater invertebrate species in two waters with hardness of 40 (soft water) and 140 mg L(-1) as CaCO(3) (hard water). Sensitivity order (most to least) was Lymnaea stagnalis > Daphnia pulex > Lumbriculus variegatus > Chironomus riparius. In all cases water hardness was protective against acute Ni toxicity with LC(50) values 3-3.5× higher in the hard water vs. soft water. In addition, higher water hardness significantly reduced Ni bioaccumulation in these organisms suggesting that competition by Ca and Mg for uptake at the biotic ligand may contribute to higher metal resistance. CBR50 values (Critical Body Residues) were less dependent on water chemistry (i.e. more consistent) than LC(50) values within and across species by ~2 fold. These data support one of the main advantages of the Tissue Residue Approach (TRA) where tissue concentrations are generally less variable than exposure concentrations with respect to toxicity. Whole body Ni bioaccumulation followed Michaelis-Menten kinetics in all organisms, with greater hardness tending to decrease B(max) with no consistent effect on K(d). Across species, acute Ni LC(50) values tended to increase with both K(d) and B(max) values - i.e. more sensitive species exhibited higher binding affinity and lower binding capacity for Ni, but there was no correlation with body size. With respect to biotic ligand modeling, log K(NiBL) values derived from Ni bioaccumulation correlated well with log K(NiBL) values derived from toxicity testing. Both whole body Na and Mg levels were disturbed, suggesting that disruption of ionoregulatory homeostasis is a mechanism of acute Ni toxicity. In L. stagnalis, Na depletion was a more sensitive endpoint than mortality, however, the opposite was true for the other organisms. This is the first study to show the relationship between Na and Ni. Copyright © 2013 Elsevier Inc. All rights reserved.
A new multi-wavelength model-based method for determination of enzyme kinetic parameters.
Sorouraddin, Mohammad-Hossein; Amini, Kaveh; Naseri, Abdolhossein; Vallipour, Javad; Hanaee, Jalal; Rashidi, Mohammad-Reza
2010-09-01
Lineweaver-Burk plot analysis is the most widely used method to determine enzyme kinetic parameters. In the spectrophotometric determination of enzyme activity using the Lineweaver-Burk plot, it is necessary to find a wavelength at which only the substrate or the product has absorbance without any spectroscopic interference of the other reaction components. Moreover, in this method, different initial concentrations of the substrate should be used to obtain the initial velocities required for Lineweaver-Burk plot analysis. In the present work, a multi-wavelength model-based method has been developed and validated to determine Michaelis-Menten constants for some enzyme reactions. In this method, a selective wavelength region and several experiments with different initial concentrations of the substrate are not required. The absorbance data of the kinetic assays are fitted by non-linear regression coupled to the numeric integration of the related differential equation. To indicate the applicability of the proposed method, the Michaelis-Menten constants for the oxidation of phenanthridine, 6-deoxypenciclovir and xanthine by molybdenum hydroxylases were determined using only a single initial concentration of the substrate, regardless of any spectral overlap.
QE+QSS for Derivation of Kinetic Equations and Stiffness Removing
Gorban, A N
2010-01-01
We present the general formalism of the Quasiequilibrium approximation (QE) with the proof of the persistence of entropy production in the QE approximation. We demonstrate, how to apply this formalism to chemical kinetics and describe the difference between QE and Quasi--Steady--State (QSS) approximations. The celebrated QSS "Michaelis--Menten" kinetics is, as a matter of fact, the "Briggs-Haldane" kinetics. Michaelis and Menten used the QE assumption that all intermediate complexes are in fast equilibrium with free substrates and enzyme. Similar approach was developed by Stuekelberg (1952) for the Boltzmann kinetics. Following them, we combine the QE (fast equilibria) and the QSS (small amounts) approaches and study the general kinetics with fast intermediates present in small amount. We prove the representation of the rate of an elementary reaction as a product of the Boltzmann factor (purely thermodynamic) and the kinetic factor, and found the basic relations between kinetic factors. In the practice of mod...
Li, Su-Juan; Wang, Chen; Wu, Zeng-Qiang; Xu, Jing-Juan; Xia, Xing-Hua; Chen, Hong-Yuan
2010-09-01
To understand the fundamentals of enzymatic reactions confined in micro-/nanosystems, the construction of a small enzyme reactor coupled with an integrated real-time detection system for monitoring the kinetic information is a significant challenge. Nano-enzyme array reactors were fabricated by covalently linking enzymes to the inner channels of a porous anodic alumina (PAA) membrane. The mechanical stability of this nanodevice enables us to integrate an electrochemical detector for the real-time monitoring of the formation of the enzyme reaction product by sputtering a thin Pt film on one side of the PAA membrane. Because the enzymatic reaction is confined in a limited nanospace, the mass transport of the substrate would influence the reaction kinetics considerably. Therefore, the oxidation of glucose by dissolved oxygen catalyzed by immobilized glucose oxidase was used as a model to investigate the mass-transport-related enzymatic reaction kinetics in confined nanospaces. The activity and stability of the enzyme immobilized in the nanochannels was enhanced. In this nano-enzyme reactor, the enzymatic reaction was controlled by mass transport if the flux was low. With an increase in the flux (e.g., >50 microL min(-1)), the enzymatic reaction kinetics became the rate-determining step. This change resulted in the decrease in the conversion efficiency of the nano-enzyme reactor and the apparent Michaelis-Menten constant with an increase in substrate flux. This nanodevice integrated with an electrochemical detector could help to understand the fundamentals of enzymatic reactions confined in nanospaces and provide a platform for the design of highly efficient enzyme reactors. In addition, we believe that such nanodevices will find widespread applications in biosensing, drug screening, and biochemical synthesis.
Kinetics and mechanism of the oxidation of formic and oxalic acids by quinolinium fluorochromate
Madhu Khurana; Pradeep K Sharma; Kalyan K Banerji
2000-04-01
Kinetics and mechanism of oxidation of formic and oxalic acids by quinolinium fluorochromate (QFC) have been studied in dimethylsulphoxide. The main product of oxidation is carbon dioxide. The reaction is first-order with respect to QFC. Michaelis-Menten type of kinetics were observed with respect to the reductants. The reaction is acid-catalysed and the acid dependence has the form: obs = + [H+]. The oxidation of -deuterioformic acid exhibits a substantial primary kinetic isotope effect (H/D = 6.01 at 303 K). The reaction has been studied in nineteen different organic solvents and the solvent effect has been analysed using Taft’s and Swain’s multiparametric equations. The temperature dependence of the kinetic isotope effect indicates the presence of a symmetrical cyclic transition state in the rate-determining step. Suitable mechanisms have been proposed
Zoe Rogers
2016-09-01
Full Text Available N-acetyltransferase 2 (NAT2 catalyzes the acetylation of isoniazid to N-acetylisoniazid. NAT2 polymorphism explains 88% of isoniazid clearance variability in adults. We examined the effects of clinical and genetic factors on Michaelis-Menten reaction kinetic constants of maximum velocity (Vmax and affinity (Km in children 0–10 years old. We measured the rates of isoniazid elimination and N-acetylisoniazid production in the blood of 30 children. Since maturation effects could be non-linear, we utilized a pharmacometric approach and the artificial intelligence method, multivariate adaptive regression splines (MARS, to identify factors predicting NAT2 Vmax and Km by examining clinical, genetic, and laboratory factors in toto. Isoniazid concentration predicted both Vmax and Km and superseded the contribution of NAT2 genotype. Age non-linearly modified the NAT2 genotype contribution until maturation at ≥5.3 years. Thus, enzyme efficiency was constrained by substrate concentration, genes, and age. Since MARS output is in the form of basis functions and equations, it allows multiscale systems modeling from the level of cellular chemical reactions to whole body physiological parameters, by automatic selection of significant predictors by the algorithm.
The kinetics of denitrification in permeable sediments
Evrard, Victor; Glud, Ronnie N.; Cook, Perran L. M.
2013-01-01
on sediments taken from six shallow coastal sites in Port Phillip Bay, Victoria, Australia. The results showed that denitrification commenced rapidly (within 30 min) after the onset of anoxia and the kinetics could be well described by Michaelis-Menten kinetics with half saturation constants (apparent K...
Studies on the kinetics of plasminogen activation by tissue plasminogen activator.
Rånby, M
1982-06-24
The steady-state rate of plasminogen activation by tissue plasminogen activator has been determined at various plasminogen concentrations. A plasmin substrate method similar to that presented by Christensen and Müllertz (Biochim. Biophys. Acta 480 (1977) 257-281) was used. The reaction was studied using one-chain type and two-chain type tissue plasminogen activator, N-terminal glutamic acid and N-terminal lysine plasminogen in the presence and in the absence of fibrin (eight studies). The kinetic data were fitted to a general Wong-Hanes equation and the simplest equation with significant parameters was found. In the absence of fibrin N-terminal glutamic acid plasminogen activation obeyed the Michaelis-Menten rate equation (Km 4.9 and 7.6 micro M and kcat 0.0013 and 0.0078 s-1 for one-chain type and two-chain type tissue plasminogen activator, respectively. In the absence of fibrin the activation of N-terminal lysine plasminogen activation failed to obey the Michaelis-Menten rate equation. Fibrin was found to stimulate greatly (up to 1000-fold) the steady-state activation rate. A theory for the fibrin stimulating mechanism is presented.
Structural simplification of chemical reaction networks in partial steady states.
Madelaine, Guillaume; Lhoussaine, Cédric; Niehren, Joachim; Tonello, Elisa
2016-11-01
We study the structural simplification of chemical reaction networks with partial steady state semantics assuming that the concentrations of some but not all species are constant. We present a simplification rule that can eliminate intermediate species that are in partial steady state, while preserving the dynamics of all other species. Our simplification rule can be applied to general reaction networks with some but few restrictions on the possible kinetic laws. We can also simplify reaction networks subject to conservation laws. We prove that our simplification rule is correct when applied to a module of a reaction network, as long as the partial steady state is assumed with respect to the complete network. Michaelis-Menten's simplification rule for enzymatic reactions falls out as a special case. We have implemented an algorithm that applies our simplification rules repeatedly and applied it to reaction networks from systems biology.
Kinetics and mechanism of oxidation of aliphatic alcohols by tetrabutylammonium tribromide
Manju Baghmar; Pradeep K Sharma
2001-04-01
Oxidation of nine primary aliphatic alcohols by tetrabutylammonium tribromide (TBATB) in aqueous acetic acid leads to the formation of the corresponding aldehydes. The reaction is first order with respect to TBATB. Michaelis-Menten type kinetics is observed with respect to alcohols. The reaction failed to induce the polymerization of acrylonitrile. Tetrabutylammonium chloride has no effect on the reaction rate. The proposed reactive oxidizing species is the tribromide ion. The oxidation of [1,1-2H2]ethanol exhibits a substantial kinetic isotope effect. The effect of solvent composition indicates that the rate increases with increase in the polarity of the solvent. The reaction is susceptible to both polar and steric effects of substituents. A mechanism involving transfer of a hydride ion in the ratedetermining step has been proposed.
Kinetics of glucose transport in rat muscle
Ploug, Thorkil; Galbo, H; Vinten, J
1987-01-01
-MG concentration exhibited Michaelis-Menten kinetics. Uptake by simple diffusion could not be detected. The maximum 3-O-MG transport velocity (Vmax) was increased more by maximum isometric contractions (10- to 40-fold, depending on fiber type) than by insulin (20,000 microU/ml; 3- to 20-fold) in both red and white...
Atypical cytochrome p450 kinetics: implications for drug discovery.
Tracy, Timothy S
2006-01-01
The Michaelis-Menten model is commonly used to estimate a drug's potential in vivo hepatic clearance based on in vitro data obtained during drug discovery and development. This paradigm assumes that the drug obeys 'typical' enzyme kinetics and thus can be described by this model. However, it is increasingly being recognised that a number of drugs metabolised not only by the cytochrome P450 enzymes but also by other enzymes and transporters can exhibit atypical kinetic profiles, and thus are not accurately modeled with the Michaelis-Menten model. Application of an incorrect model can then lead to mis-estimation of in vitro intrinsic clearance and thus affect the prediction of in vivo clearance. This review discusses several types of atypical kinetic profiles that may be observed, including examples of homotropic cooperativity (i.e. sigmoidal kinetics, biphasic kinetics and substrate inhibition kinetics) as well as heterotropic cooperativity (i.e. activation). Application of the incorrect kinetic model may profoundly affect estimations of intrinsic clearance. For example, incorrectly applying the Michaelis-Menten model to a kinetic profile exhibiting substrate inhibition kinetics will result in an underestimation of Km (Michaelis-Menten constant) and V(max) (maximal velocity), whereas application of the Michaelis-Menten model to sigmoidal kinetic data typically results in an overestimation of Km and V(max) at the lower substrate concentrations that are typically therapeutically relevant. One must also be careful of potential artefactual causes of atypical kinetic profiles, such as enzyme activation by solvents, buffer dependent kinetic profiles, or altered kinetic parameter estimates due to nonspecific binding of the substrate to proteins. Despite a plethora of data on the effects of atypical kinetic profiles in vitro, only modest effects have been noted in vivo (with the exception of substrate dependent inhibition). Thus, the clinical relevance of these phenomena
Kinetics and mechanism of the oxidation of some diols by benzyltrimethylammonium tribromide
Garima Goswami; Seema Kothari; Kalyan K Banerji
2001-02-01
The kinetics of oxidation of five vicinal and four non-vicinal diols, and two of their monoethers by benzyltrimethylammonium tribromide (BTMAB) have been studied in 3:7 (/) acetic acid-water mixture. The vicinal diols yield the carbonyl compounds arising out of the glycol bond fission while the other diols give the hydroxycarbonyl compounds. The reaction is first-order with respect to BTMAB. Michaelis-Menten type kinetics is observed with respect to diol. Addition of benzyltrimethylammonium chloride does not affect the rate. Tribromide ion is postulated to be the reactive oxidizing species. Oxidation of [1,1,2,2-2H4] ethanediol shows the absence of a kinetic isotope effect. The reaction exhibits substantial solvent isotope effect. A mechanism involving a glycol-bond fission has been proposed for the oxidation of the vicinal diols. The other diols are oxidized by a hydride ion transfer to the oxidant, as are the monohydric alcohols.
Aon, Miguel Antonio; O'Rourke, Brian; Cortassa, Sonia
2004-01-01
In this work, we highlight the links between fractals and scaling in cells and explore the kinetic consequences for biochemical reactions operating in fractal media. Based on the proposal that the cytoskeletal architecture is organized as a percolation lattice, with clusters emerging as fractal forms, the analysis of kinetics in percolation clusters is especially emphasized. A key consequence of this spatiotemporal cytoplasmic organization is that enzyme reactions following Michaelis-Menten or allosteric type kinetics exhibit higher rates in fractal media (for short times and at lower substrate concentrations) at the percolation threshold than in Euclidean media. As a result, considerably faster and higher amplification of enzymatic activity is obtained. Finally, we describe some of the properties bestowed by cytoskeletal organization and dynamics on metabolic networks.
Spectral Quasi-Equilibrium Manifold for Chemical Kinetics.
Kooshkbaghi, Mahdi; Frouzakis, Christos E; Boulouchos, Konstantinos; Karlin, Iliya V
2016-05-26
The Spectral Quasi-Equilibrium Manifold (SQEM) method is a model reduction technique for chemical kinetics based on entropy maximization under constraints built by the slowest eigenvectors at equilibrium. The method is revisited here and discussed and validated through the Michaelis-Menten kinetic scheme, and the quality of the reduction is related to the temporal evolution and the gap between eigenvalues. SQEM is then applied to detailed reaction mechanisms for the homogeneous combustion of hydrogen, syngas, and methane mixtures with air in adiabatic constant pressure reactors. The system states computed using SQEM are compared with those obtained by direct integration of the detailed mechanism, and good agreement between the reduced and the detailed descriptions is demonstrated. The SQEM reduced model of hydrogen/air combustion is also compared with another similar technique, the Rate-Controlled Constrained-Equilibrium (RCCE). For the same number of representative variables, SQEM is found to provide a more accurate description.
Krishna, Honnur; Nagaraja, Padmarajaiah; Shivakumar, Anantharaman; Chamaraja, Nelligere A.; Aradhana, Narayan
2013-02-01
The intermolecular coupling of 2,5-dimethoxyaniline (DMA) as mediated electron transfer reaction in presence of H2O2 and peroxidase in acetate buffer of pH 4.2 resulting green colored product having maximum absorption at λmax = 740 nm was investigated by spectrophotometer. Under optimum conditions, linearity range for the quantification of H2O2 was 2.0-288.0 μM and for peroxidase were 0.59-9.46 and 0.443-9.46 nM by kinetic and fixed-time method, respectively. The catalytic efficiency and catalytic power were KeffD = 2.354 × 105 M-1 min-1 and KpowD = 4.59 × 10-4 min-1, respectively. From the plot of d(1/Do) vs d(1/Vo) and d(1/Ho) vs d(1/Vo), Michaelis-Menten constants for DMA and H2O2were found that KmD = 1458 μM and KmHO = 301 μM. Applicability of the method was tested for peroxidase activity in some plant extracts and compared with guaiacol/peroxidase system. Regarding superiority of the method, it is suggested that DMA/peroxidase system can be a better hydrogen donor for HRP assay than guaiacol system as evident from kinetic data.
Krishna, Honnur; Nagaraja, Padmarajaiah; Shivakumar, Anantharaman; Chamaraja, Nelligere A; Aradhana, Narayan
2013-02-01
The intermolecular coupling of 2,5-dimethoxyaniline (DMA) as mediated electron transfer reaction in presence of H(2)O(2) and peroxidase in acetate buffer of pH 4.2 resulting green colored product having maximum absorption at λ(max)=740 nm was investigated by spectrophotometer. Under optimum conditions, linearity range for the quantification of H(2)O(2) was 2.0-288.0 μM and for peroxidase were 0.59-9.46 and 0.443-9.46 nM by kinetic and fixed-time method, respectively. The catalytic efficiency and catalytic power were K(eff)(D)=2.354 × 10(5)M(-1)min(-1) and K(pow)(D)=4.59 × 10(-4)min(-1), respectively. From the plot of d(1/D(o)) vs d(1/V(o)) and d(1/H(o)) vs d(1/V(o)), Michaelis-Menten constants for DMA and H(2)O(2)were found that K(m)(D)=1,458 μM and [Formula: see text] =301 μM. Applicability of the method was tested for peroxidase activity in some plant extracts and compared with guaiacol/peroxidase system. Regarding superiority of the method, it is suggested that DMA/peroxidase system can be a better hydrogen donor for HRP assay than guaiacol system as evident from kinetic data.
Vosika, Z.; Mitić, V. V.; Vasić, A.; Lazović, G.; Matija, L.; Kocić, Lj. M.
2017-03-01
In this paper, Caputo based Michaelis-Menten kinetic model based on Time Scale Calculus (TSC) is proposed. The main reason for its consideration is a study of tumor cells population growth dynamics. In the particular case discrete-continuous time kinetics, Michaelis-Menten model is numerically treated, using a new algorithm proposed by authors, called multistep generalized difference transformation method (MSGDETM). In addition numerical simulations are performed and is shown that it represents the upgrade of the multi-step variant of generalized differential transformation method (MSGDTM). A possible conditions for its further development are discussed and possible experimental verification is described.
David eGomez
2015-06-01
Full Text Available Molecular crowding is ubiquitous within cells and affects many biological processes including protein-protein binding, enzyme activities and gene regulation. Here we revisit some generic effects of crowding using a combination of lattice simulations and reaction-diffusion simulations with the program ReaDDy. Specifically, we implement three reactions, simple binding, a diffusion-limited reaction and a reaction with Michaelis-Menten kinetics. Histograms of binding and unbinding times provide a detailed picture how crowding affects these reactions and how the separate effects of crowding on binding equilibrium and on diffusion act together. In addition, we discuss how crowding affects processes related to gene expression such as RNA polymerase-promoter binding and translation elongation.
Gómez-Uribe, Carlos A; Verghese, George C; Tzafriri, Abraham R
2008-12-28
Widely different time scales are common in systems of chemical reactions and can be exploited to obtain reduced models applicable to the time scales of interest. These reduced models enable more efficient computation and simplify analysis. A classic example is the irreversible enzymatic reaction, for which separation of time scales in a deterministic mass action kinetics model results in approximate rate laws for the slow dynamics, such as that of Michaelis-Menten. Recently, several methods have been developed for separation of slow and fast time scales in chemical master equation (CME) descriptions of stochastic chemical kinetics, yielding separate reduced CMEs for the slow variables and the fast variables. The paper begins by systematizing the preliminary step of identifying slow and fast variables in a chemical system from a specification of the slow and fast reactions in the system. The authors then present an enhanced time-scale-separation method that can extend the validity and improve the accuracy of existing methods by better accounting for slow reactions when equilibrating the fast subsystem. The resulting method is particularly accurate in systems such as enzymatic and protein interaction networks, where the rates of the slow reactions that modify the slow variables are not a function of the slow variables. The authors apply their methodology to the case of an irreversible enzymatic reaction and show that the resulting improvements in accuracy and validity are analogous to those obtained in the deterministic case by using the total quasi-steady-state approximation rather than the classical Michaelis-Menten. The other main contribution of this paper is to show how mass fluctuation kinetics models, which give approximate evolution equations for the means, variances, and covariances of the concentrations in a chemical system, can feed into time-scale-separation methods at a variety of stages.
Chaudhury, Srabanti; Cao, Jianshu; Sinitsyn, Nikolai A
2013-01-17
We consider a generic stochastic model of ion transport through a single channel with arbitrary internal structure and kinetic rates of transitions between internal states. This model is also applicable to describe kinetics of a class of enzymes in which turnover events correspond to conversion of substrate into product by a single enzyme molecule. We show that measurement of statistics of single molecule transition time through the channel contains only restricted information about internal structure of the channel. In particular, the most accessible flux fluctuation characteristics, such as the Poisson indicator (P) and the Fano factor (F) as function of solute concentration, depend only on three parameters in addition to the parameters of the Michaelis-Menten curve that characterizes average current through the channel. Nevertheless, measurement of Poisson indicator or Fano factor for such renewal processes can discriminate reactions with multiple intermediate steps as well as provide valuable information about the internal kinetic rates.
Raghvendra Shukla; Pradeep K Sharma; Kalyan K Banerji
2004-03-01
The oxidation of eleven amino acids by tetrabutylammonium tribromide (TBATB) in aqueous acetic acid results in the formation of the corresponding carbonyl compounds and ammonia. The reaction is first order with respect to TBATB. Michaelis-Menten type kinetics is observed with some of the amino acids while others exhibit second-order dependence. It failed to induce polymerization of acrylonitrile. The effect of solvent composition indicate that the rate of reaction increases with increase in the polarity of the medium. Addition of tetrabutylammonium chloride has no effect on the rate of oxidation. Addition of bromide ion causes decrease in the oxidation rate but only to a limiting value. The reaction is susceptible to both polar and steric effects of the substituents. A suitable mechanism has been proposed.
Effect of hydrodynamics on kinetics of gluconic acid enzymatic production in bubble column reactor
Ramezani Mohammad
2013-01-01
Full Text Available Oxidation of glucose by homogeneous glucose oxidase was performed in rectangular bubble column reactor at 40°C, ambient pressure and pH of 5.5 while superficial gas (oxygen velocity was varied in the homogeneous and transition regime in the range of 0.0014 - 0.0112 m s-1. Effect of superficial gas (oxygen velocity on the apparent reaction rate and its parameters was determined and it was observed that the apparent reaction rate on the basis of volume of the liquid increased with increasing the superficial gas (oxygen velocity. The apparent reaction rate was assumed to be in the form of Michaelis-Menten equation and its apparent kinetic parameters were evaluated by the nonlinear regression method.
Multiple alternative substrate kinetics.
Anderson, Vernon E
2015-11-01
The specificity of enzymes for their respective substrates has been a focal point of enzyme kinetics since the initial characterization of metabolic chemistry. Various processes to quantify an enzyme's specificity using kinetics have been utilized over the decades. Fersht's definition of the ratio kcat/Km for two different substrates as the "specificity constant" (ref [7]), based on the premise that the important specificity existed when the substrates were competing in the same reaction, has become a consensus standard for enzymes obeying Michaelis-Menten kinetics. The expansion of the theory for the determination of the relative specificity constants for a very large number of competing substrates, e.g. those present in a combinatorial library, in a single reaction mixture has been developed in this contribution. The ratio of kcat/Km for isotopologs has also become a standard in mechanistic enzymology where kinetic isotope effects have been measured by the development of internal competition experiments with extreme precision. This contribution extends the theory of kinetic isotope effects to internal competition between three isotopologs present at non-tracer concentrations in the same reaction mix. This article is part of a special issue titled: Enzyme Transition States from Theory and Experiment.
André Rosa Martins
2015-06-01
Full Text Available ResumoOs processos enzimáticos que seguem o modelo cinético de Michaelis-Menten foram estudados a partir de diferentes propostas para descrever a etapa de inibição reversível. As propostas de inibição foram comparadas a partir de um processo genérico, onde as constantes cinéticas receberam valores unitários e o valor numérico da concentração de substrato foi dez (10 vezes superior ao valor numérico da concentração de enzima. Para cada proposta de modelo de inibição foram obtidas soluções numéricas a partir de sistema não linear de equações diferenciais ordinárias, gerando gráficos que apresentaram, separadamente, a variação das concentrações da enzima, dos complexos enzimáticos, do substrato e do produto da reação. Foi obtido um modelo, dentre as propostas avaliadas, com desempenho indicando comportamento similar ao verificado no modelo clássico de Michaelis-Menten, onde o complexo de reação é rapidamente formado e, ao longo do processo, decai até tender a zero. Em contrapartida, diferentemente do modelo clássico, na nova proposta de modelo o efeito de inibição começa em zero e, ao longo do processo, tende ao valor nominal da concentração inicial da enzima. Tais respostas mostraram-se válidas para valores distintos de concentração de enzima e de tempo de processo, mostrando robustez e indicando uma tendência do somatório do substrato e do produto atingir o valor nominal da concentração inicial do substrato ao longo do tempo de processamento.
Tavares, Ana P M; Rodríguez, Oscar; Fernández-Fernández, María; Domínguez, Alberto; Moldes, Diego; Sanromán, María A; Macedo, Eugénia A
2013-03-01
Laccase was immobilized on modified silica carrier. The immobilization conditions, pH and enzyme concentration were optimized. Operational stability of 10 reaction cycles showed that immobilized laccase in buffer was stable, presenting an activity loss 80% was obtained in ionic liquid (IL) solution. Activity of immobilized laccase was maintained when incubated in IL. After 7days of incubation, immobilized laccase lost 30-50% of its initial activity. Immobilization also improved thermal stability of laccase in the presence of IL. Enzyme kinetics was modelled with Michaelis-Menten model. The Km value for free laccase increases significantly with the IL concentration. Slight differences were found in Vm for free enzyme. Unusual kinetic behaviour was obtained for immobilized laccase in IL: Both Vm and Km increased with IL concentration, resulting in increased catalytic efficiency of the immobilized enzyme in presence of IL.
The Kinetics of Enzyme Mixtures
Simon Brown
2014-03-01
Full Text Available Even purified enzyme preparations are often heterogeneous. For example, preparations of aspartate aminotransferase or cytochrome oxidase can consist of several different forms of the enzyme. For this reason we consider how different the kinetics of the reactions catalysed by a mixture of forms of an enzyme must be to provide some indication of the characteristics of the species present. Based on the standard Michaelis-Menten model, we show that if the Michaelis constants (Km of two isoforms differ by a factor of at least 20 the steady-state kinetics can be used to characterise the mixture. However, even if heterogeneity is reflected in the kinetic data, the proportions of the different forms of the enzyme cannot be estimated from the kinetic data alone. Consequently, the heterogeneity of enzyme preparations is rarely reflected in measurements of their steady-state kinetics unless the species present have significantly different kinetic properties. This has two implications: (1 it is difficult, but not impossible, to detect molecular heterogeneity using kinetic data and (2 even when it is possible, a considerable quantity of high quality data is required.
Christiansen, Nina Høj; Andersen, Frede Østergaard; Jensen, Henning S.
2016-01-01
with the affinity at low Pi concentrations (Vmax/Km) were determined by fitting data to the Michaelis-Menten kinetics. L. uniflora showed the highest Vmax/Km in the root tissue and the lowest Km. M. alterniflorum showed the highest and E. canadensis and P. perfoliatus the lowest Vmax/Km in leaf tissue. M...
Marcus, Leanne; Plumeri, Julia; Baker, Gary M.; Miller, Jon S.
2013-01-01
A previously published classroom teaching method for helping students visualize and understand Michaelis-Menten kinetics (19) was used as an anticipatory set with high school and middle school science teachers in an Illinois Math and Science Partnership Program. As part of the activity, the teachers were asked to collect data by replicating the…
Karakhim, S A
2012-01-01
The article is dedicated to analysis of equation which expresses apparent Michaelis constant K(m)app) of enzyme-catalysed reactions with activator participation by means of the substrate constant K(s) and rate constant of enzyme-substrate complex decomposition k(cat). It has been shown that although it is possible to record the mechanisms of such reactions as a scheme similar to Michaelis-Menten model and to derive equation of apparent Michaelis constant as K(m(app) = K(s) + k(cat)/k(1), but this approach cannot be used for investigation of all reactions with activator participation. The equation mentioned above is not obeyed in the general case, it may be true for some mechanisms only or under certain ratio of kinetic parameters of enzyme-catalysed reactions.
A Century of Enzyme Kinetic Analysis, 1913 to 2013
Johnson, Kenneth A.
2013-01-01
This review traces the history and logical progression of methods for quantitative analysis of enzyme kinetics from the 1913 Michaelis and Menten paper to the application of modern computational methods today. Following a brief review of methods for fitting steady state kinetic data, modern methods are highlighted for fitting full progress curve kinetics based upon numerical integration of rate equations, including a re-analysis of the original Michaelis-Menten full time course kinetic data. ...
Kinetics of atrazine, deisopropylatrazine, and deethylatrazine soil biodecomposers.
la Cecilia, Daniele; Maggi, Federico
2016-12-01
Twenty-two experimental sets were used to determine the biodecomposition parameters of atrazine (ATZ), deisopropylatrazine (DIATZ), and deethylatrazine (DEATZ) by inverse solution of Michaelis-Menten-Monod kinetic equations. The averaged maximum specific growth rate (μ), Michaelis-Menten half-saturation concentration (K), and biomass yield (Y) ranged between 2.00 × 10(-7) and 4.62 × 10(-5) 1/s, 3.43 × 10(-6) and 1.39 × 10(1) mol/L, and 1.20 × 10(2) and 2.98 × 10(5) mg-wet-Bio/mol-Subs, respectively. Parameters grouped by reaction pathway appeared clustered by aerobic and anaerobic catabolic breakdown, and were poorly correlated between each other (R ranging from -0.27 to 0.63, p ≥ 0.05). The tested bacterial strains decomposed ATZ, DIATZ, and DEATZ relatively rapidly in laboratory conditions, with an half-life (t1/2) ranging between 3 and 6 days. Numerical modeling showed that ATZ, DIATZ, and DEATZ half-lives were particularly sensitive to their initial concentration and the initial microbial biomass concentration. This study suggests that these bacterial strains can effectively be used or enhanced for bioremediation of agricultural soils where atrazine has been applied as long as these bacteria already coexist in or can integrate with the local soil microbial population at a given location. Copyright © 2016 Elsevier Ltd. All rights reserved.
Faure, Mathilde; Sotta, Bruno; Gamby, Jean
2014-08-15
Real time monitoring of electrolyte resistance changes during hydrolysis of 4-nitrophenylphosphate (pNPP) by alkaline phosphatase (ALP) bound on paramagnetic-beads was performed into a small dielectric channel. The reaction kinetic fit with a non-competitive substrate-inhibition equation. Michaelis-Menten apparent constant, KM(app), was determined as 0.33±0.06mM and the maximum apparent rate, Vmax(app) as 98±5pMs(-1). The detection limits were 15fM for ALP and 0.75mM for pNPP. This miniaturized device constitutes a powerful tool for analysis of interaction between ligands. Copyright © 2014 Elsevier B.V. All rights reserved.
Enzymatic Reactions in Microfluidic Devices
Ristenpart, W. D.; Wan, J.; Stone, H. A.
2008-11-01
We establish simple scaling laws for enzymatic reactions in microfluidic devices, and we demonstrate that kinetic parameters obtained conventionally using multiple stop-flow experiments may instead be extracted from a single microfluidic experiment. Introduction of an enzyme and substrate species in different arms of a Y-shaped channel allows the two species to diffuse across the parallel streamlines and to begin reacting. Measurements of the product concentration versus distance down the channel provide information about the kinetics of the reaction. In the limit where the enzyme is much larger (and thus less diffusive) than the substrate, we show that near the entrance the total amount of product (P) formed varies as a power law in the distance x down the channel. For reactions that follow standard Michaelis-Menten kinetics, the power law takes the form P˜(Vmax/Km) x^5/2, where Vmax and Km are the maximum reaction rate and Michaelis constant respectively. If a large excess of substrate is used, then Km is identified by measuring Vmax far downstream where the different species are completely mixed by diffusion. Numerical simulations and experiments using the bioluminescent reaction between luciferase and ATP as a model system are both shown to accord with the model. We discuss the implications for significant savings in the amount of time and enzyme required for determination of kinetic parameters.
The total quasi-steady-state approximation for fully competitive enzyme reactions
Pedersen, Morten Gram; Bersani, A.M.; Bersani, E.
2007-01-01
The validity of the Michaelis-Menten-Briggs-Haldane approximation for single enzyme reactions has recently been improved by the formalism of the total quasi-steady-state approximation. This approach is here extended to fully competitive systems, and a criterion for its validity is provided. We show...
Zebin Wang
2012-04-01
Full Text Available A response study and the effects of different parameters (pH, temperature and enzyme dose on kinetics of isolated soy protein hydrolysis by a trypsin-like endopeptidase (TL1 were conducted. Degree of hydrolysis (%DH data varied at different times under different hydrolysis conditions. Fitting the kinetics data to Michaelis-Menten kinetics model did not result in reasonable kinetic parameters, which implied that Michaelis-Menten kinetics was invalid for such a hydrolysis process. A kinetics model proposed by (Gonzalez-Tello, Camacho, Jurado, Paez, & Guadix, 1994 was found to fit the kinetics curve well and resulted in acceptable model parameters. A simple simulation example was performed to demonstrate the concept of how the kinetics equation could be applied in process engineering.
Sims, Paul A.
2009-01-01
The King-Altman method of deriving rate equations for enzymatic reactions is applied to the derivation of the Michaelis-Menten equation, along with an explanation for how (or why) the King-Altman method works in this case. The slightly more complicated cases of competitive inhibition and a two-substrate enzyme-catalyzed reaction are then treated…
Sims, Paul A.
2009-01-01
The King-Altman method of deriving rate equations for enzymatic reactions is applied to the derivation of the Michaelis-Menten equation, along with an explanation for how (or why) the King-Altman method works in this case. The slightly more complicated cases of competitive inhibition and a two-substrate enzyme-catalyzed reaction are then treated…
Chemical kinetics of gas reactions
Kondrat'Ev, V N
2013-01-01
Chemical Kinetics of Gas Reactions explores the advances in gas kinetics and thermal, photochemical, electrical discharge, and radiation chemical reactions. This book is composed of 10 chapters, and begins with the presentation of general kinetic rules for simple and complex chemical reactions. The next chapters deal with the experimental methods for evaluating chemical reaction mechanisms and some theories of elementary chemical processes. These topics are followed by discussions on certain class of chemical reactions, including unimolecular, bimolecular, and termolecular reactions. The rema
Enzyme kinetics of conjugating enzymes: PAPS sulfotransferase.
James, Margaret O
2014-01-01
The sulfotransferase (SULT) enzymes catalyze the formation of sulfate esters or sulfamates from substrates that contain hydroxy or amine groups, utilizing 3'-phosphoadenosyl-5'-phosphosulfate (PAPS) as the donor of the sulfonic group. The rate of product formation depends on the concentrations of PAPS and substrate as well as the sulfotransferase enzyme; thus, if PAPS is held constant while varying substrate concentration (or vice versa), the kinetic constants derived are apparent constants. When studied over a narrow range of substrate concentrations, classic Michaelis-Menten kinetics can be observed with many SULT enzymes and most substrates. Some SULT enzymes exhibit positive or negative cooperativity during conversion of substrate to product, and the kinetics fit the Hill plot. A characteristic feature of most sulfotransferase-catalyzed reactions is that, when studied over a wide range of substrate concentrations, the rate of product formation initially increases as substrate concentration increases, then decreases at high substrate concentrations, i.e., they exhibit substrate inhibition or partial substrate inhibition. This chapter gives an introduction to sulfotransferases, including a historical note, the nomenclature, a description of the function of SULTs with different types of substrates, presentation of examples of enzyme kinetics with SULTs, and a discussion of what is known about mechanisms of substrate inhibition in the sulfotransferases.
2015-01-01
his chapter predicts the specific rates of reaction by means of a mathematical expression, the kinetics of the reaction. This expression can be derived through a mechanistic interpretation of an enzymatically catalyzed reaction, but it is essentially of empirical nature for cell reactions....... The models can be used in mass balances for design of processes under process conditions not yet studied experimentally. The value of the predictive kinetic model depends on the quality of the experimental data on which the model is based, and well-founded kinetic models for enzyme reactions have...... a considerable predictive power. This is also true for cell reaction models, when the model is used in its proper context. The chapter first discusses the kinetics for enzymatically catalyzed reactions (“enzyme reactions”). The kinetics can be derived from a mechanistic model. Then, the chapter derives empirical...
Novel investigation of enzymatic biodiesel reaction by isothermal calorimetry
Sotoft, Lene Fjerbaek, E-mail: lfj@kbm.sdu.dk [Institute of Chemical Engineering, Biotechnology and Environmental Technology, University of Southern Denmark, Campusvej 55, DK-5230 Odense M (Denmark); Westh, Peter [Department of Life Science and Chemistry, Roskilde University, PO Box 260, DK-4000 Roskilde (Denmark); Christensen, Knud V.; Norddahl, Birgir [Institute of Chemical Engineering, Biotechnology and Environmental Technology, University of Southern Denmark, Campusvej 55, DK-5230 Odense M (Denmark)
2010-03-30
Isothermal calorimetry (ITC) was used to investigate solvent-free enzymatic biodiesel production. The transesterification of rapeseed oil with methanol and ethanol was catalyzed by immobilized lipase Novozym 435 at 40 {sup o}C. The aim of the study was to determine reaction enthalpy for the enzymatic transesterification and to elucidate the mass transfer and energetic processes taking place. Based on the measured enthalpy and composition change in the system, the heat of reaction at 40 {sup o}C for the two systems was determined as -9.8 {+-} 0.9 kJ/mole biodiesel formed from rapeseed oil and methanol, and -9.3 {+-} 0.7 kJ/mole when rapeseed oil and ethanol was used. Simple Michaelis-Menten kinetics was not an appropriate choice for describing the kinetics of this heterogeneous system. The experiments demonstrated the possibility of investigating complex reaction mixtures using ITC. Although it is possible to determine thermodynamic properties such as reaction enthalpy and reaction rate, the difficulty in actually measuring the true non-mass-transfer-limited reaction kinetics is exposed by the high time resolution of ITC.
Enzyme kinetics: the whole picture reveals hidden meanings.
Pinto, Maria F; Estevinho, Berta N; Crespo, Rosa; Rocha, Fernando A; Damas, Ana M; Martins, Pedro M
2015-06-01
The methodology adopted by Michaelis and Menten in 1913 is still routinely used to characterize the catalytic power and selectivity of enzymes. These kinetic measurements must be performed soon after the purified enzyme is mixed with a large excess of substrate. Other time scales and solution compositions are no less physiologically relevant, but fall outside the range of applicability of the classical formalism. Here we show that the complete picture of an enzyme's mode of function is critically obscured by the limited scope of conventional kinetic analysis, even in the simplest case of a single active site without inhibition. This picture is now unveiled in a mathematically closed form that remains valid over the reaction time for all combinations of enzyme/substrate concentrations and rate constants. Algebraic simplicity is maintained in the new formalism when stationary reaction phases are considered. By achieving this century-old objective, the otherwise hidden role of the reversible binding step is revealed and atypical kinetic profiles are explained. Most singular kinetic behaviors are identified in a critical region of conditions that coincide with typical cell conditions. Because it is not covered by the Michaelis-Menten model, the critical region has been missed until now by low- and high-throughput screenings of new drugs. New possibilities are therefore raised for novel and once-promising inhibitors to therapeutically target enzymes.
Estimating the turnover number in enzyme kinetic reactions using transient and stationary state data
Sibel Uludag-Demirer
2009-12-01
Full Text Available Substrate and product concentration data obtained by simulating enzyme-substrate reaction rate equations were used to test two proposed kinetic rate constant estimation techniques in this study. In the first technique, the turnover number, k3, was calculated using early transient time domain data, which are difficult to obtain experimentally. The technique used an iterative approach to calculate k3 with a pair of data and the value of k3 could be retrieved with 35% error. The second technique calculated k3 using stationary domain data and the value of k3 could be retrieved with less than 5% error. This second technique also offered internal consistency in the calculation of k3 by calculating k3 both from the intercept and the slope of the linear plot derived in this study. A series of sensitivity analyses was conducted to understand the robustness of the second technique in estimating k3 from simulated data to the changes in the reaction rate constants (k1, k2, and k3 and the initial concentration of enzyme used for simulation. It was found that the second technique generally worked well in the estimation of k3 except for the simulated data for fast substrate conversions such as in the large k3 and [E]0 cases . This latter method, thus, shows promise for the use of late time experimental substrate/product concentration data to obtain k3. Exclusively using late time data avoids the need for difficult and expensive rapid early time measurement techniques for estimating k3. Once a reasonable estimate for k3 is obtained, the initial enzyme value can easily be determined from the maximum velocity constant established from fitting the Michaelis-Menten or Briggs-Haldane equations to substrate and product stationary state domain (late time data. While the first technique can estimate k3 with only one point in the transient domain, it is suggested that the second method generally be favored since it only requires late-time stationary domain data and
Michael E.G. Lyons
2003-01-01
Full Text Available A detailed kinetic analysis of the pertinent physical processes underlying the operation of enzyme electrodes immobilized within alkane thiol self assembled monolayers is developed. These electrodes utilize a soluble mediator, which partitions into the monolayer, regenerates the active catalytic form of the enzyme and is re-oxidized at the underlying support electrode surface giving rise to a current which reflects kinetic events at the enzyme surface. Both the enzyme/substrate and enzyme mediator kinetics have been quantified fully in terms of a ping-pong mechanism for the former and Michaelis-Menten kinetics for the latter. The effect of substrate and mediator diffusion in solution have also been specifically considered and the latter processes have been shown to result in a complex expression for the reaction flux. Four limiting kinetic cases have been enumerated and simple expressions for the reaction flux in each of these rate limiting situations have been developed. Kinetic case diagrams have been presented as an aid to mechanistic diagnosis. The complicating effects of diffusive loss of reduced mediator from the enzyme layer have also been examined and the relation between the observed flux corresponding to reduced mediator oxidation at the support electrode and the substrate reaction flux in the enzyme layer have been quantified in terms of an efficiency factor. Results extracted from recently published practical realizations of immobilized monolayer enzyme systems have been discussed in the context of the proposed model analysis.
Optimizing the Electron Transfer Reactions at the Cathode of Microbial Fuel Cells
2015-05-15
intact bacterium conformed to the Michaelis - Menten formalism. The reduced intracellular red cytochrome represented the Michaelis complex whose...expressed spectrally different biomolecules that were redox-active during aerobic respiration on iron. In all six cases, compelling kinetic evidence...that of the electro- chemically reduced cytochrome observed in the presence of Fe(II). The kinetics of aerobic respiration on soluble iron by the
Kinetics of Papain: An Introductory Biochemistry Laboratory Experiment
Cornely, Kathleen; Crespo, Eric; Earley, Michael; Kloter, Rachel; Levesque, Aime; Pickering, Mary
1999-05-01
Enzyme kinetics experiments are popular in the undergraduate laboratory. These experiments have pedagogic value because they reinforce the concepts of Michaelis-Menten kinetics covered in the lecture portion of the course and give students the experience of calculating kinetic constants from data they themselves have generated. In this experiment, we investigate the kinetics of the thiol protease papain. The source of the papain is commercially available papaya latex. A specific substrate, Na-benzoyl-arginine-p-nitroanilide (BAPNA), is used, which takes advantage of the fact that papain interacts with a phenylalanine residue two amino acids away from the peptide bond cleaved. Upon hydrolysis by papain, a bright yellow product is released, p-nitroaniline. This allows the reaction to be monitored spectrophotometrically by measuring the rate of formation of the p-nitroaniline product as a function of the increase in absorbance of the solution at the lmax of p-nitroaniline (400 nm) over time at various substrate concentrations. These data are used to plot a Lineweaver-Burk plot from which the vmax and KM are obtained. If time permits, students carry out additional investigations in which e of p-nitroaniline is measured, the enzyme solution protein concentration is measured, the enzyme purity is evaluated by SDS-PAGE, and a pH-rate profile is constructed from experimental data.
彭尚; 孙丽霞; 熊珍爱; 周利琴; 兰雄雕; 孙建华; 童张法; 廖丹葵
2016-01-01
采用等温滴定量热法(ITC)测定猪肺血管紧张素转化酶（angiotensin converting enzyme，ACE）催化水解其体外模拟底物马尿酰-组氨酰-亮氨酸（Hip-His-Leu，HHL）反应的热动力学参数，考察了温度对动力学参数的影响。结果表明，该反应的摩尔水解焓ΔHhydr为正值，是吸热反应，且随温度升高ΔHhydr增大，等压比热容 cp为0.2126kJ/(mol·K)；ACE 催化 HHL 的水解反应符合 Michaelis-Menten 机理，在实验温度范围内（298.15～313.15K），米氏常数Km随温度升高而减小，催化常数kcat随温度的升高先增大后减少，在308.15K时达到最大值2.534s−1。将该法与传统的初始速率法进行比较，传统法存在的局限性使测得的 Km相对偏大。同时使用 ITC结合动力学分析测得ACE抑制剂药物依那普利拉为竞争性抑制剂，抑制常数KI为12.1 nmol/L，与文献比较证明该法可用于抑制剂类型的判断，是一种开发 ACE 抑制剂的新方法。应用该方法确定活性多肽Arg-Tyr-Leu-Gly-Tyr（RY-5)为非竞争性抑制剂，抑制常数KI为1.0μmol/L。%Thermodynamic and kinetic parameters of angiotensin converting enzyme(ACE)catalyzed hydrolysis of simulating substrate Hippuryl-Histidyl-Leucine(HHL)in vitro were determined by isothermal titration calorimetry(ITC). The effect of temperature on kinetic parameters was investigated; the results showed that the ACE-catalyzed reaction was endothermic with a small constant pressure specific heat capacity [cp=0.2126kJ/(mol·K)]. The value of molar hydrolysis enthalpyΔHhydrwas positive and increased as temperature rose. The reaction mechanism was in accordance with the Michaelis-Menten model in the temperature range(298.15—313.15K);the effect of temperature on the Michaelis constant(Km)was negative,while catalytic constant(kcat)first increased then decreased with the increase of temperature,reaching the maximum value of 2.534s−1 at 308.15K. Initial rate
Goudar, Chetan T
2011-10-01
We have identified an error in the published integral form of the modified Michaelis-Menten equation that accounts for endogenous substrate production. The correct solution is presented and the error in both the substrate concentration, S, and the kinetic parameters Vm , Km , and R resulting from the incorrect solution was characterized. The incorrect integral form resulted in substrate concentration errors as high as 50% resulting in 7-50% error in kinetic parameter estimates. To better reflect experimental scenarios, noise containing substrate depletion data were analyzed by both the incorrect and correct integral equations. While both equations resulted in identical fits to substrate depletion data, the final estimates of Vm , Km , and R were different and Km and R estimates from the incorrect integral equation deviated substantially from the actual values. Another observation was that at R = 0, the incorrect integral equation reduced to the correct form of the Michaelis-Menten equation. We believe this combination of excellent fits to experimental data, albeit with incorrect kinetic parameter estimates, and the reduction to the Michaelis-Menten equation at R = 0 is primarily responsible for the incorrectness to go unnoticed. However, the resulting error in kinetic parameter estimates will lead to incorrect biological interpretation and we urge the use of the correct integral form presented in this study.
Das, Biswajit; Gangopadhyay, Gautam, E-mail: gautam@bose.res.in [S. N. Bose National Centre For Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700 098 (India); Banerjee, Kinshuk [Department of Chemistry, University of Calcutta, 92 A.P.C. Road, Kolkata 700 009 (India)
2013-12-28
In this work, we develop an approach to nonequilibrium thermodynamics of an open chemical reaction network in terms of the elementary reaction propensities. The method is akin to the microscopic formulation of the dissipation function in terms of the Kullback-Leibler distance of phase space trajectories in Hamiltonian system. The formalism is applied to a single oligomeric enzyme kinetics at chemiostatic condition that leads the reaction system to a nonequilibrium steady state, characterized by a positive total entropy production rate. Analytical expressions are derived, relating the individual reaction contributions towards the total entropy production rate with experimentally measurable reaction velocity. Taking a real case of Escherichia coli β-galactosidase enzyme obeying Michaelis-Menten kinetics, we thoroughly analyze the temporal as well as the steady state behavior of various thermodynamic quantities for each elementary reaction. This gives a useful insight in the relative magnitudes of various energy terms and the dissipated heat to sustain a steady state of the reaction system operating far-from-equilibrium. It is also observed that, the reaction is entropy-driven at low substrate concentration and becomes energy-driven as the substrate concentration rises.
Das, Biswajit; Banerjee, Kinshuk; Gangopadhyay, Gautam
2013-12-28
In this work, we develop an approach to nonequilibrium thermodynamics of an open chemical reaction network in terms of the elementary reaction propensities. The method is akin to the microscopic formulation of the dissipation function in terms of the Kullback-Leibler distance of phase space trajectories in Hamiltonian system. The formalism is applied to a single oligomeric enzyme kinetics at chemiostatic condition that leads the reaction system to a nonequilibrium steady state, characterized by a positive total entropy production rate. Analytical expressions are derived, relating the individual reaction contributions towards the total entropy production rate with experimentally measurable reaction velocity. Taking a real case of Escherichia coli β-galactosidase enzyme obeying Michaelis-Menten kinetics, we thoroughly analyze the temporal as well as the steady state behavior of various thermodynamic quantities for each elementary reaction. This gives a useful insight in the relative magnitudes of various energy terms and the dissipated heat to sustain a steady state of the reaction system operating far-from-equilibrium. It is also observed that, the reaction is entropy-driven at low substrate concentration and becomes energy-driven as the substrate concentration rises.
R. Ramachandrappa
2013-01-01
Full Text Available A kinetic study on RuCl3-catalysed oxidation of levocarnitine (LC by sodium N-bromo-p-toluenesulphonamide or bromamine-T (BAT has been carried out in HCl medium at 303 K. The reaction rate shows a first order dependence on [BAT]0 and fractional order with respect to both [LC]0 and [H+]. Addition of the reaction product, p-toluenesulphonamide, retards the rate. The addition of RuCl3 and chloride ions to the reaction mixture shows an increase in the rate of the reaction. The dielectric effect is positive. The variation of ionic strength of the medium has no significant effect on the rate of the reaction. The reaction fails to initiate polymerization of acrylamide. Michaelis-Menten type of kinetics has been proposed. Thermodynamic parameters have been computed from Arrhenius plot by studying the reaction at different temperatures. The reaction stoichiometry and oxidation products were identified. Based on the experimental observations a suitable mechanism was proposed and rate law deduced.
Stone, Andrew N; Mackenzie, Peter I; Galetin, Aleksandra; Houston, J Brian; Miners, John O
2003-09-01
Morphine elimination involves UDP-glucuronosyltransferase (UGT) catalyzed conjugation with glucuronic acid to form morphine 3- and 6-glucuronides (M3G and M6G, respectively). It has been proposed that UGT2B7 is the major enzyme involved in these reactions, but there is evidence to suggest that other isoforms also catalyze morphine glucuronidation in man. Thus, we have characterized the selectivity and kinetics of M3G and M6G formation by recombinant human UGTs. UGT 1A1, 1A3, 1A6, 1A8, 1A9, 1A10, and 2B7 all catalyzed M3G formation, but only UGT2B7 formed M6G. The kinetics of M3G formation by the UGT1A family isoforms was consistent with a single enzyme Michaelis-Menten model, with apparent Km values ranging from 2.6 to 37.4 mM. In contrast, M3G and M6G formation by UGT2B7 exhibited atypical kinetics. The atypical kinetics may be described by a model with high- and low-affinity Km values (0.42 and 8.3 mM for M3G, and 0.97 and 7.4 mM for M6G) from fitting to a biphasic Michaelis-Menten model. However, a multisite model with an interaction between two identical binding sites in a negative cooperative manner provides a more realistic approach to modeling these data. According to this model, the respective binding affinities (Ks) for M3G and M6G were 1.76 and 1.41 mM, respectively. These data suggest that M6G formation may be used as a selective probe for UGT2B7 activity, and morphine glucuronidation by UGT2B7 appears to involve the simultaneous binding of two substrate molecules, highlighting the need for careful analysis of morphine glucuronidation kinetics in vitro.
DRAGOMIRESCU MONICA
2007-01-01
Full Text Available Robust immobilization techniques that preserve the activity of biomolecules havemany potential applications. In recent years, a number of new bioimobilisationmethods in sol-gel-derived materials were reported. The interactions between thebiomolecule and the inorganic material determine the degree to which thebiomolecule retains its native properties. The newer technological developments inthe field of immobilized biocatalysts can offer the possibility of a wider and moreeconomical exploitation of biocatalysts in biological applications, food and feedindustry, medicine, and in the development of bioprocess monitoring devices, like thebiosensors.The aim of this study was to obtain immobilized enzymatic preparations by methodswhich affect enzyme conformations and kinetic parameters as less as possible. Weimmobilized the enzymatic preparation with protease activity produced by a Bacilluslicheniformis B 40 local strain by physical bonding on ceramics and entrapment intosol-gel-derived glasses obtained from tetraethyl orthosilicate (TEOS, deposited inthin layer on a ceramic support (entrapment/deposition. Both physically adsorbedand entrapped/deposited enzymes follow Michaelis-Menten kinetics, similar with thesoluble enzyme. In the case of immobilized enzymes, the apparent Michaelisconstant, Km, was greater than that of the native one, as it was expected. The kineticparameters indicate that the enzymatic preparations adsorbed on ceramic supportand entrapped/deposited show less affinity for the substrate, Km being 1.3 and 2.1times higher than that of the native enzyme, respectively. The maximum velocityincreased also by 3.5 and 7.9 times respectively, compared with the free counterpart(according to Lineweaver-Burk linearization.
Valencia, Pedro L; Astudillo-Castro, Carolina; Gajardo, Diego; Flores, Sebastián
2017-04-01
We provide initial rate data from enzymatic reaction experiments and tis processing to estimate the kinetic parameters from the substrate uncompetitive inhibition equation using the median method published by Eisenthal and Cornish-Bowden (Cornish-Bowden and Eisenthal, 1974; Eisenthal and Cornish-Bowden, 1974). The method was denominated the direct linear plot and consists in the calculation of the median from a dataset of kinetic parameters Vmax and Km from the Michaelis-Menten equation. In this opportunity we present the procedure to applicate the direct linear plot to the substrate uncompetitive inhibition equation; a three-parameter equation. The median method is characterized for its robustness and its insensibility to outlier. The calculations are presented in an Excel datasheet and a computational algorithm was developed in the free software Python. The kinetic parameters of the substrate uncompetitive inhibition equation Vmax , Km and Ks were calculated using three experimental points from the dataset formed by 13 experimental points. All the 286 combinations were calculated. The dataset of kinetic parameters resulting from this combinatorial was used to calculate the median which corresponds to the statistic estimator of the real kinetic parameters. A comparative statistical analyses between the median method and the least squares was published in Valencia et al. [3].
Cardoso, Franciane Pinheiro; Aquino Neto, Sidney; Ciancaglini, Pietro; de Andrade, Adalgisa R
2012-08-01
The kinetic behavior of the enzyme laccase in solution and immobilized onto carbon platforms using poly(amido amine) (PAMAM) dendrimers has been investigated. The results with the immobilized enzymes have demonstrated that almost ten times more enzyme on the carbon support is required for satisfactory kinetic rates to be achieved. Furthermore, the study as a function of the substrate concentration revealed that the kinetic behavior of the enzyme in solution fits the Michaelis-Menten model. However, when the enzyme is immobilized onto the carbon surface, the catalyzed reaction follows a particular kinetic behavior with apparent positive cooperativity. The highest activity with laccase (in solution or immobilized) is achieved around pH 4.5, and the substrate conversion rate clearly diminishes with rising pH. The optimum temperature lies around 60 °C. The enzyme displays good catalytic activity in a wide range of pH and temperature values. The stability tests evidenced that there is no appreciable reduction in the enzymatic activity after immobilization within the first 30 days. Taking into account both the kinetic and stability tests, one can infer that the use of PAMAM dendrimers seems to be a very attractive approach for the immobilization of enzymes, as well as a feasible and useful methodology for the anchoring of enzymes with potential application in many biotechnological areas.
孔俊豪; 杨秀芳; 涂云飞; 孙庆磊; 陈小强
2011-01-01
The polyphenol oxidase activity of cryopreservation fresh tea leaves was determined by spectrophotometric method. The influence of main factors, such as substrate concentration, system pH and temperature on catalytic activities of PPO were investigated. The results showed that, the optimum pH and temperature for the enzymatic reaction was 4.6~5.0 and 35~60 ℃, respectively .The Michaelis-Menten equation of PPO from cryopreservation fresh tea leaves was established, accordingly,1/v=1.168 8/[S]+3.083 3, by which the kinetic parameters obtained were as follow: Km=0.378 mol/L,vmax=0.324 U /min.%采用分光光度法对冻存处理的茶树鲜叶的多酚氧化酶(PPO)进行了活性测定,研究了底物浓度、pH值及温度对冻存茶鲜叶PPO活性的影响,建立了茶树鲜叶冻存-萎凋过程的反应动力学方程.结果表明,冻存茶鲜叶PPO酶活的最适条件为:pH值介于4.6～5.0之间,温度35～60℃.由Michelis-Menten方程1/v=1.1688/[S]+3.083 3,得到的动力学参数为:Km=0.378mol/L,vmax=0.324U/min.
Reaction kinetics of polybutylene terephthalate polycondensation reaction
Darda, P. J.; Hogendoorn, J. A.; Versteeg, G. F.; Souren, F.
2005-01-01
The kinetics of the forward polycondensation reaction of polybutylene terephthalate (PBT) has been investigated using thermogravimetric analysis (TGA). PBT - prepolymer with an initial degree of polymerization of 5.5 was used as starting material. The PBT prepolymer was prepared from dimethyl tereph
Savic, Sasa; Vojinovic, Katarina; Milenkovic, Sanja; Smelcerovic, Andrija; Lamshoeft, Marc; Petronijevic, Zivomir
2013-12-15
Flavonoid oxidation is important issue in food processing and quality. The kinetic mechanism of enzymatic oxidation of rutin by horseradish peroxidase (HRP) was studied. Rutin oxidation reaction was followed by recording of spectral changes over the time at 360 nm. The studied oxidation is mostly enzymatic and less part non-enzymatic. The reaction with HRP has a higher rate compared with the reaction without of HRP, whereby is part of non-enzymatic reaction about 10% of the total reaction. Kinetic parameters were determined from graphics of linear Michaelis-Menten equation, and it was found that investigated reactions of rutin oxidation by HRP take place in a ping-pong kinetic mechanism. High resolution HPLC-MS analysis of the mixture of oxidized products of rutin revealed the presence of rutin dimer. Because of widely distribution of rutin as well as presence of peroxidases and hydrogen peroxide in fresh foods identification of this enzymatic modification product can be beneficial for foods quality and safety.
Complete integrability of information processing by biochemical reactions
Agliari, Elena; Barra, Adriano; Dello Schiavo, Lorenzo; Moro, Antonio
2016-11-01
Statistical mechanics provides an effective framework to investigate information processing in biochemical reactions. Within such framework far-reaching analogies are established among (anti-) cooperative collective behaviors in chemical kinetics, (anti-)ferromagnetic spin models in statistical mechanics and operational amplifiers/flip-flops in cybernetics. The underlying modeling - based on spin systems - has been proved to be accurate for a wide class of systems matching classical (e.g. Michaelis-Menten, Hill, Adair) scenarios in the infinite-size approximation. However, the current research in biochemical information processing has been focusing on systems involving a relatively small number of units, where this approximation is no longer valid. Here we show that the whole statistical mechanical description of reaction kinetics can be re-formulated via a mechanical analogy - based on completely integrable hydrodynamic-type systems of PDEs - which provides explicit finite-size solutions, matching recently investigated phenomena (e.g. noise-induced cooperativity, stochastic bi-stability, quorum sensing). The resulting picture, successfully tested against a broad spectrum of data, constitutes a neat rationale for a numerically effective and theoretically consistent description of collective behaviors in biochemical reactions.
吴梅芬; 王晓岗; 刘亚菲; 许新华
2015-01-01
The mechanism of a-chymotrypsin-catalyzed hydrolysis of 4-nitrophenyl trimethylacetate includes the following steps:the reversible enzyme-substrate binding and the enzyme acylation and enzyme deacylation.This mechanism is quite different from the conventional Michaelis-Menten mechanism for enzyme-catalyzed reactions.The corresponding kinetic parameters can be expressed precisely on the basis of chemical kinetics theory,such as Michaelis constant KM ,equilibrium constant K,catalytic rate constant kcat ,and the rate constants of the elementary reactions k 2 and k 3 .The reaction is carried out at 25 °C in a pH = 8.5 buffer of tris(hydroxymethyl)aminomethane (TRIS)by means of spectrophotometry.The kinetic curves are fitted linearly and non-linearly.The kinetic parameters are in agreement with the theoretical prediction.The enzyme product used in this experiment is cheap and the activity is stable. The experimental method is simple enough to be applied in undergraduate physical chemistry laboratory courses.As an ideal model of complex reaction,the experiment will help the students to enhance the understanding and knowledge of chemical kinetics theories.%通过严格的化学反应动力学推导,得到了a-糜蛋白酶催化三甲基乙酸对硝基苯酯水解反应相关的动力学参数的表达式,包括表观米氏常数 KM、酶-底物络合物稳定常数 K 、催化速率常数 kcat 、以及基元反应步骤速率常 k2和 k3等.实验在25℃,pH ＝8．5的三羟基氨基甲烷缓冲液中进行,用分光光度法测定反应的动力学曲线.数据经过非线性拟合和线性拟合,得到相关的动力学参数,该参数与理论预测一致.该实验酶制剂价格低廉,活性稳定,实验方法简单,可作为本科物理化学实验课程中复杂反应动力学测量的一个很好的实例,加深学生对化学反应动力学相关理论和概念的理解和掌握.
Konkoli, Zoran
2012-07-21
A novel computational method for modeling reaction noise characteristics has been suggested. The method can be classified as a moment closure method. The approach is based on the concept of correlation forms which are used for describing spatially extended many body problems where particle numbers change in space and time. In here, it was shown how the formalism of spatially extended correlation forms can be adapted to study well mixed reaction systems. Stochastic fluctuations in particle numbers are described by selectively capturing correlation effects up to the desired order, ξ. The method is referred to as the ξ-level Approximation Reaction Noise Estimator method (XARNES). For example, the ξ=1 description is equivalent to the mean field theory (first-order effects), the ξ=2 case corresponds to the previously developed PARNES method (pair effects), etc. The main idea is that inclusion of higher order correlation effects should lead to better (more accurate) results. Several models were used to test the method, two versions of a simple complex formation model, the Michaelis-Menten model of enzymatic kinetics, the smallest bistable reaction network, a gene expression network with negative feedback, and a random large network. It was explicitly demonstrated that increase in ξ indeed improves accuracy in all cases investigated. The approach has been implemented as automatic software using the Mathematica programming language. The user only needs to input reaction rates, stoichiometry coefficients, and the desired level of computation ξ.
Jaya Gosain; Pradeep K Sharma
2003-04-01
Kinetics of oxidation of five vicinal and four non-vicinal diols, and two of their monoethers, by tetrabutylammonium tribromide (TBATB) has been studied. The vicinal diols yield products arising out of glycol-bond fission, while the non-vicinal diols produce the hydroxycarbonyl compounds. The reaction is first-order with respect to TBATB. Michaelis-Menten type kinetics is observed with respect to diols. The reaction fails to induce the polymerization of acrylonitrile. There is no effect of tetrabutylammonium chloride on the reaction rate. The proposed reactive oxidizing species is the tribromide ion. The effect of solvent composition indicates that the rate increases with increase in the polarity of the solvent. The oxidation of [1,1,2,2-2H4] ethanediol shows the absence of any primary kinetic isotope effect. Values of solvent isotope effect, (H2O)/(D2O), at 288 K for the oxidation of ethanediol, propane-1,3-diol and 3-methoxybutan-1-ol are 3.41, 0.98 and 1.02 respectively. A mechanism involving a glycol-bond fission has been proposed for the oxidation of vicinal diols. Non-vicinal diols are oxidised by a hydride-transfer mechanism, as they are monohydric alcohols.
Moxley, Michael A; Beard, Daniel A; Bazil, Jason N
2016-02-05
Mammalian E3 is an essential mitochondrial enzyme responsible for catalyzing the terminal reaction in the oxidative catabolism of several metabolites. E3 is a key regulator of metabolic fuel selection as a component of the pyruvate dehydrogenase complex (PDHc). E3 regulates PDHc activity by altering the affinity of pyruvate dehydrogenase kinase, an inhibitor of the enzyme complex, through changes in reduction and acetylation state of lipoamide moieties set by the NAD(+)/NADH ratio. Thus, an accurate kinetic model of E3 is needed to predict overall mammalian PDHc activity. Here, we have combined numerous literature data sets and new equilibrium spectroscopic experiments with a multitude of independently collected forward and reverse steady-state kinetic assays using pig heart E3. The latter kinetic assays demonstrate a pH-dependent transition of NAD(+) activation to inhibition, shown here, to our knowledge, for the first time in a single consistent data set. Experimental data were analyzed to yield a thermodynamically constrained four-redox-state model of E3 that simulates pH-dependent activation/inhibition and active site redox states for various conditions. The developed model was used to determine substrate/product conditions that give maximal E3 rates and show that, due to non-Michaelis-Menten behavior, the maximal flux is different compared with the classically defined kcat.
马中良; 李艳利; 鲍真真; 王旻
2005-01-01
在生物化学试验中,酶的米氏常数的测定实验是经典的实验.通过Km 测定这一实验的改进,指导学生怎样认识和把握理论知识,并将之应用科学研究中.在生物化学实验教学中,注意提高学生的动手能力,提高解决问题和分析问题的能力,从而形成对待实验结果和教材的正确观点.
林中; 苏银法
2004-01-01
目的: 获得(一级并行)米氏消除药物静脉注射给药时的血药浓度近似解.方法: 根据四阶Runge-Kutta算法,采用Excel软件编写基于药动学参数的程序.结果:输出某周期或稳态任一次给药后的预期血药浓度.结论:方法操作简单,结果可靠,可作为(一级并行)米氏消除药物静脉注射给药时药动学方程的数值解法.
苏银法; 杜乐燕
2006-01-01
目的获得(一级并行)米氏消除药物血管外给药时的血药浓度近似值.方法根据四阶Runge-Kutta算法,采用Excel软件编写基于药动学参数的血药浓度近似解表格程序.结果通过实例演示,可以输出第n周期(或稳态)第s次血管外给药后每间隔0.005 h的预期血药浓度.结论该法是(一级并行)米氏消除药物血管外给药动力学方程的一种可靠的数值解法.
祁兵; 黄大贶
2003-01-01
@@ Michaelis-Menten消除动力学(下称米氏型消除)是非线性药物动力学中的重要部分.大量临床研究表明[1],呈药动学非线性特征的药物,尤有必要进行血药浓度监测.本文对静注多次给药情况下的稳态动力学特征进行了研究,得到了稳态浓度存在的必要条件及稳态浓度的精确表达式,为临床用药提供了理论依据.
Palai, Tapas; Mitra, Shubhrajyoti; Bhattacharya, Prashant K
2012-10-01
The enzymatic synthesis of galacto-oligosaccharides (GOS) from lactose was studied using commercial grade β-galactosidase (Biolacta FN5) from Bacillus circulans. The reaction was carried out under free enzyme condition varying initial lactose concentration (ILC: 55-525 g/L), enzyme concentration (0.05-1.575 g/L), temperature (30-50°C) and pH (5.0-6.0). Reaction mixture compositions were analyzed utilizing high performance liquid chromatography (HPLC). A maximum GOS formation of 39% (dry basis) was achieved at an ILC of 525 g/L converting 60% of the lactose fed. Tri-saccharides were the major types of GOS formed, accounting approximately 24%; whereas, tetra-saccharides and penta-saccharides account approximately 12% and 3%, respectively. Design correlation was developed in order to observe the quantitative effect of operating parameters on GOS yield. Further, based on Michaelis-Menten model, four-step reaction pathways were considered for simplistic understanding of the kinetics. Apart from predicting the reaction mixture composition, the approach also provided kinetic parameters though simulation using COPASI 4.7®. Excellent agreements were observed between simulated and experimental results.
Biphasic kinetic behavior of E. coli WrbA, an FMN-dependent NAD(PH:quinone oxidoreductase.
Iryna Kishko
Full Text Available The E. coli protein WrbA is an FMN-dependent NAD(PH:quinone oxidoreductase that has been implicated in oxidative defense. Three subunits of the tetrameric enzyme contribute to each of four identical, cavernous active sites that appear to accommodate NAD(PH or various quinones, but not simultaneously, suggesting an obligate tetramer with a ping-pong mechanism in which NAD departs before oxidized quinone binds. The present work was undertaken to evaluate these suggestions and to characterize the kinetic behavior of WrbA. Steady-state kinetics results reveal that WrbA conforms to a ping-pong mechanism with respect to the constancy of the apparent Vmax to Km ratio with substrate concentration. However, the competitive/non-competitive patterns of product inhibition, though consistent with the general class of bi-substrate reactions, do not exclude a minor contribution from additional forms of the enzyme. NMR results support the presence of additional enzyme forms. Docking and energy calculations find that electron-transfer-competent binding sites for NADH and benzoquinone present severe steric overlap, consistent with the ping-pong mechanism. Unexpectedly, plots of initial velocity as a function of either NADH or benzoquinone concentration present one or two Michaelis-Menten phases depending on the temperature at which the enzyme is held prior to assay. The effect of temperature is reversible, suggesting an intramolecular conformational process. WrbA shares these and other details of its kinetic behavior with mammalian DT-diaphorase, an FAD-dependent NAD(PH:quinone oxidoreductase. An extensive literature review reveals several other enzymes with two-plateau kinetic plots, but in no case has a molecular explanation been elucidated. Preliminary sedimentation velocity analysis of WrbA indicates a large shift in size of the multimer with temperature, suggesting that subunit assembly coupled to substrate binding may underlie the two-plateau behavior. An
Mihara, H; Kurihara, T; Yoshimura, T; Esaki, N
2000-04-01
We have purified three NifS homologs from Escherichia coli, CSD, CsdB, and IscS, that appear to be involved in iron-sulfur cluster formation and/or the biosynthesis of selenophosphate. All three homologs catalyze the elimination of Se and S from L-selenocysteine and L-cysteine, respectively, to form L-alanine. These pyridoxal 5'-phosphate enzymes were inactivated by abortive transamination, yielding pyruvate and a pyridoxamine 5'-phosphate form of the enzyme. The enzymes showed non-Michaelis-Menten behavior for L-selenocysteine and L-cysteine. When pyruvate was added, they showed Michaelis-Menten behavior for L-selenocysteine but not for L-cysteine. Pyruvate significantly enhanced the activity of CSD toward L-selenocysteine. Surprisingly, the enzyme activity toward L-cysteine was not increased as much by pyruvate, suggesting the presence of different rate-limiting steps or reaction mechanisms for L-cysteine desulfurization and the degradation of L-selenocysteine. We substituted Ala for each of Cys358 in CSD, Cys364 in CsdB, and Cys328 in IscS, residues that correspond to the catalytically essential Cys325 of Azotobacter vinelandii NifS. The enzyme activity toward L-cysteine was almost completely abolished by the mutations, whereas the activity toward L-selenocysteine was much less affected. This indicates that the reaction mechanism of L-cysteine desulfurization is different from that of L-selenocysteine decomposition, and that the conserved cysteine residues play a critical role only in L-cysteine desulfurization.
Sengupta, Avery; Dey, Tanmoy; Ghosh, Mahua; Ghosh, Jaydip; Ghosh, Santinath
2012-08-01
This study investigated the successful enzymatic production of furfuryl oleate and its detailed kinetic study by Michaelis-Menten model. Esterification of oleic acid and furfuryl alcohol by Candida antarctica lipase B (Novozym 435 preparation) in a solvent free system was studied in the present work at 1:1 molar ratio of furfuryl alcohol and oleic acid. About 99 % conversion (on the basis of oleic acid) has been achieved within 6 h at 5 % enzyme concentration. Ping-pong bi-bi mechanism (inhibition phenomenon taken into account) was applied to describe the ratios as a complex kinetic model. The kinetic parameters were determined using MATLAB language programme. The two initial rate constants KA and KB respectively were found out by different progress curves plotted with the help of MATLAB language programme. It was concluded from the results that furfuryl alcohol considerably inhibited the enzymatic reaction while oleic acid had negligible inhibitory effect. It was clearly seen that the initial rate was increased with the increase in the furfuryl alcohol concentration until 2 M/L after which there was a drop in the initial rate depicting the inhibitory effect of furfuryl alcohol. Surprisingly, it has been observed that addition of 0.1 mol of product activated the esterification reaction. Finally, the model was found to be statistically fitting well with the experimental data.
Analysis of kinetic reaction mechanisms
Turányi, Tamás
2014-01-01
Chemical processes in many fields of science and technology, including combustion, atmospheric chemistry, environmental modelling, process engineering, and systems biology, can be described by detailed reaction mechanisms consisting of numerous reaction steps. This book describes methods for the analysis of reaction mechanisms that are applicable in all these fields. Topics addressed include: how sensitivity and uncertainty analyses allow the calculation of the overall uncertainty of simulation results and the identification of the most important input parameters, the ways in which mechanisms can be reduced without losing important kinetic and dynamic detail, and the application of reduced models for more accurate engineering optimizations. This monograph is invaluable for researchers and engineers dealing with detailed reaction mechanisms, but is also useful for graduate students of related courses in chemistry, mechanical engineering, energy and environmental science and biology.
Combustion kinetics and reaction pathways
Klemm, R.B.; Sutherland, J.W. [Brookhaven National Laboratory, Upton, NY (United States)
1993-12-01
This project is focused on the fundamental chemistry of combustion. The overall objectives are to determine rate constants for elementary reactions and to elucidate the pathways of multichannel reactions. A multitechnique approach that features three independent experiments provides unique capabilities in performing reliable kinetic measurements over an exceptionally wide range in temperature, 300 to 2500 K. Recent kinetic work has focused on experimental studies and theoretical calculations of the methane dissociation system (CH{sub 4} + Ar {yields} CH{sub 3} + H + Ar and H + CH{sub 4} {yields} CH{sub 3} + H{sub 2}). Additionally, a discharge flow-photoionization mass spectrometer (DF-PIMS) experiment is used to determine branching fractions for multichannel reactions and to measure ionization thresholds of free radicals. Thus, these photoionization experiments generate data that are relevant to both reaction pathways studies (reaction dynamics) and fundamental thermochemical research. Two distinct advantages of performing PIMS with high intensity, tunable vacuum ultraviolet light at the National Synchrotron Light Source are high detection sensitivity and exceptional selectivity in monitoring radical species.
Kinetic study of enzymatic hydrolysis of potato starch
Óscar Fernando Castellanos Domínguez
2010-04-01
Full Text Available This article describes the kinetic study of potato starch enzymatic hydrolysis using soluble enzymes (Novo Nordisk. Different assays divided into four groups were used: reaction time (with which it was possible to reduce the 48-72 hour duration reported in the literature to 16 hours with comparable productivity levels; selecting the set of enzymes to be used (different types were evaluated - BAN and Termamyl as alfa-amylases during dextrinisation stage, and AMG, Promozyme and Fungamyl for sacarification reaction- identifying those presenting the best performance during hydrolysis. Reaction conditions were optimised for the process's two stages (destrinisation and sacarification. Enzyme dose, calcium cofactor concentration, pH, temperature and agitation speed were studied for the first stage. Enzyme ratio, pH and agitation speed were studied for sacarification; the latter parameter reported values having no antecedents in the literature (60 rpm and 30 rpm for first and second reactions, respectively. Michaelis Menten kinetics were calculated once conditions had been optimised, varying substrate from 10-50% P/V, obtaining km and Vmax kinetic parameters for each reaction. A kinetic model was found according to local working conditions which was able to explain potato starch conversion to glucose syrup, achieving 96 dextrose equivalents by the end of the reaction, being well within the maximum range reported in the literature (94-98. Laboratory equipment was constructed prior to carrying out assays which was able to reproduce and improve the conditions reported in the literature, making it a useful, reliable tool for use in assays returning good results.
A kinetic model for the penicillin biosynthetic pathway in
Nielsen, Jens; Jørgensen, Henrik
1996-01-01
A kinetic model for the first two steps in the penicillin biosynthetic pathway, i.e. the ACV synthetase (ACVS) and the isopenicillin N synthetase (IPNS) is proposed. The model is based on Michaelis-Menten type kinetics with non-competitive inhibition of the ACVS by ACV, and competitive inhibition...... of the IPNS by glutathione. The model predicted flux through the pathway corresponds well with the measured rate of penicillin biosynthesis. From the kinetic model the elasticity coefficients and the flux control coefficients are calculated throughout a fed-batch cultivation, and it is found...
Electrochemical evaluation of glutathione S-transferase kinetic parameters.
Enache, Teodor Adrian; Oliveira-Brett, Ana Maria
2015-02-01
Glutathione S-transferases (GSTs), are a family of enzymes belonging to the phase II metabolism that catalyse the formation of thioether conjugates between the endogenous tripeptide glutathione and xenobiotic compounds. The voltammetric behaviour of glutathione (GSH), 1-chloro-2,4-dinitrobenzene (CDNB) and glutathione S-transferase (GST), as well as the catalytic conjugation reaction of GSH to CDNB by GST was investigated at room temperature, T=298.15K (25°C), at pH6.5, for low concentration of substrates and enzyme, using differential pulse (DP) voltammetry at a glassy carbon electrode. Only GSH can be oxidized; a sensitivity of 0.14nA/μM and a LOD of 6.4μM were obtained. The GST kinetic parameter electrochemical evaluation, in relation to its substrates, GSH and CDNB, using reciprocal Michaelis-Menten and Lineweaver-Burk double reciprocal plots, was determined. A value of KM~100μM was obtained for either GSH or CDNB, and Vmax varied between 40 and 60μmol/min per mg of GST.
Probing the kinetics of quantum dot-based proteolytic sensors.
Díaz, Sebastián A; Malonoski, Anthony P; Susumu, Kimihiro; Hofele, Romina V; Oh, Eunkeu; Medintz, Igor L
2015-09-01
As an enzyme superfamily, proteases are rivaled only by kinases in terms of their abundance within the human genome. Two ratiometric quantum dot (QD) Förster resonance energy transfer-based sensors designed to monitor the activity of the proteolytic enzymes collagenase and elastase are investigated here. Given the unique material constraints of these sensing constructs, assays are realized utilizing excess enzyme and fixed substrate in progress curve format to yield enzyme specificity or k cat/K m ratios. The range of k cat/Km values derived is 0.5-1.1 mM(-1) s(-1) for the collagenase sensor and 3.7-4.2 mM(-1) s(-1) for the elastase sensor. Of greater interest is the observation that the elastase sensor can be well represented by the Michaelis-Menten model while the collagenase sensor cannot. The latter demonstrates increased specificity at higher peptide substrate/QD loading values and an apparent QD-caused reversible inhibition as the reaction progresses. Understanding the detailed kinetic mechanisms that underpin these types of sensors will be important especially for their further quantitative utilization.
Z. R. Yelebe
2014-03-01
Full Text Available This paper addresses the challenge of estimating various kinetic parameters for the design of an optimized enzyme catalysed batch bioreactor of high efficiency and yield. Mathematical models were developed to describe the batch reaction time in relation to the substrate, enzyme and product concentration. The results obtained from the plots generated were: 35.50gmol/l.hr for the velocity of reaction of the enzymes (Vmax, 0.10049hr-1 for the maximum specific growth rate (µmax 826.45gmol/l for the Michaelis-Menten constant (Km, 0.005402577 for maintenance coefficient (Ms, 10.104kgCx/kgCs for yield of cell weight per unit weight of substrate (Ycx/CS, 0.05436kgCp/kgCs for yield of product weight per unit weight of substrate utilized (Ycp/CS and 0.01416 for endogenous decay coefficient (Kd for the design of the batch biochemical reactor. Hence, they are useful parameters for predicting the most appropriate batch reaction conditions and the efficiency of the bioreactor. The mathematical model predictions showed that it can be considered as a good complimentary tool to real system since the simulation results of the mathematical model agrees with experimental data reported in literature.
Farazdaghi, Hadi
2011-02-01
Photosynthesis is the origin of oxygenic life on the planet, and its models are the core of all models of plant biology, agriculture, environmental quality and global climate change. A theory is presented here, based on single process biochemical reactions of Rubisco, recognizing that: In the light, Rubisco activase helps separate Rubisco from the stored ribulose-1,5-bisphosphate (RuBP), activates Rubisco with carbamylation and addition of Mg²(+), and then produces two products, in two steps: (Step 1) Reaction of Rubisco with RuBP produces a Rubisco-enediol complex, which is the carboxylase-oxygenase enzyme (Enco) and (Step 2) Enco captures CO₂ and/or O₂ and produces intermediate products leading to production and release of 3-phosphoglycerate (PGA) and Rubisco. PGA interactively controls (1) the carboxylation-oxygenation, (2) electron transport, and (3) triosephosphate pathway of the Calvin-Benson cycle that leads to the release of glucose and regeneration of RuBP. Initially, the total enzyme participates in the two steps of the reaction transitionally and its rate follows Michaelis-Menten kinetics. But, for a continuous steady state, Rubisco must be divided into two concurrently active segments for the two steps. This causes a deviation of the steady state from the transitional rate. Kinetic models are developed that integrate the transitional and the steady state reactions. They are tested and successfully validated with verifiable experimental data. The single-process theory is compared to the widely used two-process theory of Farquhar et al. (1980. Planta 149, 78-90), which assumes that the carboxylation rate is either Rubisco-limited at low CO₂ levels such as CO₂ compensation point, or RuBP regeneration-limited at high CO₂. Since the photosynthesis rate cannot increase beyond the two-process theory's Rubisco limit at the CO₂ compensation point, net photosynthesis cannot increase above zero in daylight, and since there is always respiration at
Jin, Jian; Ma, Haile; Qu, Wenjuan; Wang, Kai; Zhou, Cunshan; He, Ronghai; Luo, Lin; Owusu, John
2015-11-01
The effects of multi-frequency power ultrasound (MPU) pretreatment on the kinetics and thermodynamics of corn gluten meal (CGM) were investigated in this research. The apparent constant (KM), apparent break-down rate constant (kA), reaction rate constants (k), energy of activation (Ea), enthalpy of activation (ΔH), entropy of activation (ΔS) and Gibbs free energy of activation (ΔG) were determined by means of the Michaelis-Menten equation, first-order kinetics model, Arrhenius equation and transition state theory, respectively. The results showed that MPU pretreatment can accelerate the enzymolysis of CGM under different enzymolysis conditions, viz. substrate concentration, enzyme concentration, pH, and temperature. Kinetics analysis revealed that MPU pretreatment decreased the KM value by 26.1% and increased the kA value by 7.3%, indicating ultrasound pretreatment increased the affinity between enzyme and substrate. In addition, the values of k for ultrasound pretreatment were increased by 84.8%, 41.9%, 28.9%, and 18.8% at the temperature of 293, 303, 313 and 323 K, respectively. For the thermodynamic parameters, ultrasound decreased Ea, ΔH and ΔS by 23.0%, 24.3% and 25.3%, respectively, but ultrasound had little change in ΔG value in the temperature range of 293-323 K. In conclusion, MPU pretreatment could remarkably enhance the enzymolysis of CGM, and this method can be applied to protein proteolysis industry to produce peptides.
Kinetic studies on the inhibition of GABA-T by gamma-vinyl GABA and taurine.
Sulaiman, Saba A J; Suliman, Fakhr Eldin O; Barghouthi, Samira
2003-08-01
Gamma-aminobutyric acid transaminase (GABA-T, EC 2.6.1.19) is a pyridoxal phosphate (PLP) dependent enzyme that catalyzes the degradation of gamma-aminobutyric acid. The kinetics of this reaction are studied in vitro, both in the absence, and in the presence of two inhibitors: gamma-vinyl GABA (4-aminohex-5-enoic acid), and a natural product, taurine (ethylamine-2-sulfonic acid). A kinetic model that describes the transamination process is proposed. GABA-T from Pseudomonas fluorescens is inhibited by gamma-vinyl GABA and taurine at concentrations of 51.0 and 78.5 mM. Both inhibitors show competitive inhibition behavior when GABA is the substrate and the inhibition constant (Ki) values for gamma-vinyl GABA and taurine were found to be 26 +/- 3 mM and 68 +/- 7 mM respectively. The transamination process of alpha-ketoglutarate was not affected by the presence of gamma-vinyl GABA, whereas, taurine was a noncompetitive inhibitor of GABA-T when alpha-ketoglutarate was the substrate. The inhibition dissociation constant (Kii) for this system was found to be 96 +/- 10 mM. The Michaelis-Menten constant (Km) in the absence of inhibition, was found to be 0.79 +/- 0.11 mM, and 0.47 +/- 0.10 mM for GABA and alpha-ketoglutarate respectively.
Korla, Kalyani; Vadlakonda, Lakshmipathi; Mitra, Chanchal K
2015-01-01
In the present work, we have kinetically simulated two mitochondrial shuttles, malate-aspartate shuttle (used for transferring reducing equivalents) and citrate-pyruvate shuttle (used for transferring carbon skeletons). However, the functions of these shuttles are not limited to the points mentioned above, and they can be used in different arrangements to meet different cellular requirements. Both the shuttles are intricately associated with Krebs cycle through the metabolites involved. The study of this system of shuttles and Krebs cycle explores the response of the system in different metabolic environments. Here, we have simulated these subsets individually and then combined them to study the interactions among them and to bring out the dynamics of these pathways in focus. Four antiports and a pyruvate pump were modelled along with the metabolic reactions on both sides of the inner mitochondrial membrane. Michaelis-Menten approach was extended for deriving rate equations of every component of the system. Kinetic simulation was carried out using ordinary differential equation solver in GNU Octave. It was observed that all the components attained steady state, sooner or later, depending on the system conditions. Progress curves and phase plots were plotted to understand the steady state behaviour of the metabolites involved. A comparative analysis between experimental and simulated data show fair agreement thus validating the usefulness and applicability of the model.
Kinetics of heterogeneous catalytic reactions
Boudart, Michel
2014-01-01
This book is a critical account of the principles of the kinetics of heterogeneous catalytic reactions in the light of recent developments in surface science and catalysis science. Originally published in 1984. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase acc
Kinetics of Mn(II) oxidation by spores of the marine Bacillus sp. SG-1
Toyoda, Kazuhiro; Tebo, Bradley M.
2016-09-01
The kinetics of Mn(II) oxidation by spores of the marine Bacillus sp. SG-1 was measured under controlled conditions of the initial Mn(II) concentration, spore concentration, chemical speciation, pH, O2, and temperature. Mn(II) oxidation experiments were performed with spore concentrations ranging from 0.7 to 11 × 109 spores/L, a pH range from 5.8 to 8.1, temperatures between 4 and 58 °C, a range of dissolved oxygen from 2 to 270 μM, and initial Mn(II) concentrations from 1 to 200 μM. The Mn(II) oxidation rates were directly proportional to the spore concentrations over these ranges of concentration. The Mn(II) oxidation rate increased with increasing initial Mn(II) concentration to a critical concentration, as described by the Michaelis-Menten model (Km = ca. 3 μM). Whereas with starting Mn(II) concentrations above the critical concentration, the rate was almost constant in low ionic solution (I = 0.05, 0.08). At high ionic solution (I = 0.53, 0.68), the rate was inversely correlated with Mn(II) concentration. Increase in the Mn(II) oxidation rate with the dissolved oxygen concentration followed the Michaelis-Menten model (Km = 12-19 μM DO) in both a HEPES-buffered commercial drinking (soft) water and in artificial and natural seawater. Overall, our results suggest that the mass transport limitations of Mn(II) ions due to secondary Mn oxide products accumulating on the spores cause a significant decrease of the oxidation rate at higher initial Mn(II) concentration on a spore basis, as well as in more concentrated ionic solutions. The optimum pH for Mn(II) oxidation was approximately 7.0 in low ionic solutions (I = 0.08). The high rates at the alkaline side (pH > 7.5) may suggest a contribution by heterogeneous reactions on manganese bio-oxides. The effect of temperature on the Mn(II) oxidation rate was studied in three solutions (500 mM NaCl, ASW, NSW solutions). Thermal denaturation occurred at 58 °C and spore germination was evident at 40 °C in all three
Fernández-Fernández, María; Moldes, Diego; Domínguez, Alberto; Sanromán, M Ángeles; Tavares, Ana Paula M; Rodríguez, Oscar; Macedo, Eugénia A
2014-01-01
The use of ionic liquids (ILs) as reaction media for enzymatic reactions has increased their potential because they can improve enzyme activity and stability. Kinetic and stability properties of immobilized commercial laccase from Myceliophthora thermophila in the water-soluble IL 1-ethyl-3-methylimidazolium ethylsulfate ([emim][EtSO4 ]) have been studied and compared with free laccase. Laccase immobilization was carried out by covalent binding on glyoxyl-agarose beads. The immobilization yield was 100%, and the activity was totally recovered. The Michaelis-Menten model fitted well to the kinetic data of enzymatic oxidation of a model substrate in the presence of the IL [emim][EtSO4 ]. When concentration of the IL was augmented, the values of Vmax for free and immobilized laccases showed an increase and slight decrease, respectively. The laccase-glyoxyl-agarose derivative improved the laccase stability in comparison with the free laccase regarding the enzymatic inactivation in [emim][EtSO4 ]. The stability of both free and immobilized laccase was slightly affected by small amounts of IL (<50%). A high concentration of the IL (75%) produced a large inactivation of free laccase. However, immobilization prevented deactivation beyond 50%. Free and immobilized laccase showed a first-order thermal inactivation profile between 55 and 70°C in the presence of the IL [emim][EtSO4 ]. Finally, thermal stability was scarcely affected by the presence of the IL.
Enzyme Kinetics: A critique of the quasi-steady-state approximation
Bhattacharyya, Kamal
2013-01-01
The standard two-step model of homogeneous-catalyzed reactions had been theoretically analyzed at various levels of approximations from time to time. The primary aim was to check the validity of the quasi-steady-state approximation, and hence emergence of the Michaelis-Menten kinetics, with various substrate-enzyme ratios. But, conclusions vary. We solve here the desired set of coupled nonlinear differential equations by invoking a new set of dimensionless variables. Approximate solutions are obtained via the power-series method aided by Pade approximants. The scheme works very successfully in furnishing the initial dynamics at least up to the region where existence of any steady state can be checked. A few conditions for its validity are put forward and tested against the findings. Temporal profiles of the substrate and the product are analyzed in addition to that of the complex to gain further insights into legitimacy of the above approximation. Some recent observations like the reactant stationary approxim...
Macromolecular crowding and the steady-state kinetics of malate dehydrogenase.
Poggi, Christopher G; Slade, Kristin M
2015-01-20
To understand how macromolecular crowding affects enzyme activity, we quantified the Michaelis-Menten kinetics of mitochondrial malate dehydrogenase (MDH) in the presence of hen egg white (HEW), lysozyme, bovine serum albumin (BSA), gum arabic, poly(vinylpyrrolidone) (PVP), and dextrans of various molecular weights. Although crowding tended to decrease Km and Vmax values, the magnitude depended on the crowding agent, reaction direction, and isozyme (mitochondrial porcine heart or thermophlic TaqMDH from Thermus flavus). Crowding slowed oxaloacetate reduction more significantly than malate oxidation, which may suggest that mitochondrial enzymes have evolved to function optimally under the crowded constraints in which they are immersed. Since direct comparisons of neutral to charged crowders are underrepresented in the literature, we performed these studies and found that neutral crowding agents lowered Vmax values more than charged crowders of similar size. The exception was hen egg white, a mixture of charged proteins that caused the largest observed decreases in both Km and Vmax. Finally, the data provide insight about the mechanism by corroborating MDH subunit dependence.
Siddiqui, Khawar Sohail; Ertan, Haluk; Charlton, Timothy; Poljak, Anne; Daud Khaled, A K; Yang, Xuexia; Marshall, Gavin; Cavicchioli, Ricardo
2014-05-20
The kinetic constants of a hybrid versatile-peroxidase (VP) which oxidizes complex polymeric humic substances (HS) derived from lignin (humic and fulvic acids) and industrial wastes were determined for the first time using isothermal titration calorimetry (iTC). The reaction conditions were manipulated to enable manganese-peroxidase (MnP) and/or lignin-peroxidase (LiP) activities to be evaluated. The peroxidase reactions exhibited varying degrees of product inhibition or activation; properties which have not previously been reported for VP enzymes. In contrast to previous work (Ertan et al., 2012) on small non-polymeric substrates (MnSO4, veratryl alcohol and dyes), all kinetic plots for polymeric HS were sigmoidal, lacked Michaelis-Menten characteristics, and were indicative of positive cooperativity. Under conditions when both LiP and MnP were active, the kinetic data fitted to a novel biphasic Hill Equation, and the rate of enzymatic reaction was significantly greater than the sum of individual LiP plus MnP activities implying synergistic activation. By employing size-exclusion chromatography and electrospray ionization mass spectrometry, the characteristics of the oxidative degradation products of the HS were also monitored. Our study showed that the allosteric behaviour of the VP enzyme promotes a high level of regulation of activity during the breakdown of model and industrial ligninolytic substrates. The work was extended to examine the kinetics of breakdown of industrial wastes (effluent from a pulp and paper plant, and fouled membrane solids extracted from a ground water treatment membrane) revealing unique, VP-mediated, kinetic responses. This work demonstrates that iTC can be successfully employed to study the kinetic properties of VP enzymes in order to devise reaction conditions optimized for oxidative degradation of HS present in materials used in a wide range of industries. Crown Copyright © 2014. Published by Elsevier B.V. All rights reserved.
Takayanagi, Toshiaki
2013-12-01
The basic model for chronic hepatitis B virus (HBV) or hepatitis C virus (HCV) infection during therapy enables us to analyze short-term viral kinetics. However, the model is not useful for analyzing long-term viral kinetics. Here, I suggest a new model that was obtained by introducing Michaelis-Menten kinetics into the basic model. The new model can exhibit long-term viral kinetics without rebound and oscillation, unlike the basic model. The value of the parameter K in the new model is analogous to the Michaelis constant Km and is predicted to be approximately less than 10(10)/ml.
Bouyahia, Naima; Hamlaoui, Mohamed Larbi; Hnaien, Mouna; Lagarde, Florence; Jaffrezic-Renault, Nicole
2011-02-01
In this work, a new biosensor was prepared through immobilization of bovine liver catalase in a photoreticulated poly (vinyl alcohol) membrane at the surface of a conductometric transducer. This biosensor was used to study the kinetics of catalase-H(2)0(2) reaction and its inhibition by cyanide. Immobilized catalase exhibited a Michaelis-Menten behaviour at low H(2)0(2) concentrations (biosensor response by increasing cyanide concentration was linear up to 50μM, with a cyanide detection limit of 6μM. In parallel, electrochemical characteristics of the catalase/PVA biomembrane and its interaction with cyanide were studied by cyclic voltammetry and impedance spectroscopy. Addition of the biomembrane onto the gold electrodes induced a significant increase of the interfacial polarization resistance R(P). On the contrary, cyanide binding resulted in a decrease of Rp proportional to KCN concentration in the 4 to 50μM range. Inhibition coefficient I(50) calculated by this powerful label-free and substrate-free technique (24.3μM) was in good agreement with that determined from the substrate-dependent conductometric biosensor (24.9μM).
Modeling uptake kinetics of cadmium by field-grown lettuce
Chen Weiping [Department of Environmental Sciences, University of California, 900 University Avenue, Riverside, CA 92521 (United States)], E-mail: chenweip@yahoo.com.cn; Li Lianqing [Institute of Resources, Ecosystem and Environment of Agriculture, Nanjing Agricultural University, Nanjing 210095 (China); Chang, Andrew C.; Wu Laosheng [Department of Environmental Sciences, University of California, 900 University Avenue, Riverside, CA 92521 (United States); Kwon, Soon-Ik [Agricultural Environmental and Ecology Division, National Institute of Agricultural Science and Technology, Suwon 441-707 (Korea, Republic of); Bottoms, Rick [Desert Research and Extension Center, 1004 East Holton Road, El Centro, CA 92243 (United States)
2008-03-15
Cadmium uptake by field grown Romaine lettuce treated with P-fertilizers of different Cd levels was investigated over an entire growing season. Results indicated that the rate of Cd uptake at a given time of the season can be satisfactorily described by the Michaelis-Menten kinetics, that is, plant uptake increases as the Cd concentration in soil solution increases, and it gradually approaches a saturation level. However, the rate constant of the Michaelis-Menten kinetics changes over the growing season. Under a given soil Cd level, the cadmium content in plant tissue decreases exponentially with time. To account for the dynamic nature of Cd uptake, a kinetic model integrating the time factor was developed to simulate Cd plant uptake over the growing season: C{sub Plant} = C{sub Solution} . PUF{sub max} . exp[-b . t], where C{sub Plant} and C{sub Solution} refer to the Cd content in plant tissue and soil solution, respectively, PUF{sub max} and b are kinetic constants. - A kinetic model was developed to evaluate the uptake of Cd under field conditions.
Preventing Corrosion by Controlling Cathodic Reaction Kinetics
2016-03-25
Preventing corrosion by controlling cathodic reaction kinetics Progress Report for Period: 1 SEP 2015-31 MAR 2016 John Keith Department of...25 March 2016 Preventing corrosion by controlling cathodic reaction kinetics Annual Summary Report: FY16 PI: John Keith, 412-624-7016,jakeith...dominate the metal’s cathodic behavior. Within an alkaline environment, we expect the following reduction reactions to be catalyzed on the oxide
Kinetic studies of elementary chemical reactions
Durant, J.L. Jr. [Sandia National Laboratories, Livermore, CA (United States)
1993-12-01
This program concerning kinetic studies of elementary chemical reactions is presently focussed on understanding reactions of NH{sub x} species. To reach this goal, the author is pursuing experimental studies of reaction rate coefficients and product branching fractions as well as using electronic structure calculations to calculate transition state properties and reaction rate calculations to relate these properties to predicted kinetic behavior. The synergy existing between the experimental and theoretical studies allow one to gain a deeper insight into more complex elementary reactions.
Marcos De Souza
2013-10-01
Full Text Available The cyclodextrins (CDs are cyclic maltooligosaccharides obtained by cyclization of linear chains of starch, catalyzed by the enzyme cyclomaltodextringlucanotransferase (CGTase. The interest in CD production results from the formation of inclusion complexes, which allow many important applications, especially in food, pharmaceutical and cosmetic industries. The substances complexed generally have their properties modified by complexation. It is appreciated if increased solubility and higher thermal and chemical stabilities are obtained. In this work, a kinetic model was developed for the production of cyclodextrins in the presence of CGTase from alkalophilic Bacillus sp., taking into account the reversibility of the cyclization reaction, the simultaneous production of b and g-CD and also the inhibitory influence of the substrate and products (CDs, on the enzymatic activity of the CGTase. The substrate formed from a solution of maltodextrins was treated as a single substrate. The model was compared with experimental results of 24h of reaction and this comparison demonstrated that there was a very good representation of the data throughout the test period. The model also allowed explaining the observation of different experimental values for each Michaelis-Menten constant and substrate inhibition constant for each CD, although the CDs are produced from the same substrate.
Kinetic study of enzymatic hydrolysis of acid-pretreated coconut coir
Fatmawati, Akbarningrum; Agustriyanto, Rudy
2015-12-01
Biomass waste utilization for biofuel production such as bioethanol, has become more prominent currently. Coconut coir is one of lignocellulosic food wastes, which is abundant in Indonesia. Bioethanol production from such materials consists of more than one step. Pretreatment and enzymatic hydrolysis is crucial steps to produce sugar which can then be fermented into bioethanol. In this research, ground coconut coir was pretreated using dilute sulfuric acid at 121°C. This pretreatment had increased the cellulose content and decreased the lignin content of coconut coir. The pretreated coconut coir was hydrolyzed using a mix of two commercial cellulase enzymes at pH of 4.8 and temperature of 50°C. The enzymatic hydrolysis was conducted at several initial coconut coir slurry concentrations (0.1-2 g/100 mL) and reaction times (2-72 hours). The reducing sugar concentration profiles had been produced and can be used to obtain reaction rates. The highest reducing sugar concentration obtained was 1,152.567 mg/L, which was produced at initial slurry concentration of 2 g/100 mL and 72 hours reaction time. In this paper, the reducing sugar concentrations were empirically modeled as a function of reaction time using power equations. Michaelis-Menten kinetic model for enzymatic hydrolysis reaction is adopted. The kinetic parameters of that model for sulfuric acid-pretreated coconut coir enzymatic hydrolysis had been obtained which are Vm of 3.587×104 mg/L.h, and KM of 130.6 mg/L.
Chemical kinetics and reaction dynamics
Houston, Paul L
2006-01-01
This text teaches the principles underlying modern chemical kinetics in a clear, direct fashion, using several examples to enhance basic understanding. It features solutions to selected problems, with separate sections and appendices that cover more technical applications.Each chapter is self-contained and features an introduction that identifies its basic goals, their significance, and a general plan for their achievement. This text's important aims are to demonstrate that the basic kinetic principles are essential to the solution of modern chemical problems, and to show how the underlying qu
Moate, P J; Boston, R C; Jenkins, T C; Lean, I J
2008-02-01
Previous investigations into ruminal lipolysis of triacylglycerol and ruminal biohydrogenation (BH) of unsaturated long-chain fatty acids have generally quantified these processes with either zero-order or first-order kinetics. This investigation examined if Michaelis-Menten and other nonlinear kinetics might be useful for quantifying these processes. Data from 2 previously published in vitro experiments employing rumen fluid from sheep to investigate the lipolysis of trilinolein, the BH of cis-9, cis-12 linoleic acid (LA), and the BH of fatty acids derived from the lipolysis of trilinolein were used for the development of a multi-compartmental model. The model described the lipolysis of triacylglycerol well. The model also provided a good mathematical description of the resulting production of nonesterified fatty acids, the isomerization of nonesterified LA, and subsequent production of rumenic acid (RA), vaccenic acid (VA), and stearic acid (SA). However, the model described poorly the patterns of the concentrations of LA, RA, VA, and SA after incubation of trilinolein in rumen fluid. The model is consistent with known stoichiometry and biochemistry and is parsimonious in that it employs a minimal number of parameters to describe all of the major aspects of lipolysis and BH. The first step in the lipolysis of trilinolein was described by Michaelis-Menten kinetics (Vmax = 529 +/- 16 mg/L per h; Km = 698 +/- 41 mg/L). Both subsequent lipolysis steps were approximated by a first-order (linear kinetics) rate constant (k = 2.64 +/- 0.041 /h). Isomerization of LA to RA was modeled by simple Michaelis-Menten kinetics (Vmax = 2,421 +/- 83 mg/L per h; Km = 440 +/- 22 mg/L). The kinetics of the BH of RA to VA was described by a Michaelis-Menten-type process involving competitive inhibition by VA (Vmax = 492 +/- 6.5 mg/L per h; Km = 1 mg/L). The final step, the BH of VA to SA, was modeled by a quasi-first-order process (k = 0.533 +/- 0.021 /h), but as the concentration of
Effect in vitro of propoxur on kinetics of K+ stimulated PNPPase and protection by thiol reagents.
Babu, G R; Reddy, G R; Rajendra, W; Chetty, C S
1990-09-01
Kinetics analysis of K+ stimulated PNPPase was studied in the rat brain synaptosomes in the presence of propoxur. Non-competitive inhibition with respect to activation by PNPP was seen by the decreased maximal velocity (Vmax) without change in Michaelis-Menten Constant (Km). Activation energy values (delta E) were increased suggesting the decreased catalytic potential of the enzyme. It is also observed that dithiothrietol (DTT) (76 microM), cysteine (82 microM) and glutathione (120 microM) neutralized the inhibition of K(+)-PNPPase by propoxur to different extents.
Sivuk, V F; Rusina, I M; Luchko, T A; Makarchikov, A F
2008-01-01
Soluble nucleoside triphosphatase differing in its properties from all known proteins with NTPase activity was partially purified from bovine kidneys. The enzyme has pH optimum of 7.5, molecular mass of 60 kDa, as estimated by gel chromatography, and shows an absolute dependence on divalent metal ions. NTPase obeyed Michaelis-Menten kinetics in the range of substrate concentration tested from 45 to 440 microM; the apparent Km for inosine-5'-triphosphate was calculated to be 23.3 microM. The enzyme was found to possess a broad substrate specificity, being capable of hydrolyzing various nucleoside-5'-tri- as well as diphosphates.
Lipase-catalyzed ethanolysis of fish oils: multi-response kinetics.
Torres, Carlos F; Moeljadi, Marlina; Hill, Charles G
2003-08-05
The kinetics of the lipase-catalyzed (Pseudomonas cepacia) ethanolysis of fish oil has been studied in a batch reactor using menhaden oil, tuna oil, and acylglycerol mixtures derived from menhaden oil. Multi-response models derived from a generalized Michaelis-Menten mechanism were developed to describe the rates of formation of ethyl esters of the primary fatty acids present in the precursor oil. A first-order model for deactivation of the lipase was fit simultaneously to one of the data sets.
Pedruzzi, Israel; da Silva, Eduardo A Borges; Rodrigues, Alírio E
2011-07-10
In this work, we have investigated the kinetics of the biotechnological production of lactobionic acid (LBA) and sorbitol by the catalytic action of glucose-fructose oxidoreductase (GFOR) and glucono-δ-lactonase (GL) enzymes. The cells of bacterium Zymomonas mobilis ATCC 29191 containing this enzymatic complex were submitted to permeabilization and reticulation procedures. The effect of the concentration of substrates on the rate of product formation using a mobilized cell system was investigated. The application of higher fructose concentration seems to not affect the initial rate of formation of the bionic acid. Under conditions of low initial concentration of lactose, the experimental kinetic data of the bi-substrate reaction were modelled by assuming a rate equation of the classical ping-pong mechanism. The found kinetic parameters displayed a low affinity of the GFOR enzyme for both substrates. The enzymatic system did not exhibit normal Michaelis-Menten kinetics in response to a change of concentration of lactose, when fructose was held constant, presenting a sigmoid relationship between initial velocity and substrate concentration. A rate equation based on Hill kinetics was used to describe the kinetic behaviour of this enzyme-substituted reaction at higher lactose concentrations. The results from batch experiments using immobilized cells within Ca-alginate beads revealed that there is no pronounced occurrence of mass transfer limitations on LBA production for beads with 1.2 mm in average diameter. This discussion aids for defining the best operating conditions to maximize the productivity for LBA and sorbitol in this bioconversion and also for reducing the complexity of downstream separation processes.
José L. Gómez
2005-01-01
Full Text Available A new method for determining the intrinsic parameters of reaction in processes involving a high initial rate has been developed. The usefulness of this alternative, which consists of determining several sets of apparent parameters at different times and then extrapolating these to time zero, is demonstrated proved by the linear dependence obtained between the apparent parameters and the reaction time. The method permitted the values of the intrinsic parameters (enzyme specific activity and Michaelis-Menten constants of both substrates to be obtained for the system under study and was checked with experimental reaction rate data for the soybean peroxidase/phenol/hydrogen peroxide system.
Reaction networks and kinetics of biochemical systems.
Arceo, Carlene Perpetua P; Jose, Editha C; Lao, Angelyn R; Mendoza, Eduardo R
2017-01-01
This paper further develops the connection between Chemical Reaction Network Theory (CRNT) and Biochemical Systems Theory (BST) that we recently introduced [1]. We first use algebraic properties of kinetic sets to study the set of complex factorizable kinetics CFK(N) on a CRN, which shares many characteristics with its subset of mass action kinetics. In particular, we extend the Theorem of Feinberg-Horn [9] on the coincidence of the kinetic and stoichiometric subsets of a mass action system to CF kinetics, using the concept of span surjectivity. We also introduce the branching type of a network, which determines the availability of kinetics on it and allows us to characterize the networks for which all kinetics are complex factorizable: A "Kinetics Landscape" provides an overview of kinetics sets, their algebraic properties and containment relationships. We then apply our results and those (of other CRNT researchers) reviewed in [1] to fifteen BST models of complex biological systems and discover novel network and kinetic properties that so far have not been widely studied in CRNT. In our view, these findings show an important benefit of connecting CRNT and BST modeling efforts. Copyright © 2016 Elsevier Inc. All rights reserved.
Prévoteau, Antonin; Geirnaert, Annelies; Arends, Jan B. A.; Lannebère, Sylvain; van de Wiele, Tom; Rabaey, Korneel
2015-07-01
Monitoring in vitro the metabolic activity of microorganisms aids bioprocesses and enables better understanding of microbial metabolism. Redox mediators can be used for this purpose via different electrochemical techniques that are either complex or only provide non-continuous data. Hydrodynamic chronoamperometry using a rotating disc electrode (RDE) can alleviate these issues but was seldom used and is poorly characterized. The kinetics of Faecalibacterium prausnitzii A2-165, a beneficial gut microbe, were determined using a RDE with riboflavin as redox probe. This butyrate producer anaerobically ferments glucose and reduces riboflavin whose continuous monitoring on a RDE provided highly accurate kinetic measurements of its metabolism, even at low cell densities. The metabolic reaction rate increased linearly over a broad range of cell concentrations (9 × 104 to 5 × 107 cells.mL-1). Apparent Michaelis-Menten kinetics was observed with respect to riboflavin (KM = 6 μM kcat = 5.3×105 s-1, at 37 °C) and glucose (KM = 6 μM kcat = 2.4 × 105 s-1). The short temporal resolution allows continuous monitoring of fast cellular events such as kinetics inhibition with butyrate. Furthermore, we detected for the first time riboflavin reduction by another potential probiotic, Butyricicoccus pullicaecorum. The ability of the RDE for fast, accurate, simple and continuous measurements makes it an ad hoc tool for assessing bioprocesses at high resolution.
Biochemical kinetics in changing volumes.
Pawłowski, Piotr H; Zielenkiewicz, Piotr
2004-01-01
The need of taking into account the change of compartment volume when developing chemical kinetics analysis inside the living cell is discussed. Literature models of a single enzymatic Michaelis-Menten process, glycolytic oscillations, and mitotic cyclin oscillations were tested with appropriate theoretical extension in the direction of volume modification allowance. Linear and exponential type of volume increase regimes were compared. Due to the above, in a growing cell damping of the amplitude, phase shift, and time pattern deformation of the metabolic rhythms considered were detected, depending on the volume change character. The performed computer simulations allow us to conclude that evolution of the cell volume can be an essential factor of the chemical kinetics in a growing cell. The phenomenon of additional metabolite oscillations caused by the periodic cell growth and division was theoretically predicted and mathematically described. Also, the hypothesis of the periodized state in the growing cell as the generalization of the steady-state was formulated.
Reaction Kinetics of Nanostructured Silicon Carbide
Wallis, Kendra; Zerda, T. W.
2006-10-01
Nanostructured silicon carbide (SiC) is of interest particularly for use in nanocomposites that demonstrate high hardness as well as for use in semiconductor applications. Reaction kinetics studies of solid-solid reactions are relatively recent and present a method of determining the reaction mechanism and activation energy by measuring reaction rates. We have used induction heating to heat quickly, thus reducing the error in reaction time measurements. Data will be presented for reactions using silicon nanopowder (melting point of silicon. Using the well-known Avrami-Erofeev model, a two-parameter chi- square fit of the data provided a rate constant (k) and parameter (n), related to the reaction mechanism, for each temperature. From these data, an activation energy of 138 kJ/mol was calculated. In addition, the parameter n suggests the reaction mechanism, which will also be discussed. Experiments are continuing at higher temperatures to consider the liquid- solid reaction as well.
Maggi, F.; Riley, W. J.
2016-12-01
We propose a mathematical framework to introduce the concept of differential free energy of activation in enzymatically catalyzed reactions, and apply it to N uptake by microalgae and bacteria. This framework extends the thermodynamic capabilities of the classical transition-state theory in and harmonizes the consolidated definitions of kinetic parameters with their thermodynamic and physical meaning. Here, the activation energy is assumed to be a necessary energetic level for equilibrium complexation between reactants and activated complex; however, an additional energy contribution is required for the equilibrium activated complex to release reaction products. We call this "differential free energy of activation"; it can be described by a Boltzmann distribution, and corresponds to a free energy level different from that of complexation. Whether this level is above or below the free energy of activation depends on the reaction, and defines energy domains that correspond to "superactivated", "activated", and "subactivated" complexes. The activated complex reaching one of those states will eventually release the products from an energy level different than that of activation. The concept of differential free energy of activation was tested on 57 independent experiments of NH4+ and NO3- uptake by various microalgae and bacteria at temperatures ranging between 1 and 45oC. Results showed that the complexation equilibrium always favored the activated complex, but the differential energy of activation led to an apparent energy barrier consistent with observations. Temperature affected all energy levels within this framework but did not alter substantially these thermodynamic features. Overall the approach: (1) provides a thermodynamic and mathematical link between Michaelis-Menten and rate constants; (2) shows that both kinetic parameters can be described or approximated by Arrhenius' like equations; (3) describes the likelihood of formation of sub-, super-, and
Controlling enzymatic activity and kinetics in swollen mesophases by physical nano-confinement
Sun, Wenjie; Vallooran, Jijo J.; Zabara, Alexandru; Mezzenga, Raffaele
2014-05-01
into a highly confined environment. We show that the enzymatic activity of a model enzyme, horseradish peroxidase (HRP), can be accurately controlled by relaxing its confinement within the cubic phases' water channels, when the aqueous channel diameters are systematically swollen with varying amount of hydration-enhancing sugar ester. The in-meso activity and kinetics of HRP are then systematically investigated by UV-vis spectroscopy, as a function of the size of the aqueous mesophase channels. The enzymatic activity of HRP increases with the swelling of the water channels. In swollen mesophases with water channel diameter larger than the HRP size, the enzymatic activity is more than double that measured in standard mesophases, approaching again the enzymatic activity of free HRP in bulk water. We also show that the physically-entrapped enzymes in the mesophases exhibit a restricted-diffusion-induced initial lag period and report the first observation of in-meso enzymatic kinetics significantly deviating from the normal Michaelis-Menten behaviour observed in free solutions, with deviations vanishing when enzyme confinement is released by swelling the mesophase. Electronic supplementary information (ESI) available: Visual appearance of the standard mesophase before and after HRP enzymatic reaction (Fig. S1); SAXS results of four Pn3m phases with increasing amount of SE 0%, 10%, 15% and 20% just below maximum hydration (Fig. S2); calibration curve for determining the partition coefficient of ABTS in lipids (Fig. S3); progress curves of the HRP catalytic reaction in pure water (Fig. S4) and reactions at varying ABTS concentrations for the in-meso enzymatic kinetics studies (Fig. S5); SAXS characterization of the influence of the added H2O2 (Fig. S6) and HRP (Fig. S7) on the hosted mesophases; initial rate as function of H2O2 concentration in 3 varying environments (Fig. S8). See DOI: 10.1039/c4nr01394h
The hydrothermal reaction kinetics of aspartic acid
Cox, Jenny S.; Seward, Terry M.
2007-02-01
Experimental data on the hydrothermal reaction kinetics of aspartic acid were acquired using a custom-built spectrophotometric reaction cell which permits in situ observation under hydrothermal conditions. The results of this study indicate that the reaction kinetics of dilute aspartic acid solutions are significantly different depending on the presence or absence of catalytic surfaces such as standard metal alloys. The spectroscopic data presented here represent the first direct observations, in situ and in real time, of an amino acid reacting in a hydrothermal solution. Quantitative kinetic information, including rate constants, concentration versus time profiles, and calculations of the individual component spectra, was obtained from the data using a chemometric approach based on factor analysis/principle component analysis which treats the rate expressions simultaneously as a system of differential algebraic equations (DAE) of index 1. Identification of the products was confirmed where possible by high pressure anion exchange chromatography with pulsed amperometric detection (HPAEC-PAD). The reaction kinetics of aspartic acid under hydrothermal conditions was observed to be highly complex, in contrast to previous studies which indicated almost exclusively deamination. At lower temperatures (120-170 °C), several different reaction pathways were observed, including decarboxylation and polymerization, and the catalytic effects of reactor surfaces on the aspartic acid system were clearly demonstrated. At higher temperatures (above 170 °C), aspartic acid exhibited highly complex behaviour, with evidence indicating that it can simultaneously dimerize and cyclize, deaminate (by up to two pathways), and decarboxylate (by up to two pathways). These higher temperature kinetics were not fully resolvable in a quantitative manner due to the complexity of the system and the constraints of UV spectroscopy. The results of this study provide strong evidence that the reaction
SBMLsqueezer: A CellDesigner plug-in to generate kinetic rate equations for biochemical networks
Schröder Adrian
2008-04-01
Full Text Available Abstract Background The development of complex biochemical models has been facilitated through the standardization of machine-readable representations like SBML (Systems Biology Markup Language. This effort is accompanied by the ongoing development of the human-readable diagrammatic representation SBGN (Systems Biology Graphical Notation. The graphical SBML editor CellDesigner allows direct translation of SBGN into SBML, and vice versa. For the assignment of kinetic rate laws, however, this process is not straightforward, as it often requires manual assembly and specific knowledge of kinetic equations. Results SBMLsqueezer facilitates exactly this modeling step via automated equation generation, overcoming the highly error-prone and cumbersome process of manually assigning kinetic equations. For each reaction the kinetic equation is derived from the stoichiometry, the participating species (e.g., proteins, mRNA or simple molecules as well as the regulatory relations (activation, inhibition or other modulations of the SBGN diagram. Such information allows distinctions between, for example, translation, phosphorylation or state transitions. The types of kinetics considered are numerous, for instance generalized mass-action, Hill, convenience and several Michaelis-Menten-based kinetics, each including activation and inhibition. These kinetics allow SBMLsqueezer to cover metabolic, gene regulatory, signal transduction and mixed networks. Whenever multiple kinetics are applicable to one reaction, parameter settings allow for user-defined specifications. After invoking SBMLsqueezer, the kinetic formulas are generated and assigned to the model, which can then be simulated in CellDesigner or with external ODE solvers. Furthermore, the equations can be exported to SBML, LaTeX or plain text format. Conclusion SBMLsqueezer considers the annotation of all participating reactants, products and regulators when generating rate laws for reactions. Thus, for
Pedersen, Morten Gram; Bersani, A.M.; Bersani, E.
2008-01-01
Enzyme reactions play a pivotal role in intracellular signal transduction. Many enzymes are known to possess Michaelis-Menten (MM) kinetics and the MM approximation is often used when modeling enzyme reactions. However, it is known that the MM approximation is only valid at low enzyme concentrati......Enzyme reactions play a pivotal role in intracellular signal transduction. Many enzymes are known to possess Michaelis-Menten (MM) kinetics and the MM approximation is often used when modeling enzyme reactions. However, it is known that the MM approximation is only valid at low enzyme...
Kinetic modeling of reactions in Foods
Boekel, van M.A.J.S.
2008-01-01
The level of quality that food maintains as it travels down the production-to-consumption path is largely determined by the chemical, biochemical, physical, and microbiological changes that take place during its processing and storage. Kinetic Modeling of Reactions in Foods demonstrates how to effec
Kinetic study of the enzymatic hydrolysis of sugarcane bagasse
M. L. Carvalho
2013-09-01
Full Text Available This work presents a kinetic study of the enzymatic hydrolysis of three cellulosic substrates: filter paper (FP, used as a low recalcitrance substrate model; steam exploded sugarcane bagasse (SB; and weak acid pretreated SB (1:20 dry bagasse:H2SO4 solution 1% w/w, the last two delignified with 4% NaOH (w/w. The influence of substrate concentration was assessed in hydrolysis experiments in a shaker, using Accellerase® 1500, at pH 4.8, in 50 mM sodium citrate buffer. Cellulose loads (weight substrate/weight total were changed between 0.5%-13% (for FP and 0.99%-9.09% (for SB. For FP and low loads of steam exploded SB, it was possible to fit pseudo-homogeneous Michaelis-Menten models (with inhibition. For FP and higher loads of steam exploded SB, modified Michaelis-Menten models were fitted. Besides, it was observed that, after retuning of the model parameters, it is possible to apply a model fitted for one situation to a different case. Chrastil models were also fitted and they were the only feasible approach for the highly recalcitrant acid-treated SB.
Ordens não inteiras em cinética química Non-integer orders in chemical kinetics
André P. Oliveira
2010-01-01
Full Text Available Starting from zero-, first-, and second-order integrated laws for chemical kinetics, some cases are shown which produce fractional orders. Taking the Michaelis-Menten mechanism as a first example, it is shown that substrate order can go from 1 to zero, depending on relative concentration of enzyme and substrate. Using other examples which show fractional orders higher than one and even negative (inhibition, it is shown that the presence of an equilibrium before or parallel to the rate determining step can be the reason for fractional orders, which is an indication of a more complex mechanism.
Andric, Pavle; Meyer, Anne S.; Jensen, Peter Arendt
2010-01-01
, during 96 h of reaction. When glucose was removed by dialysis during the enzymatic hydrolysis, the cellulose conversion rates and glucose yields increased. In fact, with dialytic in situ glucose removal, the rate of enzyme-catalyzed glucose release during 48-72 h of reaction recovered from 20......-40% to become approximate to 70% of the rate recorded during 6-24 h of reaction. Although Michaelis-Menten kinetics do not suffice to model the kinetics of the complex multi-enzymatic degradation of cellulose, the data for the glucose inhibition were surprisingly well described by simple Michaelis......-Menten inhibition models without great significance of the inhibition mechanism. Moreover, the experimental in situ removal of glucose could be simulated by a Michaelis-Menten inhibition model. The data provide an important base for design of novel reactors and operating regimes which include continuous product...
Stiripentol kinetics in epilepsy: nonlinearity and interactions.
Levy, R H; Loiseau, P; Guyot, M; Blehaut, H M; Tor, J; Moreland, T A
1984-11-01
Stiripentol kinetics during oral therapy were assessed in six patients with epilepsy who were receiving other antiepileptic drugs. Steady-state levels at 600, 1200, and 2400 mg/day increased in a nonlinear fashion, indicating Michaelis-Menten kinetics. Oral clearance of stiripentol at 600 mg/day was 41.5 +/- 23.4 l/day/kg (mean +/- SD), greater than that at 1200 mg/day (20.3 +/- 8.8 l/day/kg; P less than 0.05) or 2400 mg/day (8.5 +/- 3.8 l/day/kg; P less than 0.01). The apparent in vivo Michaelis-Menten parameters were determined from three mean steady-state concentrations. The average velocity of conversion of stiripentol to its metabolites (Vm), Michaelis constant (Km), and the ratio Vm/Km were 49.3 +/- 13.1 mg/day/kg, 1.35 +/- 1.08 mg/l, and 50.2 +/- 27.5 l/day/kg. Stiripentol reduced the elimination clearances of concomitant antiepileptic drugs. Phenytoin clearance was reduced in all five subjects who received this drug, from a mean control of 29.5 +/- 13.4 l/day to 18.5 +/- 4.6 l/day at a stiripentol dose of 1200 mg/day (P = 0.05) and to 6.48 +/- 2.59 l/day at 2400 mg/day (P less than 0.01). Stiripentol reduced the clearance of carbamazepine in one subject from a control value of 209 l/day to 128 l/day (1200 mg/day) and 61 l/day (2400 mg/day). Stiripentol reduced phenobarbital clearance in two subjects from 3.8 and 5.1 l/day to 2.3 and 3.4 l/day (2400 mg/day). The Michaelis-Menten kinetics of stiripentol, as well as its interactions with other antiepileptic drugs, have important implications in the designing of controlled clinical trials.
An Integrated Circuit for Chip-Based Analysis of Enzyme Kinetics and Metabolite Quantification.
Cheah, Boon Chong; Macdonald, Alasdair Iain; Martin, Christopher; Streklas, Angelos J; Campbell, Gordon; Al-Rawhani, Mohammed A; Nemeth, Balazs; Grant, James P; Barrett, Michael P; Cumming, David R S
2016-06-01
We have created a novel chip-based diagnostic tools based upon quantification of metabolites using enzymes specific for their chemical conversion. Using this device we show for the first time that a solid-state circuit can be used to measure enzyme kinetics and calculate the Michaelis-Menten constant. Substrate concentration dependency of enzyme reaction rates is central to this aim. Ion-sensitive field effect transistors (ISFET) are excellent transducers for biosensing applications that are reliant upon enzyme assays, especially since they can be fabricated using mainstream microelectronics technology to ensure low unit cost, mass-manufacture, scaling to make many sensors and straightforward miniaturisation for use in point-of-care devices. Here, we describe an integrated ISFET array comprising 2(16) sensors. The device was fabricated with a complementary metal oxide semiconductor (CMOS) process. Unlike traditional CMOS ISFET sensors that use the Si3N4 passivation of the foundry for ion detection, the device reported here was processed with a layer of Ta2O5 that increased the detection sensitivity to 45 mV/pH unit at the sensor readout. The drift was reduced to 0.8 mV/hour with a linear pH response between pH 2-12. A high-speed instrumentation system capable of acquiring nearly 500 fps was developed to stream out the data. The device was then used to measure glucose concentration through the activity of hexokinase in the range of 0.05 mM-231 mM, encompassing glucose's physiological range in blood. Localised and temporal enzyme kinetics of hexokinase was studied in detail. These results present a roadmap towards a viable personal metabolome machine.
Leong, Sze Ying; Oey, Indrawati
2014-03-01
The objective of this research was to study the enzyme kinetics and thermostability of endogenous ascorbic acid oxidase (AAO) in carrot purée (Daucus carota cv. Nantes) after being treated with pulsed electric field (PEF) processing. Various PEF treatments using electric field strength between 0.2 and 1.2kV/cm and pulsed electrical energy between 1 and 520kJ/kg were conducted. The enzyme kinetics and the kinetics of AAO thermal inactivation (55-70°C) were described using Michaelis-Menten model and first order reaction model, respectively. Overall, the estimated Vmax and KM values were situated in the same order of magnitude as the untreated carrot purée after being exposed to pulsed electrical energy between 1 and 400kJ/kg, but slightly changed at pulsed electrical energy above 500kJ/kg. However, AAO presented different thermostability depending on the electric field strength applied. After PEF treatment at the electric field strength between 0.2 and 0.5kV/cm, AAO became thermolabile (i.e. increase in inactivation rate (k value) at reference temperature) but the temperature dependence of k value (Ea value) for AAO inactivation in carrot purée decreased, indicating that the changes in k values were less temperature dependent. It is obvious that PEF treatment affects the temperature stability of endogenous AAO. The changes in enzyme kinetics and thermostability of AAO in carrot purée could be related to the resulting carrot purée composition, alteration in intracellular environment and the effective concentration of AAO released after being subjected to PEF treatment. Copyright © 2013 Elsevier Ltd. All rights reserved.
Transport Reversal during Heteroexchange: A Kinetic Study
V. Makarov
2013-01-01
Full Text Available It is known that secondary transporters, which utilize transmembrane ionic gradients to drive their substrates up a concentration gradient, can reverse the uptake and instead release their substrates. Unfortunately, the Michaelis-Menten kinetic scheme, which is popular in transporter studies, does not include transporter reversal, and it completely neglects the possibility of equilibrium between the substrate concentrations on both sides of the membrane. We have developed a complex two-substrate kinetic model that includes transport reversal. This model allows us to construct analytical formulas allowing the calculation of a “heteroexchange” and “transacceleration” using standard Michaelis coefficients for respective substrates. This approach can help to understand how glial and other cells accumulate substrates without synthesis and are able to release such substrates and gliotransmitters.
Reaction kinetics of bond rotations in graphene
Skowron, Stephen T.
2016-04-12
The formation and healing processes of the fundamental topological defect in graphitic materials, the Stone-Wales (SW) defect, are brought into a chemical context by considering the rotation of a carbon-carbon bond as chemical reaction. We investigate the rates and mechanisms of these SW transformations in graphene at the atomic scale using transmission electron microscopy. We develop a statistical atomic kinetics formalism, using direct observations obtained under different conditions to determine key kinetic parameters of the reactions. Based on the obtained statistics we quantify thermally and irradiation induced routes, identifying a thermal process of healing with an activation energy consistent with predicted adatom catalysed mechanisms. We discover exceptionally high rates for irradiation induced SW healing, incompatible with the previously assumed mechanism of direct knock-on damage and indicating the presence of an efficient nonadiabatic coupling healing mechanism involving beam induced electronic excitations of the SW defect.
Hezbollah: The Dynamics of Recruitment
2011-05-19
fundamental Michaelis - Menten kinetic interaction of the enzyme- substrate complex over time. As substrates are converted by enzymes 0 to the intermediate... Michaelis - Menten , Sensitivity Analysis, Nonlinear Differential Equations 16. PRICE CODE 17. SECURITY CLASSIFICATION UNCLASSIFIED OF REPORT 18...Illustrations Figures Figure 1. Concentration over time for the Michaelis - Menten equations. ...................................... 38 Figure 2
Kinetics of catalytic reactions solutions manual
Vannice, M Albert
2005-01-01
Including countless exercises and worked examples, this advanced reference work and textbook will be extremely useful for the work of many industrial scientists. It teaches readers to design kinetic experiments involving heterogeneous catalysts, to characterize these catalysts, to acquire rate data, to find heat and mass transfer limitations in these data, to select reaction models, to derive rate expressions based on these models, and to assess the consistency of these rate equations.
Kinetics of trypsin-catalyzed hydrolysis determined by isothermal titration calorimetry.
Maximova, Ksenia; Trylska, Joanna
2015-10-01
Isothermal titration calorimetry (ITC) was applied to determine enzymatic activity and inhibition. We measured the Michaelis-Menten kinetics for trypsin-catalyzed hydrolysis of two substrates, casein (an insoluble macromolecule substrate) and Nα-benzoyl-dl-arginine β-naphthylamide (a small substrate), and estimated the thermodynamic parameters in the temperature range from 20 to 37°C. The inhibitory activities of reversible (small molecule benzamidine) and irreversible (small molecule phenylmethanesulfonyl fluoride and macromolecule α1-antitrypsin) inhibitors of trypsin were also determined. We showed the usefulness of ITC for fast and direct measurement of inhibition constants and half-maximal inhibitory concentrations and for predictions of the mechanism of inhibition. ITC kinetic assays could be an easy and straightforward way to estimate Michaelis-Menten constants and the effectiveness of inhibitors as well as to predict the inhibition mechanism. ITC efficiency was found to be similar to that of classical spectrophotometric enzymatic assays. Copyright © 2015 Elsevier Inc. All rights reserved.
A Critical View on In Vitro Analysis of P-glycoprotein (P-gp) Transport Kinetics.
Saaby, Lasse; Brodin, Birger
2017-09-01
Transport proteins expressed in the different barriers of the human body can have great implications on absorption, distribution, and excretion of drug compounds. Inhibition or saturation of a transporter can potentially alter these absorbtion, distribution, metabolism and elimination properties and thereby also the pharmacokinetic profile and bioavailability of drug compounds. P-glycoprotein (P-gp, ABCB1) is an efflux transporter which is present in most of the barriers of the body, including the small intestine, the blood-brain barrier, the liver, and the kidney. In all these tissues, P-gp may mediate efflux of drug compounds and may also be a potential site for drug-drug interactions. Consequently, there is a need to be able to predict the saturation and inhibition of P-gp and other transporters in vivo. For this purpose, Michaelis-Menten steady-state analysis has been applied to estimate kinetic parameters, such as Km and Vmax, for carrier-mediated transport, whereas half-maximal inhibitor concentration (IC50) and the disassociation constant for an inhibitor/P-gp complex (Ki) have been determined to estimate P-gp inhibition. This review addresses in vitro methods commonly used to study P-gp transport kinetics and aims at providing a critical evaluation of the application of steady-state Michaelis-Menten analysis of kinetic parameters for substrate/P-gp interactions. Copyright © 2017 American Pharmacists Association®. Published by Elsevier Inc. All rights reserved.
Pozzolanic Reaction Kinetics of Coal Ashes
ZHENG Hongwei; WANG Zhijuan; QIAN Jueshi; SONG Yuanming; WANG Zhi
2009-01-01
The pozzolanic reactivity was determined by the hydration kinetics of pozzolanic reaction based on the fact that the hydration products of active SiO_2 and Al_2O_3 with lime were soluble in dilute hydrochloric acid.The results show that the pozzolanic reaction of active SiO_2 and Al2O3 of coal ashes follows apparent first-order kinetics.The reaction rate constant of FBC ashes is greater than that of PC ashes,while the activation energy of the former is lower than that of the latter.It is confirmed that the pozzolanic activity of fluidized bed combustion(FBC)ashes is significantly higher than that of PC ashes,and the reaction barrier of the former is lower than that of the latter,because the microstructures of FBC ashes,such as mineralogical composition,morphology and polymerization degree of [SiO_4]and[AlO_6]are more favorable to the pozzolanic activity development than those of PC ashes.
Modelling atypical CYP3A4 kinetics: principles and pragmatism.
Houston, J Brian; Galetin, Aleksandra
2005-01-15
The Michaelis-Menten model, and the existence of a single active site for the interaction of substrate with drug metabolizing enzyme, adequately describes a substantial number of in vitro metabolite kinetic data sets for both clearance and inhibition determination. However, in an increasing number of cases (involving most notably, but not exclusively, CYP3A4), atypical kinetic features are observed, e.g., auto- and heteroactivation; partial, cooperative, and substrate inhibition; concentration-dependent effector responses (activation/inhibition); limited substrate substitution and inhibitory reciprocity necessitating sub-group classification. The phenomena listed above cannot be readily interpreted using single active site models and the literature indicates that three types of approaches have been adopted. First the 'nai ve' approach of using the Michaelis-Menten model regardless of the kinetic behaviour, second the 'empirical' approach (e.g., employing the Hill or uncompetitive inhibition equations to model homotropic phenomena of sigmoidicity and substrate inhibition, respectively) and finally, the 'mechanistic' approach. The later includes multisite kinetic models derived using the same rapid equilibrium/steady-state assumptions as the single-site model. These models indicate that 2 or 3 binding sites exist for a given CYP3A4 substrate and/or effector. Multisite kinetic models share common features, depending on the substrate kinetics and the nature of the effector response observed in vitro, which allow a generic model to be proposed. Thus although more complex than the other two approaches, they show more utility and can be comprehensively applied in relatively simple versions that can be readily generated from generic model. Multisite kinetic features, observed in isolated hepatocytes as well as in microsomes from hepatic tissue and heterologous expression systems, may be evident in substrate depletion-time profiles as well as in metabolite formation rates
Tang, J. Y.; Riley, W. J.
2013-12-01
We demonstrate that substrate uptake kinetics in any consumer-substrate network subject to the total quasi-steady-state assumption can be formulated as an equilibrium chemistry (EC) problem. If the consumer-substrate complexes equilibrate much faster than other metabolic processes, then the relationships between consumers, substrates, and consumer-substrate complexes are in quasi-equilibrium and the change of a given total substrate (free plus consumer-bounded) is determined by the degradation of all its consumer-substrate complexes. In this EC formulation, the corresponding equilibrium reaction constants are the conventional Michaelis-Menten (MM) substrate affinity constants. When all of the elements in a given network are either consumer or substrate (but not both), we derived a first-order accurate EC approximation (ECA). The ECA kinetics is compatible with almost every existing extension of MM kinetics. In particular, for microbial organic matter decomposition modeling, ECA kinetics explicitly predicts a specific microbe's uptake for a specific substrate as a function of the microbe's affinity for the substrate, other microbes' affinity for the substrate, and the shielding effect on substrate uptake by environmental factors, such as mineral surface adsorption. By taking the EC solution as a reference, we evaluated MM and ECA kinetics for their abilities to represent several differently configured enzyme-substrate reaction networks. In applying the ECA and MM kinetics to microbial models of different complexities, we found (i) both the ECA and MM kinetics accurately reproduced the EC solution when multiple microbes are competing for a single substrate; (ii) ECA outperformed MM kinetics in reproducing the EC solution when a single microbe is feeding on multiple substrates; (iii) the MM kinetics failed, while the ECA kinetics succeeded, in reproducing the EC solution when multiple consumers (i.e., microbes and mineral surfaces) were competing for multiple
Van den Eede, Nele; Tomy, Gregg; Tao, Fang; Halldorson, Thor; Harrad, Stuart; Neels, Hugo; Covaci, Adrian
2016-02-01
Tris(1-chloro-2-propyl) phosphate (TCIPP) is an emerging contaminant which is ubiquitous in the indoor and outdoor environment. Moreover, its presence in human body fluids and biota has been evidenced. Since no quantitative data exist on the biotransformation or stability of TCIPP in the human body, we performed an in vitro incubation of TCIPP with human liver microsomes (HLM) and human serum (HS). Two metabolites, namely bis(2-chloro-isopropyl) phosphate (BCIPP) and bis(1-chloro-2-propyl) 1-hydroxy-2-propyl phosphate (BCIPHIPP), were quantified in a kinetic study using HLM or HS (only BCIPP, the hydrolysis product) and LC-MS. The Michaelis-Menten model fitted best the NADPH-dependent formation of BCIPHIPP and BCIPP in HLM, with respective V(MAX) of 154 ± 4 and 1470 ± 110 pmol/min/mg protein and respective apparent K(m) of 80.2 ± 4.4 and 96.1 ± 14.5 μM. Hydrolases, which are naturally present in HLM, were also involved in the production of BCIPP. A HS paraoxonase assay could not detect any BCIPP formation above 38.6 ± 10.8 pmol/min/μL serum. Our data indicate that BCIPP is the major metabolite of TCIPP formed in the liver. To our knowledge, this is the first quantitative assessment of the stability of TCIPP in tissues of humans or any other species. Further research is needed to confirm whether these biotransformation reactions are associated with a decrease or increase in toxicity.
Kinetic Study on Flooded Soil Recovery Using Soil Containing Arbuscular Mycorrhizal Fungi
Zainol N.
2016-01-01
Full Text Available The purpose of this research was to determine the kinetic parameters for flooded soil recovery via soil containing Arbuscular Mycorrhizal fungi (AMF. The general procedures of this experiment started by preparation of simulated flooded soil (FS and soil containing AMF (SA. Mixed soil was prepared by mixing FS and SA with ratio 1:1. Onion plant was chosen as a host plant and planted in the mixed soil for 14 days. The plantation was conducted in ambient temperature. The nutrients (nitrogen, phosphorus and potassium concentrations in the soil were tested using HACH Spectrophotomer. The Michaelis-Menten equation was used to study the nutrients recovery in soil. The Lineweaver-Bulk plot was used to solve the Michaelis-Menten equation. From the experiment conducted, the maximum nutrient uptake (Vmax and bonding affinity (Km obtained for nitrogen (N were 6.28mg/l.d and 82.17 mg/l, for phosphorus (P were 9.80 mg/l.d and 60.96 mg/l.d and for potassium (K were 0.07mg/l.d and 4.55mg/l. By comparing the result with other researcher, it showed that the Vmax and Km of nitrogen (N and phosphorus (P obtained were higher than other research. This was because the onion required a high level of N and P in the soil compared to other host plant.
Kinetic treatment of radiation reaction effects
Noble, Adam; Gratus, Jonathan; Burton, David; Ersfeld, Bernhard; Islam, M. Ranaul; Kravets, Yevgen; Raj, Gaurav; Jaroszynski, Dino
2011-05-01
Modern accelerators and light sources subject bunches of charged particles to quasiperiodic motion in extremely high electric fields, under which they may emit a substantial fraction of their energy. To properly describe the motion of these particle bunches, we require a kinetic theory of radiation reaction. We develop such a theory based on the notorious Lorentz-Dirac equation, and explore how it reduces to the usual Vlasov theory in the appropriate limit. As a simple illustration of the theory, we explore the radiative damping of Langmuir waves.
Reaction kinetic analysis of reactor surveillance data
Yoshiie, T.; Kinomura, A.; Nagai, Y.
2017-02-01
In the reactor pressure vessel surveillance data of a European-type pressurized water reactor (low-Cu steel), it was found that the concentration of matrix defects was very high, and a large number of precipitates existed. In this study, defect structure evolution obtained from surveillance data was simulated by reaction kinetic analysis using 15 rate equations. The saturation of precipitation and the growth of loops were simulated, but it was not possible to explain the increase in DBTT on the basis of the defect structures. The sub-grain boundary segregation of solutes was discussed for the origin of the DBTT increase.
Kinetics of Reaction Important in Oxygen Steelmaking
Coley, Kenneth S.; Chen, Elaine; Pomeroy, Michael
Recent work on modeling of BOF steelmaking is reviewed, highlighting the critical aspects of each approach. It is concluded that the most successful models should be based on a deep understanding of the mechanisms and kinetics of the critical reactions. The importance of the decarburization mechanism is discussed with particular reference to its role in droplet swelling or bloating which has a profound influence on the droplet residence time in the slag. Conditions which cause bloating are discussed and the rate determining step is proposed to be primarily nucleation of CO bubbles inside the metal droplet with some influence from growth by reaction at the bubble/metal interface. The discrepancy in the super-saturation ratio required for classical nucleation is discussed and an approach using a surface tension modifying parameter is illustrated. Finally, the role of CO nucleation in controlling the driving force for dephosphorization is discussed.
Löppmann, Sebastian; Blagodatskaya, Evgenia; Kuzyakov, Yakov
2014-05-01
Rhizosphere and detritusphere are soil microsites with very high resource availability for microorganisms affecting their biomass, composition and functions. In the rhizosphere low molecular compounds occur with root exudates and low available polymeric compounds, as belowground plant senescence. In detritusphere the substrate for decomposition is mainly a polymeric material of low availability. We hypothesized that microorganisms adapted to contrasting quality and availability of substrates in the rhizosphere and detritusphere are strongly different in affinity of hydrolytic enzymes responsible for decomposition of organic compounds. According to common ecological principles easily available substrates are quickly consumed by microorganisms with enzymes of low substrate affinity (i.e. r-strategists). The slow-growing K-strategists with enzymes of high substrate affinity are better adapted for growth on substrates of low availability. Estimation of affinity of enzyme systems to the substrate is based on Michaelis-Menten kinetics, reflecting the dependency of decomposition rates on substrate amount. As enzymes-mediated reactions are substrate-dependent, we further hypothesized that the largest differences in hydrolytic activity between the rhizosphere and detritusphere occur at substrate saturation and that these differences are smoothed with increasing limitation of substrate. Affected by substrate limitation, microbial species follow a certain adaptation strategy. To achieve different depth gradients of substrate availability 12 plots on an agricultural field were established in the north-west of Göttingen, Germany: 1) 4 plots planted with maize, reflecting lower substrate availability with depth; 2) 4 unplanted plots with maize litter input (0.8 kg m-2 dry maize residues), corresponding to detritusphere; 3) 4 bare fallow plots as control. Maize litter was grubbed homogenously into the soil at the first 5 cm to ensure comparable conditions for the herbivore and
Reaction rates for mesoscopic reaction-diffusion kinetics.
Hellander, Stefan; Hellander, Andreas; Petzold, Linda
2015-02-01
The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.
Reaction rates for mesoscopic reaction-diffusion kinetics
Hellander, Stefan; Hellander, Andreas; Petzold, Linda
2015-02-01
The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.
Kinetics of methane oxidation in selected mineral soils
Walkiewicz, A.; Bulak, P.; Brzeziñska, M.; Włodarczyk, T.; Polakowski, C.
2012-10-01
The kinetic parameters of methane oxidation in three mineral soils were measured under laboratory conditions. Incubationswere preceded by a 24-day preincubationwith 10%vol. of methane. All soils showed potential to the consumption of added methane. None of the soils, however, consumed atmospheric CH4. Methane oxidation followed the Michaelis-Menten kinetics, with relatively low values of parameters for Eutric Cambisol, while high values for Haplic Podzol, and especially for Mollic Gleysol which showed the highest methanotrophic activity and much lower affinity to methane. The high values of parameters for methane oxidation are typical for organic soils and mineral soils from landfill cover. The possibility of the involvement of nitrifying microorganisms, which inhabit the ammonia-fertilized agricultural soils should be verified.
Computer prediction system on solid/solid reaction kinetics
无
2001-01-01
A computer software system of kinetic predication of solid/solid reaction, KinPreSSR, was developed using Visual C++ and FoxPro. It includes two main modules, REACTION and DIFFUSION. KinPreSSR deals with the kinetics on the diffusion in solids as well as solid/solid reactions. The REACTION module in KinPreSSR was mainly described, which has organized the commonly recognized kinetic models, parameters, and employed both numerical and graphical methods for data analyses. The proper combination between the kinetic contents and the analytical methods enables users to use KinPreSSR for the evaluation and prediction of solid/solid reactions interested. As an example to show some of functions of KinPreSSR, the kinetics analysis for the reaction between SrCO3 and TiO2 powders to form SrTiO3 with a series of kinetic data from isothermal measurements was demonstrated.
Mathematics analysis of polymerase chain reaction kinetic curves.
Sochivko, D G; Fedorov, A A; Varlamov, D A; Kurochkin, V E; Petrov, R V
2016-01-01
The paper reviews different approaches to the mathematical analysis of polymerase chain reaction (PCR) kinetic curves. The basic principles of PCR mathematical analysis are presented. Approximation of PCR kinetic curves and PCR efficiency curves by various functions is described. Several PCR models based on chemical kinetics equations are suggested. Decision criteria for an optimal function to describe PCR efficiency are proposed.
Enzymatic Production of Ceramide from Sphingomyelin
Zhang, Long; Hellgren, Lars; Xu, Xuebing
activity. After seven recycles, immobilized enzyme retains around 70% of its initial activity. Through kinetic study, it has been found that the hydrolysis reactions catalyzed by both soluble and immobilized enzyme follow the Michaelis-Menten equation. The presentation will describe the research background...
Understanding Chemical Reaction Kinetics and Equilibrium with Interlocking Building Blocks
Cloonan, Carrie A.; Nichol, Carolyn A.; Hutchinson, John S.
2011-01-01
Chemical reaction kinetics and equilibrium are essential core concepts of chemistry but are challenging topics for many students, both at the high school and undergraduate university level. Visualization at the molecular level is valuable to aid understanding of reaction kinetics and equilibrium. This activity provides a discovery-based method to…
Degradation kinetics and metabolites in continuous biodegradation of isoprene.
Srivastva, Navnita; Singh, Ram S; Upadhyay, Siddh N; Dubey, Suresh K
2016-04-01
The kinetic parameters of isoprene biodegradation were studied in a bioreactor, comprising of bioscrubber and polyurethane foam packed biofilter in series and inoculated with Pseudomonas sp., using a Michaelis-Menten type model. The maximum elimination capacity, ECmax; substrate constant, Ks and ECmax/Ks values for bioscrubber were found to be 666.7 g m(-3) h(-1), 9.86 g m(-3) and 67.56 h(-1), respectively while those for biofilter were 3333 g m(-3) h(-1), 13.96 g m(-3) and 238.7 h(-1), respectively. The biofilter section exhibited better degradation efficiency compared to the bioscrubber unit. Around 62-75% of the feed isoprene got converted to carbon dioxide, indicating the efficient capability of bacteria to mineralize isoprene. The FTIR and GC-MS analyses of degradation products indicated oxidative cleavage of unsaturated bond of isoprene. These results were used for proposing a plausible degradation pathway for isoprene.
Kinetics of ozone-phenol reaction in aqueous solutions
Joshi, M.G.; Shambaugh, R.L.
1982-01-01
The kinetics of the reaction of ozone and phenol in aqueous medium was studied. The reaction was first order with respect to both ozone and phenol. The rate constant was found to increase with increase in the pH of the reaction mixture. Four different catalysts were examined for their effect on the rate of reaction. 30 refs.
Christley Scott
2010-07-01
Full Text Available Abstract Background Stochastic effects can be important for the behavior of processes involving small population numbers, so the study of stochastic models has become an important topic in the burgeoning field of computational systems biology. However analysis techniques for stochastic models have tended to lag behind their deterministic cousins due to the heavier computational demands of the statistical approaches for fitting the models to experimental data. There is a continuing need for more effective and efficient algorithms. In this article we focus on the parameter inference problem for stochastic kinetic models of biochemical reactions given discrete time-course observations of either some or all of the molecular species. Results We propose an algorithm for inference of kinetic rate parameters based upon maximum likelihood using stochastic gradient descent (SGD. We derive a general formula for the gradient of the likelihood function given discrete time-course observations. The formula applies to any explicit functional form of the kinetic rate laws such as mass-action, Michaelis-Menten, etc. Our algorithm estimates the gradient of the likelihood function by reversible jump Markov chain Monte Carlo sampling (RJMCMC, and then gradient descent method is employed to obtain the maximum likelihood estimation of parameter values. Furthermore, we utilize flux balance analysis and show how to automatically construct reversible jump samplers for arbitrary biochemical reaction models. We provide RJMCMC sampling algorithms for both fully observed and partially observed time-course observation data. Our methods are illustrated with two examples: a birth-death model and an auto-regulatory gene network. We find good agreement of the inferred parameters with the actual parameters in both models. Conclusions The SGD method proposed in the paper presents a general framework of inferring parameters for stochastic kinetic models. The method is
Generaux, Claudia N; Ainslie, Garrett R; Bridges, Arlene S; Ismail, Mohamed A; Boykin, David W; Tidwell, Richard R; Thakker, Dhiren R; Paine, Mary F
2013-02-01
DB868 [2,5-bis [5-(N-methoxyamidino)-2-pyridyl] furan], a prodrug of the diamidine DB829 [2,5-bis(5-amidino-2-pyridyl) furan], has demonstrated efficacy in murine models of human African trypanosomiasis. A cross-species evaluation of prodrug bioconversion to the active drug is required to predict the disposition of prodrug, metabolites, and active drug in humans. The phase I biotransformation of DB868 was elucidated using liver microsomes and sandwich-cultured hepatocytes from humans and rats. All systems produced four NADPH-dependent metabolites via O-demethylation (M1, M2) and N-dehydroxylation (M3, M4). Compartmental kinetic modeling of the DB868 metabolic pathway suggested an unusual N-demethoxylation reaction that was supported experimentally. A unienzyme Michaelis-Menten model described the kinetics of M1 formation by human liver microsomes (HLMs) (K(m), 11 μM; V(max), 340 pmol/min/mg), whereas a two-enzyme model described the kinetics of M1 formation by rat liver microsomes (RLMs) (K(m1), 0.5 μM; V(max1), 12 pmol/min/mg; K(m2), 27 μM; V(max2), 70 pmol/min/mg). Human recombinant CYP1A2, CYP3A4, and CYP4F2, rat recombinant Cyp1a2 and Cyp2d2, and rat purified Cyp4f1 catalyzed M1 formation. M2 formation by HLMs exhibited allosteric kinetics (S(50), 18 μM; V(max), 180 pmol/mg), whereas M2 formation by RLMs was negligible. Recombinant CYP1A2/Cyp1a2 catalyzed M2 formation. DB829 was detected in trace amounts in HLMs at the end of the 180-min incubation and was detected readily in sandwich-cultured hepatocytes from both species throughout the 24-h incubation. These studies demonstrated that DB868 biotransformation to DB829 is conserved between humans and rats. An improved understanding of species differences in the kinetics of DB829 formation would facilitate preclinical development of a promising antitrypanosomal prodrug.
Catalytic and Inhibitory Kinetic Behavior of Horseradish Peroxidase on the Electrode Surface
Titi Wang
2012-10-01
Full Text Available Enzymatic biosensors are often used to detect trace levels of some specific substance. An alternative methodology is applied for enzymatic assays, in which the electrocatalytic kinetic behavior of enzymes is monitored by measuring the faradaic current for a variety of substrate and inhibitor concentrations. Here we examine a steady-state and pre-steady-state reduction of H2O2 on the horseradish peroxidase electrode. The results indicate the substrate-concentration dependence of the steady-state current strictly obeys Michaelis-Menten kinetics rules; in other cases there is ambiguity, whereby he inhibitor-concentration dependence of the steady-state current has a discontinuity under moderate concentration conditions. For pre-steady-state phases, both catalysis and inhibition show an abrupt change of the output current. These anomalous phenomena are universal and there might be an underlying biochemical or electrochemical rationale.
Kinetics of Phosphatase of Regenerating Liver-3 (PRL-3) Inhibition by Small-molecular Inhibitors
无
2006-01-01
Phosphatase of Regenerating Liver-3 (PRL-3) is a newly identified colorectal cancer metastasis-related protein,which isa 22 kDa non-classical protein tyrosine phosphatase with a C-terminal prenylation motif. In this study, the inhibition kinetics of protein tyrosine phosphatases (PTPs) by a fluorescent substrate, 6,8-difluoro-4-methylumbelliferyl phosphate (DiFMUP) was evaluated. PRL-3 exhibits classical Michaelis-Menten kinetics with a vmax value of the inhibitor magnolol can cause Km to increase, but does not alter the vmax value, which suggests the competitive inhibition of PRL-3. At the same time, it was found that DiFMUP is a more sensitive substrate for PRL-3 than para-nitrophenyl phosphate(pNPP) that is more frequently used at present. Furthermore, the method of screening for PTPs by the use of DiFMUP was developed, which studied the acceptance of DiFMUP by other PTPs.
谢晶; 刘晓丹
2006-01-01
对香菇分别在273 K、283 K和293 K的密闭容器中氧气和二氧化碳随时间、浓度的变化进行了测定,根据酶动力学原理,利用非线性估计法、多重回归分析分别获得气体成分的变化率曲线和米式方程,从而获得相应的参数,求得反映呼吸状态的呼吸熵动态变化规律以及温度影响参数--活化能,并以此求出在任意温度、有氧呼吸气体环境条件下果蔬的最大呼吸速率,为气调包装系统设计提供理论依据.
Kinetic Study of the Heck Reaction: An Interdisciplinary Experiment
Gozzi, Christel; Bouzidi, Naoual
2008-01-01
The aim of this experiment is to study and calculate the kinetic constant of a Heck reaction: the arylation of but-3-en-2-ol by iodobenzene catalyzed by palladium acetate in presence of triethylamine in DMF. The reaction leads to a mixture of two ketones. Students use GC analysis to quantify reagents and products of reaction. They control the…
Complex kinetics of fluctuating enzymes: phase diagram characterization of a minimal kinetic scheme.
Min, Wei; Jiang, Liang; Xie, X Sunney
2010-05-03
Enzyme molecules are dynamic entities with stochastic fluctuation in both protein conformation and enzymatic activity. However, such a notion of fluctuating enzymes, best characterized by recent single-molecule experiments, was not considered in the classic Michaelis-Menten (MM) kinetic scheme. Here we incorporate the fluctuation concept into the reversible MM scheme, and solve analytically all the possible kinetics (i.e., substrate concentration dependent enzymatic velocity) for a minimal model of fluctuating enzymes. Such a minimal model is found to display a variety of distinct kinetic behaviors (phases) in addition to the classic MM kinetics; excess substrate inhibition, sigmoidal kinetics, and concave biphasic kinetics. We find that all these kinetic phases are interrelated and unified under the framework of fluctuating enzymes and can be adequately described by a phase diagram that consists of two master parameters. Functionally, substrate inhibition, sigmoidal kinetics, and convex biphasic phases exhibit positive cooperativity, whereas concave biphasic phases display negative cooperativity. Remarkably, all these complex kinetics are produced by fluctuating enzymes with single substrate binding site, but the two conformations are, therefore, fundamentally different from the classic MWC and KNF models that require multiple subunit or binding sites. This model also suggests that, for a given enzyme/substrate pair, the non-MM behaviors could undergo transitions among different kinetic phases induced by varying product concentrations, owing to the fundamental Haldane symmetry in the reversible MM scheme.
Complex Kinetics in the Reaction of Taurine with Aqueous Bromine ...
Complex Kinetics in the Reaction of Taurine with Aqueous Bromine and Acidic Bromate : A Possible Cytoprotective Role against Hypobromous Acid. ... toxicity of bromine and hypobromous acid in the slightly basic physiological environments.
A relativistic correlationless kinetic equation with radiation reaction fully incorporated
Lai, H. M.
1984-06-01
The Landau-Lifshitz expression for the Lorentz-Dirac equation is used to derive a relativistic correlationless kinetic equation for a system of electrons with radiation reaction fully incorporated. Various situations and possible applications are discussed.
The thermodynamic natural path in chemical reaction kinetics
Moishe garfinkle
2000-01-01
Full Text Available The Natural Path approach to chemical reaction kinetics was developed to bridge the considerable gap between the Mass Action mechanistic approach and the non-mechanistic irreversible thermodynamic approach. The Natural Path approach can correlate empirical kinetic data with a high degree precision, as least equal to that achievable by the Mass-Action rate equations, but without recourse mechanistic considerations. The reaction velocities arising from the particular rate equation chosen by kineticists to best represent the kinetic behavior of a chemical reaction are the natural outcome of the Natural Path approach. Moreover, by virtue of its thermodynamic roots, equilibrium thermodynamic functions can be extracted from reaction kinetic data with considerable accuracy. These results support the intrinsic validity of the Natural Path approach.
Moment equations for chromatography based on Langmuir type reaction kinetics.
Miyabe, Kanji
2014-08-22
Moment equations were derived for chromatography, in which the reaction kinetics between solute molecules and functional ligands on the stationary phase was represented by the Langmuir type rate equation. A set of basic equations of the general rate model of chromatography representing the mass balance, mass transfer rate, and reaction kinetics in the column were analytically solved in the Laplace domain. The moment equations for the first absolute moment and the second central moment in the real time domain were derived from the analytical solution in the Laplace domain. The moment equations were used for predicting the chromatographic behavior under hypothetical HPLC conditions. The influence of the parameters relating to the adsorption equilibrium and to the reaction kinetics on the chromatographic behavior was quantitatively evaluated. It is expected that the moment equations are effective for a detailed analysis of the influence of the mass transfer rates and of the Langmuir type reaction kinetics on the column efficiency.
Kinetics of Acid Reactions: Making Sense of Associated Concepts
Tan, Kim Chwee Daniel; Treagust, David F.; Chandrasegaran, A. L.; Mocerino, Mauro
2010-01-01
In chemical kinetics, in addition to the concepts related to kinetics, stoichiometry, chemical equilibrium and the characteristics of the reactants are often involved when comparing the rates of different reactions, making such comparisons very challenging for students at all levels, as well as for pre-service science teachers. Consequently, four…
Kinetics of the Exothermic Decomposition Reaction of s-Tripicryaminotrinitrobenzene
ZHAO Feng-qi; HU Rong-zu; GAO Hong-xu; LUO Yang; GAO Sheng-li; SONG Ji-rong; SHI Qi-zhen
2007-01-01
The kinetic parameters of the exothermic decomposition reaction of s-Tripicryaminotrinitrobenzene under linear temperature rise condition are studied by means of DSC. The results show that the empirical kinetic model function in difs-1, respectively. The critical temperature of thermal explosion of the compound is 267.36 ℃.
Belousov-Zhabotinsky oscillatory reaction. Kinetics of malonic acid decomposition
LJILJANA KOLAR-ANIC
2000-10-01
Full Text Available The kinetics of the Belousov-Zhabotinsky (BZ oscillatory reaction was analyzed. With this aim, the time evolution of a reaction mixture composed of malonic acid, bromate, sulfuric acid and cerium(III was studied at 298 K. Pseudo-first order kinetics with respect to malonic acid as the species undergoing decomposition with a corresponding rate constant, k = 7.5×10-3 min-1, was found.
pH wave-front propagation in the urea-urease reaction.
Wrobel, Magdalena M; Bánsági, Tamás; Scott, Stephen K; Taylor, Annette F; Bounds, Chris O; Carranza, Arturo; Carranzo, Arturo; Pojman, John A
2012-08-08
The urease-catalyzed hydrolysis of urea displays feedback that results in a switch from acid (pH ~3) to base (pH ~9) after a controllable period of time (from 10 to >5000 s). Here we show that the spatially distributed reaction can support pH wave fronts propagating with a speed of the order of 0.1-1 mm min(-1). The experimental results were reproduced qualitatively in reaction-diffusion simulations including a Michaelis-Menten expression for the urease reaction with a bell-shaped rate-pH dependence. However, this model fails to predict that at lower enzyme concentrations, the unstirred reaction does not always support fronts when the well-stirred reaction still rapidly switches to high pH.
Kinetics of Model Reactions for Interfacial Polymerization
Henry Hall
2012-02-01
Full Text Available To model the rates of interfacial polycondensations, the rates of reaction of benzoyl chloride and methyl chloroformate with various aliphatic monoamines in acetonitrile were determined at 25 °C. Buffering with picric acid slowed these extremely fast reactions so the rate constants could be determined from the rate of disappearance of picrate ion. The rates of the amine reactions correlated linearly with their Swain-Scott nucleophilicities.
2009-01-01
with phenyl acetate and paraoxonwere determined by Michaelis - Menten steady state kinetics . The data from four or more independent experiments were fit...paraoxon was followed atA412 for 20 min at room temperature as described above. The data were fit using Michaelis - Menten steady state kinetics to derive...for 4 h at room temperature as described above. The data were fit using Michaelis - Menten steady state kinetics to derive the KM and Vmax values of
Photocatalytic Water-Splitting Reaction from Catalytic and Kinetic Perspectives
Hisatomi, Takashi
2014-10-16
Abstract: Some particulate semiconductors loaded with nanoparticulate catalysts exhibit photocatalytic activity for the water-splitting reaction. The photocatalysis is distinct from the thermal catalysis because photocatalysis involves photophysical processes in particulate semiconductors. This review article presents a brief introduction to photocatalysis, followed by kinetic aspects of the photocatalytic water-splitting reaction.Graphical Abstract: [Figure not available: see fulltext.
Kinetic and molecular analyses reveal isoprene degradation potential of Methylobacterium sp.
Srivastva, Navnita; Vishwakarma, P; Bhardwaj, Y; Singh, A; Manjunath, K; Dubey, Suresh K
2017-10-01
Efforts were made to isolate and characterize bacteria capable of growing on methane and organic compounds, and to achieve the simultaneous degradation of more than one pollutant. Among the methanotrophs, species of Methylobacterium was able to catabolize a variety of hydrocarbons, including the branched-chain alkenes. Therefore, laboratory incubations experiments were carried out in batch mode to assess the potential of Methylobacterium sp. PV1 for degrading isoprene, the low-molecular-weight alkene, the most abundant non-methane volatile hydrocarbon present in the environment. Methylobacterium sp. PV1, isolated from paddy field soil, was characterized by pmoA and 16S rRNA gene sequencing and FAME analysis, and used for isoprene degradation. The kinetics of biodegradation is studied using the Michaelis-Menten model. The optimum degradation (80%) with maximum average relative degradation rate was observed at 150ppm isoprene. The degradation products were also analyzed using FTIR. Copyright © 2017 Elsevier Ltd. All rights reserved.
Effect of montmorillonite on kinetics of polyurethane preparation reaction
You Cao; Yu Jiang; Shu Lu Zhao; Xiao Jun Cai; Mei Long Hu; Bing Liao
2008-01-01
The prepolymerization and curing reaction kinetics of polyurethane/montmorillonite have been studied with end group analysisand FTIR respectively. It was found that the prepolymerization and curing reaction followed the 2nd-order kinetics. But theactivation energy of prepolymerization increased from 42.7 k J/mol to 56.5 k J/mol after the montmorillonite was added in thereaction system, and activation energy of curing reaction decreased from 64.4 kJ/mol to 17.5 k J/mol.
Russo, Karen Ann
Methacrylate-based monomers are routinely used in medical biomaterials. Monomers undergo polymerization reactions to form the solid resin. These polymerization reactions can be incomplete thus making unpolymerized monomer available for possible biodistribution. Understanding the fate of these monomers is essential not only for their toxicological profile but also for development of future biomaterials. Aromatic methacrylate-based monomers included in this study were bisphenol A dimethacrylate and bisphenol A diglycidyl dimethathacrylate; aliphatic methacrylate monomers were 2-hydroxyethyl methacrylate and triethyleneglycol dimethacrylate. These compounds contain ester moieties thought to be susceptible to esterase-mediated hydrolysis. The hypothesis was that the ester bond of the methacrylate monomers can be hydrolyzed by esterases and these reactions would occur in a measurable, time-dependent manner confirmed by specific Michaelis-Menten kinetic relationships. Including aliphatic and aromatic methacrylate monomers in this work allowed for structure-based comparisons. In vitro enzymolysis of the test compounds by acetylcholinesterase and cholesterol esterase was performed in buffered solutions. The hydrolysis reactions were monitored by high performance liquid chromatography with ultraviolet detection. The disappearance of parent compound and appearance of hydrolysis products were quantitated. The aromatic methacrylate monomers, bisphenol A dimethacrylate and bisphenol A diglycidyl dimethacrylate, were resistant to acetylcholine esterase hydrolysis but were converted by cholesterol esterase. The putative xenoestrogen, bisphenol A, was identified as a hydrolysis product from bisphenol A dimethacrylate conversion. Cholesterol esterase induced hydrolysis of bisphenol A diglycidyl dimethacrylate yielded a Km value of 1584 muM and Vmax of 14 muM min-1. Triethyleneglycol was converted by both esterases with calculated Km values of 394 and 1311 muM for acetylcholine
Reaction rates for reaction-diffusion kinetics on unstructured meshes
Hellander, Stefan; Petzold, Linda
2017-02-01
The reaction-diffusion master equation is a stochastic model often utilized in the study of biochemical reaction networks in living cells. It is applied when the spatial distribution of molecules is important to the dynamics of the system. A viable approach to resolve the complex geometry of cells accurately is to discretize space with an unstructured mesh. Diffusion is modeled as discrete jumps between nodes on the mesh, and the diffusion jump rates can be obtained through a discretization of the diffusion equation on the mesh. Reactions can occur when molecules occupy the same voxel. In this paper, we develop a method for computing accurate reaction rates between molecules occupying the same voxel in an unstructured mesh. For large voxels, these rates are known to be well approximated by the reaction rates derived by Collins and Kimball, but as the mesh is refined, no analytical expression for the rates exists. We reduce the problem of computing accurate reaction rates to a pure preprocessing step, depending only on the mesh and not on the model parameters, and we devise an efficient numerical scheme to estimate them to high accuracy. We show in several numerical examples that as we refine the mesh, the results obtained with the reaction-diffusion master equation approach those of a more fine-grained Smoluchowski particle-tracking model.
Reaction wheels for kinetic energy storage
Studer, P. A.
1984-01-01
In contrast to all existing reaction wheel implementations, an order of magnitude increase in speed can be obtained efficiently if power to the actuators can be recovered. This allows a combined attitude control-energy storage system to be developed with structure mounted reaction wheels. The feasibility of combining reaction wheels with energy storage wwheels is demonstrated. The power required for control torques is a function of wheel speed but this energy is not dissipated; it is stored in the wheel. The I(2)R loss resulting from a given torque is shown to be constant, independent of the design speed of the motor. What remains, in order to efficiently use high speed wheels (essential for energy storage) for control purposes, is to reduce rotational losses to acceptable levels. Progress was made in permanent magnet motor design for high speed operation. Variable field motors offer more control flexibility and efficiency over a broader speed range.
Development of Optimized Guidelines for Therapeutic Strategies for Organophosphate Poisoning
2011-03-01
Hoang, 1995). Metabolism is a complex mechanism, but is implemented into PBPK models in the form of zero order, first order, or Michaelis - Menten ...kinetics. The Vmax and Km required in the Michaelis - Menten equation are derived from in vitro and in vivo 22 measurements. Most PBPK models...metabolism occurs in the liver and follows Michaelis - Menten kinetics (Hoang, 1995). PBPK modeling of organophosphates The consideration of developing a
Modeling of Complex Mixtures: JP-8 Toxicokinetics
2008-10-01
diffusion, including metabolic loss via the cytochrome P-450 system, described by non-linear Michaelis - Menten kinetics as shown in the following...point. Inhalation and iv were the dose routes for the rat study. The modelers used saturable ( Michaelis - Menten ) kinetics as well as a second... Michaelis - Menten liver metabolic constants for n-decane have been measured (Km = 1.5 mg/L and Vmax = 0.4 mg/hour) using rat liver slices in a vial
A unifying kinetic framework for modeling oxidoreductase-catalyzed reactions
Chang, Ivan; Baldi, Pierre
2013-01-01
Motivation: Oxidoreductases are a fundamental class of enzymes responsible for the catalysis of oxidation–reduction reactions, crucial in most bioenergetic metabolic pathways. From their common root in the ancient prebiotic environment, oxidoreductases have evolved into diverse and elaborate protein structures with specific kinetic properties and mechanisms adapted to their individual functional roles and environmental conditions. While accurate kinetic modeling of oxidoreductases is thus imp...
Kinetic model for hydroisomerization reaction of C8-aromatics
Ouguan XU; Hongye SU; Xiaoming JIN; Jian CHU
2008-01-01
Based on the reported reaction networks, a novel six-component hydroisomerization reaction net-work with a new lumped species including C8-naphthenes and Cs-paraffins is proposed and a kinetic model for a commercial unit is also developed. An empirical catalyst deactivation function is incorporated into the model accounting for the loss in activity because of coke forma-tion on the catalyst surface during the long-term opera-tion. The Runge-Kutta method is used to solve the ordinary differential equations of the model. The reaction kinetic parameters are benchmarked with several sets of balanced plant data and estimated by the differential vari-able metric optimization method (BFGS). The kinetic model is validated by an industrial unit with sets of plant data under different operating conditions and simulation results show a good agreement between the model predic-tions and the plant observations.
The influence of gas-kinetic evolution on plasma reactions
Diver, D A; MacLachlan, C S; Potts, H E
2008-01-01
Plasmas in which there is a threshold for a dominant reaction to take place (such as recombination or attachment) will have particle distributions that evolve as the reaction progresses. The form of the Boltzmann collision term in such a context will cause the distribution to drift from its initial form, and so cause for example temperature fluctuations in the plasma if the distribution is originally Maxwellian. This behaviour will impact on the relevant reaction rates in a feedback loop that is missing from simple chemical kinetic descriptions since the plasma cannot be considered to be isothermal, as is the case in the latter approach. In this article we present a simple kinetic model that captures these essential features, showing how cumulative differences in the instantaneous species levels can arise over the purely chemical kinetic description, with implications for process yields and efficiencies.
The bainite reaction kinetics in austempered ductile iron
Taran, Yu.N.; Uzlov, K.I.; Kutsov, A.Yu. [State Metall. Acad., Dnepropetrovsk (Ukraine). Phys. Metall. Dept.
1997-11-01
Bainitic reaction kinetics in ductile iron contained according to Ukrainian standard (weight%) 3.60-3.80 carbon, 2.60-2.80 Si, {proportional_to}0.12 Mn, {proportional_to}0.60 Cu and additionally alloyed by Mo (0.15-0.20) has been studied. It was found that the overall transformation kinetics becomes slower as transformation temperature increase. This is because more intensive redistribution of carbon into austenite at higher temperatures. Two austenites with different carbon content have been fixed and kinetics of their lattices parameters has been studied. (orig.). 6 refs.
Julius Kwagh-Har Ikya
2014-02-01
Full Text Available The ability of Commercial Native Linamarase (CNLIN and Engineered Linamarase (GELIN extracts from Saccharomyces cerevisiae to hydrolyse cassava linamarin was challenged. CNLIN acting as control was used together with GELIN extracts from Saccharomyces cerevisiae to evaluate the kinetic data for test enzymes at pH 3.5, 6.8 and 10.5, respectively and ambient temperature (35°C. Data obtained from the varying activity versus substrate concentrations were fitted with the Michaelis-Menten plots and Lineweaver-Burk model to obtain maximum velocity (Vmax, affinity coefficient (Km, physiological efficiency (Vmax/Km and r2 (linear regressing coefficient. The results indicated that the engineered linamarase conferred different enzyme kinetic data showing degradation of cassava linamarin by CNLIN and GELIN from Saccharomyces cerevisiae at the optimum pH and temperature. The relation was best described by the characteristic sigmoid Michaelis-Menten plots and Lineweaver-Burk model evidence from the high coefficient of linear regression (r2>0.976. Vmax and Km derived from the Lineweaver-Burk model varied from 10.0 to 13.0 µmol/min and 0.5 to 0.9 &muM respectively for engineered enzymes and 0.0-10.0 mol/min and 0.0 to 0.9 &muM respectively for CNLIN. The kinetics profiles of the studied enzymes showed their actions on cassava linamarin were influenced by degree of genetic manipulation, purification and pH at ambient temperature. The wide pH tolerance in the degradation of linamarin suggests a possible use of the engineered linamarase from Saccharomyces cerevisiae in detoxifying linamarin in cassava for the production of cyanide-free cassava-based food products.
Interpolated lattice Boltzmann boundary conditions for surface reaction kinetics.
Walsh, S D C; Saar, M O
2010-12-01
This paper describes a method for implementing surface reaction kinetics in lattice Boltzmann simulations. The interpolated boundary conditions are capable of simulating surface reactions and dissolution at both stationary and moving solid-fluid and fluid-fluid interfaces. Results obtained with the boundary conditions are compared to analytical solutions for first-order and constant-flux kinetic surface reactions in a one-dimensional half space, as well as to the analytical solution for evaporation from the surface of a cylinder. Excellent agreement between analytical and simulated results is obtained for a wide range of diffusivities, lattice velocities, and surface reaction rates. The boundary model's ability to represent dissolution in binary fluid mixtures is demonstrated by modeling diffusion from a rising bubble and dissolution of a droplet near a flat plate.
Aslam, M.; Travis, R. L.; Huffaker, R. C.
1992-01-01
Nitrate and NO2- transport by roots of 8-day-old uninduced and induced intact barley (Hordeum vulgare L. var CM 72) seedlings were compared to kinetic patterns, reciprocal inhibition of the transport systems, and the effect of the inhibitor, p-hydroxymercuribenzoate. Net uptake of NO3- and NO2- was measured by following the depletion of the ions from the uptake solutions. The roots of uninduced seedlings possessed a low concentration, saturable, low Km, possibly a constitutive uptake system, and a linear system for both NO3- and NO2-. The low Km system followed Michaelis-Menten kinetics and approached saturation between 40 and 100 micromolar, whereas the linear system was detected between 100 and 500 micromolar. In roots of induced seedlings, rates for both NO3- and NO2- uptake followed Michaelis-Menten kinetics and approached saturation at about 200 micromolar. In induced roots, two kinetically identifiable transport systems were resolved for each anion. At the lower substrate concentrations, less than 10 micromolar, the apparent low Kms of NO3- and NO2- uptake were 7 and 9 micromolar, respectively, and were similar to those of the low Km system in uninduced roots. At substrate concentrations between 10 and 200 micromolar, the apparent high Km values of NO3- uptake ranged from 34 to 36 micromolar and of NO2- uptake ranged from 41 to 49 micromolar. A linear system was also found in induced seedlings at concentrations above 500 micromolar. Double reciprocal plots indicated that NO3- and NO2- inhibited the uptake of each other competitively in both uninduced and induced seedlings; however, Ki values showed that NO3- was a more effective inhibitor than NO2-. Nitrate and NO2- transport by both the low and high Km systems were greatly inhibited by p-hydroxymercuribenzoate, whereas the linear system was only slightly inhibited.
Diagnostic Appraisal of Grade 12 Students' Understanding of Reaction Kinetics
Yan, Yaw Kai; Subramaniam, R.
2016-01-01
The study explored grade 12 students' understanding of reaction kinetics, a topic which has not been extensively explored in the chemistry education literature at this level. A 3-tier diagnostic instrument with 11 questions was developed--this format is of very recent origin and has been the subject of only a handful of studies. The findings…
REACTION KINETICS OF CA-BASED SORBENTS WITH HC1
The kinetics of the reaction between CaO and HCl were investigated under conditions that minimize bulk mass transfer and pore diffusion limitations. Reactivity data from 0.2- to 1-s exposure to 5000 ppm HCl in a fixed bed reactor were analyzed by a shrinking core model of diffusi...
Reaction kinetics of fluorite in flow systems and surface chemistry
张荣华; 胡书敏
1996-01-01
The kinetic experiments of fluorite in water-HCl solution in an open-flow system at the temperatures ≤100℃ reveal that the variation of flow rate (U) can change the reaction rate orders from 0 to 2 or higher. In the far from equilibrium systems, the dissolution rates of fluorite in aqueous solutions have a zero order.The reaction rates are controlled by pH values of input solutions. In fact, the reaction rates are related to the concentrations of the active sites occupied by H+ on fluorite surface [SOH]. X-ray photospectroscopy observations on fluorite surface before and after reaction indicate that surface chemical processes control the reaction rates: Cl- cations attach on and enter into surface of fluorite besides H+ when fluorites react with HCl solutions, which affect the reaction rates.
Developing the reaction kinetics for a biodiesel reactor.
Slinn, Matthew; Kendall, Kevin
2009-04-01
The aim of this paper was to investigate the kinetics of the biodiesel reaction in order to find out how best to reach 96.5% methyl ester. The purity of the biodiesel product was examined using gas chromatography to the EN14214 FAME standard and real-time optical microscopy was used to observe the reaction. The problem was the reaction does not reach completion and the mechanism is not understood. It was observed that droplet size had a major influence on reaction end point and that the reaction was mass-transfer limited. This observation was confirmed by developing a mass-transfer based reaction model using the data from the batch reactor which agreed with results from other researchers. The model predicted better conversion with more mixing intensity. The results show that significant improvements could be made to the conventional FAME process.
Thermodynamic Basis for the Emergence of Genomes during Prebiotic Evolution
2012-05-01
affected by the action of polymerases. If one ignores the reverse reaction under the condition of ½PPi?0, the Michaelis - Menten kinetics applies for the...spontaneity of changes. Following a recent theoretical approach, we applied the quasispecies theory combined with kinetic /thermodynamic descriptions of...RNA replication to analyze the collective behavior of RNA replicators based on known experimental kinetics data. We find that, with increasing fidelity
Evaluation of true kinetic parameters for reversible immobilized enzyme reactions
Ishikawa, H.; Tanaka, T.; Kurose, K.; Hikita, H.
1987-06-01
For a reversible one-substrate reaction system that follows the Haldane reaction mechanism, a new and effective method has been proposed to extract true or intrinsic kinetic parameters of immobilized enzymes from diffusion limited rate data. The method utilizes the effectiveness factors correlated in terms of the general modulus defined by Aris and Bischoff, and a new modulus defined in the present study. It requires a trial-and-error calculation, but only a few data points. Furthermore, it provides a saving of materials such as substrates and enzymes, and takes less time for experiments compared to the initial rate methods. The usefulness of the method is demonstrated by determining the kinetic parameters for membrane bound fumarase which catalyzes the reaction of the conversion of fumarate to L-malate, for which the equilibrium constant is circa 4. (Refs. 20).
Reaction Mechanism Generator: Automatic construction of chemical kinetic mechanisms
Gao, Connie W.; Allen, Joshua W.; Green, William H.; West, Richard H.
2016-06-01
Reaction Mechanism Generator (RMG) constructs kinetic models composed of elementary chemical reaction steps using a general understanding of how molecules react. Species thermochemistry is estimated through Benson group additivity and reaction rate coefficients are estimated using a database of known rate rules and reaction templates. At its core, RMG relies on two fundamental data structures: graphs and trees. Graphs are used to represent chemical structures, and trees are used to represent thermodynamic and kinetic data. Models are generated using a rate-based algorithm which excludes species from the model based on reaction fluxes. RMG can generate reaction mechanisms for species involving carbon, hydrogen, oxygen, sulfur, and nitrogen. It also has capabilities for estimating transport and solvation properties, and it automatically computes pressure-dependent rate coefficients and identifies chemically-activated reaction paths. RMG is an object-oriented program written in Python, which provides a stable, robust programming architecture for developing an extensible and modular code base with a large suite of unit tests. Computationally intensive functions are cythonized for speed improvements.
Reaction kinetics of cellulose hydrolysis in subcritical and supercritical water
Olanrewaju, Kazeem Bode
The uncertainties in the continuous supply of fossil fuels from the crisis-ridden oil-rich region of the world is fast shifting focus on the need to utilize cellulosic biomass and develop more efficient technologies for its conversion to fuels and chemicals. One such technology is the rapid degradation of cellulose in supercritical water without the need for an enzyme or inorganic catalyst such as acid. This project focused on the study of reaction kinetics of cellulose hydrolysis in subcritical and supercritical water. Cellulose reactions at hydrothermal conditions can proceed via the homogeneous route involving dissolution and hydrolysis or the heterogeneous path of surface hydrolysis. The work is divided into three main parts. First, the detailed kinetic analysis of cellulose reactions in micro- and tubular reactors was conducted. Reaction kinetics models were applied, and kinetics parameters at both subcritical and supercritical conditions were evaluated. The second major task was the evaluation of yields of water soluble hydrolysates obtained from the hydrolysis of cellulose and starch in hydrothermal reactors. Lastly, changes in molecular weight distribution due to hydrothermolytic degradation of cellulose were investigated. These changes were also simulated based on different modes of scission, and the pattern generated from simulation was compared with the distribution pattern from experiments. For a better understanding of the reaction kinetics of cellulose in subcritical and supercritical water, a series of reactions was conducted in the microreactor. Hydrolysis of cellulose was performed at subcritical temperatures ranging from 270 to 340 °C (tau = 0.40--0.88 s). For the dissolution of cellulose, the reaction was conducted at supercritical temperatures ranging from 375 to 395 °C (tau = 0.27--0.44 s). The operating pressure for the reactions at both subcritical and supercritical conditions was 5000 psig. The results show that the rate-limiting step in
Comparative kinetic analysis of two fungal β-glucosidases
Casanave Dominique
2010-02-01
Full Text Available Abstract Background The enzymatic hydrolysis of cellulose is still considered as one of the main limiting steps of the biological production of biofuels from lignocellulosic biomass. It is a complex multistep process, and various kinetic models have been proposed. The cellulase enzymatic cocktail secreted by Trichoderma reesei has been intensively investigated. β-glucosidases are one of a number of cellulolytic enzymes, and catalyze the last step releasing glucose from the inhibitory cellobiose. β-glucosidase (BGL1 is very poorly secreted by Trichoderma reesei strains, and complete hydrolysis of cellulose often requires supplementation with a commercial β-glucosidase preparation such as that from Aspergillus niger (Novozymes SP188. Surprisingly, kinetic modeling of β-glucosidases lacks reliable data, and the possible differences between native T. reesei and supplemented β-glucosidases are not taken into consideration, possibly because of the difficulty of purifying BGL1. Results A comparative kinetic analysis of β-glucosidase from Aspergillus niger and BGL1 from Trichoderma reesei, purified using a new and efficient fast protein liquid chromatography protocol, was performed. This purification is characterized by two major steps, including the adsorption of the major cellulases onto crystalline cellulose, and a final purification factor of 53. Quantitative analysis of the resulting β-glucosidase fraction from T. reesei showed it to be 95% pure. Kinetic parameters were determined using cellobiose and a chromogenic artificial substrate. A new method allowing easy and rapid determination of the kinetic parameters was also developed. β-Glucosidase SP188 (Km = 0.57 mM; Kp = 2.70 mM has a lower specific activity than BGL1 (Km = 0.38 mM; Kp = 3.25 mM and is also more sensitive to glucose inhibition. A Michaelis-Menten model integrating competitive inhibition by the product (glucose has been validated and is able to predict the
Autocatalysis-driven clock reaction II: kinetics of the pentathionate-periodate reaction.
Xu, Li; Horváth, Attila K
2014-10-23
The pentathionate-periodate reaction has been investigated by spectrophotometrically monitoring the total amount of iodine evolved in the presence of phosphoric acid/dihydrogen phosphate buffer at 468 nm. The majority of the main characteristics of the title system is very reminiscent of that found recently in the pentathionate-iodate reaction, a system that led us to classify generally the clock reactions. Along with the pentathionate-iodate reaction the title system is proposed to belong to the autocatalysis-driven clock reactions as well. The kinetic model of the pentathionate-iodate system published recently was implemented by the necessary reactions of periodate to compose a 24-step kinetic model in which the mechanisms of the pentathionate-iodine, pentathionate-iodate, bisulfite-periodate, bisulfite-iodate, iodide-periodate, and the well-known Dushman reactions are combined. A thorough analysis revealed that the direct pentathionate-periodate reaction plays a role only to produce iodide ion via a finite sequence of reactions, and once its concentration reaches a certain level, the reaction is almost exclusively governed by the pentathionate-iodine, the iodide-periodate, and the Dushman reactions. As expected strong catalytic effect of the buffer composition is also found that can readily be explained by its well-known catalytic influence on the Dushman reaction.
Study on the kinetics of saccharifying enzymes of Luzhou-flavor daqu%浓香型大曲糖化动力学研究
任飞; 张晓宇
2013-01-01
In order to study on the kinetics of saccharifying enzymes of Luzhou-flavor Daqu, using the enzymes of 5% Daqu hydrolyzed soluble starch, at pH 4. 6, 30℃ , an Michaelis-Menten equation was deduced. The optimum pH value for the catalysis of saccharifying enzymes of Luzhou-flavor Daqu was 6. 0. Studying the catalytic reaction rate under different temperatures, the calculation results showed that the activation energy of the enzyme catalytic reaction was 40. 966 kJ/mol. The kinetics of saccharifying enzymes of Luzhou-fla-vor Daqu was similar to a single enzyme, During the production of Luzhou-flavor liquor, it will contribute to manage the saccharification and fermentation process simultaneously by controlling the conditions of pits input into the cellar, such as the concentration of starch and starter, initial acidity and temperature.%为研究浓香型大曲的糖化动力学,用5％的大曲浸出液水解可溶性淀粉,在pH4.6、30℃的条件下,用菲林试剂法测定还原糖的含量,得出米氏方程；浓香型大曲糖化反应的最适pH值为6.0；在不同温度下测定糖化反应速率,计算得到活化能E为40.966 kJ/mol.试验证明,浓香型大曲糖化酶类的糖化反应动力学与单一酶相似.通过控制淀粉浓度(投粮量)、用曲量、入窖酸度和温度可以使浓香型大曲酒的糖化、发酵过程协调进行.
Privman, Eve; Venton, B Jill
2015-11-01
Dopamine release and uptake have been studied in the Drosophila larval ventral nerve cord (VNC) using optogenetics to stimulate endogenous release. However, other areas of the central nervous system remain uncharacterized. Here, we compare dopamine release in the VNC and protocerebrum of larval Drosophila. Stimulations were performed with CsChrimson, a new, improved, red light-activated channelrhodopsin. In both regions, dopamine release was observed after only a single, 4 ms duration light pulse. Michaelis-Menten modeling was used to understand release and uptake parameters for dopamine. The amount of dopamine released ([DA]p ) on the first stimulation pulse is higher than the average [DA]p released from subsequent pulses. The initial and average amount of dopamine released per stimulation pulse is smaller in the protocerebrum than in the VNC. The average Vmax of 0.08 μM/s in the protocerebrum was significantly higher than the Vmax of 0.05 μM/s in the VNC. The average Km of 0.11 μM in the protocerebrum was not significantly different from the Km of 0.10 μM in the VNC. When the competitive dopamine transporter (DAT) inhibitor nisoxetine was applied, the Km increased significantly in both regions while Vmax stayed the same. This work demonstrates regional differences in dopamine release and uptake kinetics, indicating important variation in the amount of dopamine available for neurotransmission and neuromodulation. We use a new optogenetic tool, red light activated CsChrimson, to stimulate the release of dopamine in the ventral nerve cord and medial protocerebrum of the larval Drosophila central nervous system. We monitored extracellular dopamine by fast scan cyclic voltammetry and used Michaelis-Menten modeling to probe the regulation of extracellular dopamine, discovering important similarities and differences in these two regions.
Nanoconfinement effects: glucose oxidase reaction kinetics in nanofluidics.
Wang, Chen; Sheng, Zhen-Huan; Ouyang, Jun; Xu, Jing-Juan; Chen, Hong-Yuan; Xia, Xing-Hua
2012-02-01
Size-tunable nanofluidic devices coupled to an electrochemical detector have been designed and then used to study glucose oxidase (GOx) reaction kinetics confined in nanospaces. The devices are fabricated via a photochemical decomposition reaction, which forms nanochannels covered with carboxyl groups. The generated carboxyl groups enable us to chemically pattern biological molecules on the polymer surfaces via covalent bonding. With this approach, the activity of the immobilized biological molecules confined in nanospaces with different sizes has been investigated. GOx species are chemically immobilized on the surface of the nanochannels, catalyzing the oxidation of substrate glucose as it flows through the channels. The enzyme reaction product, hydrogen peroxide, passing through the nanochannels, reaches an electrochemical detector, giving rise to an increase in anodic current. This steady-state electrochemical current, which responds to various glucose concentrations, can be used to evaluate the GOx activity under confinement conditions. The results show significant nanoconfinement effects that are dependent on the channel size where the reaction occurs, demonstrating the importance of spatial confinement on the GOx reaction kinetics. The present approach provides an effective method for the study of enzyme activity and other bioassay systems, such as cell assays, drug discovery, and clinical diagnosis. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Kinetics of the reversible reaction of struvite crystallisation.
Crutchik, D; Garrido, J M
2016-07-01
The crystallisation of struvite could be a sustainable and economical alternative for recovering phosphorus from wastewater streams with high phosphate concentrations. Knowledge regarding the kinetics and thermodynamics that are involved in the crystallisation of struvite is the key to determine the optimal conditions for obtaining an efficient process. This study was conducted in a continuous stirred batch reactor. Different sets of experiments were performed in which struvite was either dissolved (undersaturated) or precipitated (oversaturated). These experiments were conducted at different temperatures (25, 30 and 35 °C) and pH values (8.2, 8.5 and 8.8) to determine the kinetics of struvite precipitation and dissolution. Struvite crystallisation was modelled as a reversible reaction. The kinetic rate parameters of struvite precipitation were 1.03·10(-4), 1.25·10(-4) and 1.54·10(-4) mol m(-2) min(-1) at 25, 30 and 35 °C, respectively. Similar kinetic rate parameters were determined for struvite dissolution. Struvite heterogeneous crystallisation can be represented by a first-order kinetic model that fitted well the experimental data.
Kinetics of oxytetracycline reaction with a hydrous manganese oxide.
Rubert, Kennedy F; Pedersen, Joel A
2006-12-01
Tetracycline antibiotics comprise a class of broad spectrum antimicrobial agents finding application in human therapy, animal husbandry, aquaculture, and fruit crop production. To better understand the processes affecting these antibiotics in soils and sediments, the kinetics of oxytetracycline transformation by a hydrous manganese oxide (MnO2) were investigated as a function of reactant concentration, pH, and temperature. Oxytetracycline was rapidly degraded by MnO2. Initial reaction rates exhibited pronounced pH-dependence, increasing as pH decreased. Reaction of oxytetracycline with MnO2 was accompanied by generation of Mn(II) ions, suggesting oxidative transformation of the antibiotic. At pH 5.6, apparent reaction orders for oxytetracycline and MnO2 were 0.7 and 0.8. Reaction order with respect to H+ was 0.6 between pH 4 and 9. Initial reaction rates increased by a factor of approximately 2.4 for 10 degrees C temperature increases; the apparent activation energy (60 kJ x mol(-1)) was consistent with a surface-controlled reaction. Reactivity of tetracycline antibiotics toward MnO2 increased in the following order: rolitetracyline oxytetracycline manganese oxides in soils and sediments are likely to promote appreciable degradation of tetracycline antibiotics, and that reaction rates are strongly dependent on reaction time scale and solution conditions.
Kinetics and mechanism of the chlorine dioxide-trithionate reaction.
Cseko, György; Horváth, Attila K
2012-03-22
The trithionate-chlorine dioxide reaction has been studied spectrophotometrically in a slightly acidic medium at 25.0 ± 0.1 °C in acetate/acetic acid buffer monitoring the decay of chlorine dioxide at constant ionic strength (I = 0.5 M) adjusted by sodium perchlorate. We found that under our experimental conditions two limiting stoichiometries exist and the pH, the concentration of the reactants, and even the concentration of chloride ion affects the actual stoichiometry of the reaction that can be augmented by an appropriate linear combination of these limiting processes. It is also shown that although the formal kinetic order of trithionate is strictly one that of chlorine dioxide varies between 1 and 2, depending on the actual chlorine dioxide excess and the pH. Moreover, the otherwise sluggish chloride ion, which is also a product of the reaction, slightly accelerates the initial rate of chlorine dioxide consumption and may therefore act as an autocatalyst. In addition to that, overshoot-undershoot behavior is also observed in the [(·)ClO(2)]-time curves in the presence of chloride ion at chlorine dioxide excess. On the basis of the experiments, a 13-step kinetic model with 6 fitted kinetic parameter is proposed by nonlinear parameter estimation. © 2012 American Chemical Society
A robust methodology for kinetic model parameter estimation for biocatalytic reactions
Al-Haque, Naweed; Andrade Santacoloma, Paloma de Gracia; Lima Afonso Neto, Watson;
2012-01-01
Effective estimation of parameters in biocatalytic reaction kinetic expressions are very important when building process models to enable evaluation of process technology options and alternative biocatalysts. The kinetic models used to describe enzyme-catalyzed reactions generally include several...
Funk, M; Gath, I; Seidel, A; Platt, K L; Oesch, F; Zeller, H D
1994-02-09
The enzyme-catalysed conjugation of each of the four stereoisomers of trans-3,4-dihydroxy-1,2-epoxy-1,2,3,4-tetrahydrobenzo[c]phenanthrene (B[c]PhDE) with glutathione (GSH) by HTP II, a novel isolated mu-class GSH transferase from the liver of untreated rat, was studied. All four stereoisomers were substrates for GSH transferase HTP II. The enzymatic reaction shows three different types of enzyme kinetics: substrate inhibition for (-)-anti-B[c]PhDE with (R,S,S,R)-absolute configuration, allosteric behavior using (+)-anti-B[c]PhDE with (S,R,R,S)-absolute configuration and Henri-Michaelis-Menten kinetics with both the (-)-syn- and (+)-syn-enantiomers, with (S,R,S,R)- and (R,S,R,S)-absolute configuration, respectively. When the concentration of these diolepoxides was varied (using 2 mM GSH), the apparent Vmax values were 1975 nmol/min x mg for (-)-anti-B[c]PhDE and about 60 nmol/min x mg for both (-)-syn- and (+)-syn-B[c]PhDE, with the corresponding Km values of 1.05 and 0.20 mM. The reaction of (+)-anti-B[c]PhDE determined by applying the Hill equation had an estimated Vmax value of 930 nmol/min x mg. On varying the concentration of GSH, linear Lineweaver-Burk plots were obtained. No competitive effect could be observed using a mixture of (-)-anti- and (+)-anti-enantiomers, indicating that their binding sites are different and independent. It was also shown, that the binding sites of (+)-anti- and both syn-enantiomers were different and independent of each other, while there was a small effect on the binding of the syn-enantiomers caused by (-)-anti-B[c]PhDE. All products of the reaction between GSH and the dihydrodiol epoxides of benzo[c]phenanthrene could be resolved by HPLC and were identified and quantitated using the corresponding synthetic GSH conjugates.
Reaction Path Optimization with Holonomic Constraints and Kinetic Energy Potentials.
Brokaw, Jason B; Haas, Kevin R; Chu, Jhih-Wei
2009-08-11
Two methods are developed to enhance the stability, efficiency, and robustness of reaction path optimization using a chain of replicas. First, distances between replicas are kept equal during path optimization via holonomic constraints. Finding a reaction path is, thus, transformed into a constrained optimization problem. This approach avoids force projections for finding minimum energy paths (MEPs), and fast-converging schemes such as quasi-Newton methods can be readily applied. Second, we define a new objective function - the total Hamiltonian - for reaction path optimization, by combining the kinetic energy potential of each replica with its potential energy function. Minimizing the total Hamiltonian of a chain determines a minimum Hamiltonian path (MHP). If the distances between replicas are kept equal and a consistent force constant is used, then the kinetic energy potentials of all replicas have the same value. The MHP in this case is the most probable isokinetic path. Our results indicate that low-temperature kinetic energy potentials (optimization and can significantly reduce the required steps of minimization by 2-3 times without causing noticeable differences between a MHP and MEP. These methods are applied to three test cases, the C7eq-to-Cax isomerization of an alanine dipeptide, the (4)C1-to-(1)C4 transition of an α-d-glucopyranose, and the helix-to-sheet transition of a GNNQQNY heptapeptide. By applying the methods developed in this work, convergence of reaction path optimization can be achieved for these complex transitions, involving full atomic details and a large number of replicas (>100). For the case of helix-to-sheet transition, we identify pathways whose energy barriers are consistent with experimental measurements. Further, we develop a method based on the work energy theorem to quantify the accuracy of reaction paths and to determine whether the atoms used to define a path are enough to provide quantitative estimation of energy barriers.
M Iyan Sofyan
2004-12-01
Full Text Available The objectives of this research were: 1 to determine aeration rate and substrate concentration of pure cellulose to produce maximum glucose by Trichoderma reesei QM 9414 at 30 oC, and agitation 150 rpm; 2 to study the kinetics of pure cellulose fermentation by Trichoderma reesei QM 9414 to glucose and its implication upon fermentation of the lignin free rice straw. The experiment was arranged in factorial randomized complete design in three times replication. Treatments consisted of three levels of aeration (1,00 vvm; 1,5 vvm; 2,0 vvm and three levels of substrate concentration (0,75 ; 1,00 ; 1,25 % w/v. The results showed that at the exponential phase the average specific growth of Trichoderma reesei QM 9414 was 0,05374 hour-1, the maximum glucose product concentration of pure cellulose was 0.1644 gL-1,and the oxygen transfer was 0,0328 mg L-1 hour-1. According to t-test, the kinetics of pure cellulose fermentation model just the same as the lignin free rice straw fermentation.The enzymes produced by Trichoderma reesei QM 9414 in pure cellulose fermentation media followed the Michaelis-Menten model. The enzyme kinetic parameters were the maximum growth rate was 37x10-3 hour-1 and Michaelis-Menten constant was Ã‚Â½ maximum μ =17,5x10-3 hour-1. The volumetric oxygen transfer (KLa using rice straw was 0,0337 mg.hour-1. The value of KLa could be used for conversion from bioreactor at laboratory scale to commercial scale design.
The Impact of Deviation from Michaelis-Menten Saturation on Mathematical Model Stability Properties
Blackwell, Charles; Kliss, Mark (Technical Monitor)
1998-01-01
Based on purely abstract ecological theory, it has been argued that a system composed of two or more consumers competing for the same resource cannot persist. By analysis on a Monod format mathematical model, Hubble and others demonstrated that this assertion is true for all but very special cases of such competing organisms which are determined by an index formed by a grouping of. the parameters which characterize the biological processes of the competing organisms. In the laboratory, using a bioreactor, Hansen and Hubble obtained confirmatory results for several cases of two competing species, and they characterized it as "qualitative confirmation" of the assertion. This result is amazing, since the analysis required the exact equality of the hey index, and it seems certain that no pair of organism species could have exactly equal values. It is quite plausible, however, that pairs of organism species could have approximately equal indices, and the question of how different they could be and still have coexistence of the two (or more) presents itself. In this paper, the pursuit of this question and a compatible resolution is presented.
Estimation of Michaelis-Menten constant of efflux transporter considering asymmetric permeability.
Sugano, Kiyohiko; Shirasaka, Yoshiyuki; Yamashita, Shinji
2011-10-14
It was previously reported that the apparent K(m) values of P-gp in apical to basal (A to B) and basal to apical (B to A) directions were different. The purpose of the present study was to derive a theoretical framework by which this asymmetric concentration-permeability profile can be explained using a single intrinsic K(m) value. A three compartment model was used to represent the apical, cytosol and basal compartments. The difference of passive permeability and the surface areas between the apical and basolateral membrane were explicitly taken into account. Applying the steady state approximation and considering the mass balance in the cytosol compartment, an open analytical solution was obtained. By using this equation, the asymmetric concentration-permeability profile was appropriately reproduced. In addition, the expression level dependency of apparent K(m) was also reproduced. Copyright © 2011 Elsevier B.V. All rights reserved.
Estudio de bioequivalencia de teofilina considerando cinética de Michaelis-Menten
Fagiolino, Pietro; Turlier, M.; Payssé, Helena; Aiache, Jean-Marc
1994-01-01
Se presenta un estudio de bioequivalencia de dos formas farmacéuticas de Teofilina de liberación prolongada, teniendo en cuenta la cinética no lineal de eliminación de esta droga. Una dosis de 300 mg de Teofilina fue administrada a 12 voluntarios sanos, en un diseno aleatorio, cruzado y compensado. Se utilizó una forma farmacéutica elixir, a los efectos de estimar los parámetros farmacocinéticos de eliminación en cada individuo. Como parámetros de evaluación de la biodisponibilidad se utilizó...
Kinetics and Mechanisms of Calcite Reactions with Saline Waters
Gorman, Brian P [Colorado School of Mines, Golden, CO (United States)
2015-09-02
Project Description: The general objective of the proposed research is to determine the kinetics and mechanisms of calcite reactions with saline waters over a wide range of saline water composition, pCO_{2}, and modest ranges in T and P. This will be accomplished by studying both reaction rates and solubility from changes in solution chemistry, and making nanoscale observations of calcite precipitate surface morphology and composition at the micro-to-nano-scale to provide an understanding of controlling reaction mechanisms and pathways. The specific objectives necessary to reach the general objective are: a) determination of how pCO_{2}, Ca^{2+}, ionic strength and “foreign” ions influence reaction rates; and b) investigate the influence of these parameters on apparent kinetic solubility from dissolution and precipitation reactions. This information will clearly be central to the construction of reliable reaction-transport models to predict reservoir and formation response to increased CO_{2} in saline waters. This program was initially collaborative with John Morse at Texas A&M, however his passing shortly after the beginning of this program resulted in abbreviated research time and effort. Summary of Results: Early studies using electron microscopy and spectroscopy indicated that carbonate precipitation from natural seawater (NSW) conditions onto aragonite substrates was mediated by a surface amorphous calcium carbonate layer. It was hypothesized that this ACC layer (observed after < 5days reaction time) was responsible for the abnormal reaction kinetics and also served as a metastable seed layer for growth of epitaxial aragonite. Further studies of the ACC formation mechanism indicated a strong dependence on the Mg concentration in solution. Subsequent studies at shorter times (10 hrs) on calcite substrates and in a wide range of supersaturation conditions did not indicate any ACC layer. Instead, an epitaxial layer by layer
Variation of kinetic isotope effect in multiple proton transfer reactions
B Saritha; M Durga Prasad
2012-01-01
Recently, we had suggested that the motion along the promoter mode in the first part of the IRC of proton transfer reaction enhances the delocalization of electrons on the acceptor atom into the * orbital of the donor-hydrogen covalent bond, and as a consequence weakens it. This leads to a reduction of the barrier to the proton transfer as well as the stretching frequency of donor-hydrogen bond. An extension of this to the concerted multiple proton transfer reactions implies that the kinetic isotope effect in such reaction depends exponentially on the number of protons that are being transferred. Computational evidence on three systems, (HF)3, formic acid dimer, and (H2O) clusters is provided to support this assertion.
Kipriyanov, Alexander A; Kipriyanov, Alexey A; Doktorov, Alexander B
2010-11-07
The applicability of the Encounter Theory (ET) (the prototype of the Collision Theory) concepts for widely occurring diffusion assisted irreversible bulk reaction A+B→C (for example, radical reaction) in dilute solutions with arbitrary ratio of initial concentrations of reactants has been treated theoretically with modern many-particle method for the derivation of non-Markovian binary kinetic equations. The method shows that, just as in the reaction A+A→C considered earlier, the agreement with the Encounter Theory is observed when the familiar Integral Encounter Theory is used which is just a step in the derivation of kinetic equations in the framework of the method employed. It allows for two-particle correlations only, and fails to consider the correlation of reactant simultaneously with a partner and with a reactant in the bulk. However, the next step leading to the Modified Encounter Theory under reduction of equations to a regular form both extends the time applicability interval of ET homogeneous rate equation (as for reactions proceeding in excess of one of the reactants), and yields the inhomogeneous equation of the Generalized Encounter Theory (GET) that reveals macroscopic correlations induced by the encounters in a reservoir of free walks in full agreement with physical considerations. This means that the encounters of reactants in solution are correlated at rather large time interval of the reaction course. However, unlike the reaction A+A→C of identical reactants, the reaction A+B→C accumulation of the above macroscopic correlations (even with the initial concentrations of reactants being equal) proceeds much slower. Another distinction is that for the reaction A+A→C the long-term behavior of ET and GET kinetics is the same, while in the reaction A+B→C these kinetics behave differently. It is of interest that just taking account of the above macroscopic correlations in the reaction A+B→C (in GET) results in the universal character of the
Thermodynamic criteria for estimating the kinetic parameters of catalytic reactions
Mitrichev, I. I.; Zhensa, A. V.; Kol'tsova, E. M.
2017-01-01
Kinetic parameters are estimated using two criteria in addition to the traditional criterion that considers the consistency between experimental and modeled conversion data: thermodynamic consistency and the consistency with entropy production (i.e., the absolute rate of the change in entropy due to exchange with the environment is consistent with the rate of entropy production in the steady state). A special procedure is developed and executed on a computer to achieve the thermodynamic consistency of a set of kinetic parameters with respect to both the standard entropy of a reaction and the standard enthalpy of a reaction. A problem of multi-criterion optimization, reduced to a single-criterion problem by summing weighted values of the three criteria listed above, is solved. Using the reaction of NO reduction with CO on a platinum catalyst as an example, it is shown that the set of parameters proposed by D.B. Mantri and P. Aghalayam gives much worse agreement with experimental values than the set obtained on the basis of three criteria: the sum of the squares of deviations for conversion, the thermodynamic consistency, and the consistency with entropy production.
Hargono Hargono
2017-05-01
Full Text Available Starch is a potential substrate for this purpose, but the extra cost is needed to hydrolyze it into reducing sugar. As an alternative to the expensive and energy demanding conventional hydrolysis process, the low-temperature hydrolysis is being studied. Granular Starch Hydrolysing Enzyme (GSHE was used in the process to degrade starch into reducing sugar at 30°C and pH 4. The substrates included bitter cassava flour, sweet cassava starch, and gadung flour. Starch concentrations studied were 50, 100, 150, 200, 250, 300, 350, and 400 g/L, respectively, while concentration of enzyme was 1.5 % (w/w. The optimum condition of the process was hydrolysis using 200 g/L of substrate concentration and enzyme concentration of 1.5% for 12 h. It was found that the reducing sugar was 49.3 g/L and the productivity of reducing sugar (Qrs was 4.11 (gL-1 h-1. Lineweaver-Burk plot of Michaelis-Menten equation was used to study the inhibition kinetics. The Michaelis-Menten constants (Km for these three substrates were determined as 141.64 g/L, 137,64 g/L and 140.84 g/L for bitter cassava flour, sweet cassava starch, and gadung flour, respectively. The value of Vm/Km, which denotes the affinity of the enzyme to the substrate, were determined and compared, and the result showed that the affinity (Vm to the enzyme to this substrate followed the order of sweet cassava starch˃ bitter cassava flour˃ gadung flour, and all are non-competitive inhibitor, while the Ki value was 0.022 h -1.
Kinetics and mechanisms of reactions involving small aromatic reactive intermediates
Lin, M.C. [Emory Univ., Atlanta, GA (United States)
1993-12-01
Small aromatic radicals such as C{sub 6}H{sub 5}, C{sub 6}H{sub 5}O and C{sub 6}H{sub 4} are key prototype species of their homologs. C{sub 6}H{sub 5} and its oxidation product, C{sub 6}H{sub 5}O are believed to be important intermediates which play a pivotal role in hydrocarbon combustion, particularly with regard to soot formation. Despite their fundamental importance, experimental data on the reaction mechanisms and reactivities of these species are very limited. For C{sub 6}H{sub 5}, most kinetic data except its reactions with NO and NO{sub 2}, were obtained by relative rate measurements. For C{sub 6}H{sub 5}O, the authors have earlier measured its fragmentation reaction producing C{sub 5}H{sub 5} + CO in shock waves. For C{sub 6}H{sub 4}, the only rate constant measured in the gas phase is its recombination rate at room temperature. The authors have proposed to investigate systematically the kinetics and mechanisms of this important class of molecules using two parallel laser diagnostic techniques--laser resonance absorption (LRA) and resonance enhanced multiphoton ionization mass spectrometry (REMPI/MS). In the past two years, study has been focused on the development of a new multipass adsorption technique--the {open_quotes}cavity-ring-down{close_quotes} technique for kinetic applications. The preliminary results of this study appear to be quite good and the sensitivity of the technique is at least comparable to that of the laser-induced fluorescence method.
Kinetic Study of the Austempering Reactions in Ductile Irons
Pérez, M. J.; Cisneros, M. M.; Almanza, E.; Haro, S.
2012-11-01
Kinetics of the reaction that occur during the austempering heat treatment in unalloyed and alloyed ductile irons with 1Cu-0.25Mo, 1Ni-0.25Mo, and 0.7Cu-1Ni-0.25Mo, was studied. The austenitization and austempering cycles were achieved by isothermal dilatometry in cylindrical samples of 2 mm in diameter and 12 mm in length. The specimens were austenitized at 870 °C for 120 min, followed by isothermal holding for 300 min at temperatures between 270 and 420 °C. Kinetic parameters such as the order of reaction " n" and the rate of reaction " k" were calculated using the Johnson-Mehl equation while the empirical activation energy was calculated by means of the Arrhenius equation. It was found that the values of " k" decreased with the addition of Cu, Ni, and Mo as well as with the reduction of the isothermal temperature. The activation energy changes with the austempering temperature, in the range 30,348-58,250 J/mol when the heat treatment was carried out between 370 and 420 °C and 10,336-26,683 J/mol when the temperature varied from 270 to 350 °C. The microstructures in samples austempered at 370 and 315 °C were observed by transmission electron microscopy. No carbides precipitation was observed on samples heat treated at 370 °C for less than 120 min, while at 315 °C carbides of hexagonal structure ɛ(Fe2.4C) were found from the beginning of the transformation. The smallest value of activation energy and a slower kinetic transformation seem to be related with the presence of a carbide phase. Additionally, the time results obtained for transformation fractions of 0.05 and 0.95 by the dilatometry analysis were used to build the temperature-time-transformation diagrams for the irons.
The reaction kinetics of amino radicals with sulfur dioxide
Gao, Yide; Glarborg, Peter; Marshall, Paul
2015-01-01
Application of the laser photolysis-laser-induced fluorescence method to the reaction NH2+SO2 in argon bath gas yields pressure-dependent, third-order kinetics which may be summarized as k = (1.49 ± 0.15) × 10-31 (T/298 K)-0.83cm6 molecule-2 s-1 over 292-555K, where the uncertainty is the 95...... yields a H2N-SO2 dissociation enthalpy of 73.5 kJ mol-1, and comparison with RRKM theory and the exponential down model for energy transfer yields down = 350 cm-1 for Ar at room temperature....
Kinetics of Reduction Reaction in Micro-Fluidized Bed
LINYin-he; GUOZhan—cheng; TANGHui—qing; REN Shan; LIJing—wei
2012-01-01
Micro-fluidized bed reactor is a new research method for the reduction of iron ore fines. The reactor is op- erated as a differential reactor to ensure a constant gas concentration and temperature within the reactor volume. In order to understand the dynamic process of the reduction reaction in micro-fluidized bed, a series of kinetic experi- ments were designed. In the micro fluidized bed, the use of shrinking core model describes the dynamic behavior of reduction of iron ore. And the apparent activation energy is calculated in the range of 700--850 ~C while the initial atmosphere is 100% content of CO.
KINETIC MODELS STUDY OF HYDRODESULPHURIZATION VACUUM DISTILLATE REACTION
AbdulMunem A. Karim
2013-05-01
Full Text Available This study deals with kinetics of hydrodesulphurization (HDS reaction of vacuum gas oil (611-833 K which was distillated from Kirkuk crude oil and which was obtained by blending the fractions, light vacuum gas oil (611 - 650 K, medium vacuum gas oil (650-690 K, heavy vacuum gas oil (690-727 K and very heavy vacuum gas oil (727-833 K. The vacuum gas oil was hydrotreated on a commercial cobalt-molybdenum alumina catalyst presulfied at specified conditions in a laboratory trickle bed reactor. The reaction temperature range (583-643 K,liquid hourly space velocity range (1.5-3.75 h-1 and hydrogen pressure was kept constant at 3.5 MPa with hydrogen to oil ratio about 250 lt/lt. The conversion results for desulphurization reaction appeared to obey the second order reaction. According to this model, the rate constants for desulphurization reaction were determined. Finally, the apparent activation energy (Ea, enthalpy of activation ( H* and entropy ( S* were calculated based on the values of rate constant (k2 and were equal 80.3792 KJ/mole, 75.2974 KJ/mole and 197.493 J/mole, respectively.
Python framework for kinetic modeling of electronically excited reaction pathways
Verboncoeur, John; Parsey, Guy; Guclu, Yaman; Christlieb, Andrew
2012-10-01
The use of plasma energy to enhance and control the chemical reactions during combustion, a technology referred to as ``plasma assisted combustion'' (PAC), can result in a variety of beneficial effects: e.g. stable lean operation, pollution reduction, and wider range of p-T operating conditions. While experimental evidence abounds, theoretical understanding of PAC is at best incomplete, and numerical tools still lack in reliable predictive capabilities. In the context of a joint experimental-numerical effort at Michigan State University, we present here an open-source modular Python framework dedicated to the dynamic optimization of non-equilibrium PAC systems. Multiple sources of experimental reaction data, e.g. reaction rates, cross-sections and oscillator strengths, are used in order to quantify the effect of data uncertainty and limiting assumptions. A collisional-radiative model (CRM) is implemented to organize reactions by importance and as a potential means of measuring a non-Maxwellian electron energy distribution function (EEDF), when coupled to optical emission spectroscopy data. Finally, we explore scaling laws in PAC parameter space using a kinetic global model (KGM) accelerated with CRM optimized reaction sequences and sparse stiff integrators.
Single-molecule chemical reaction reveals molecular reaction kinetics and dynamics.
Zhang, Yuwei; Song, Ping; Fu, Qiang; Ruan, Mingbo; Xu, Weilin
2014-06-25
Understanding the microscopic elementary process of chemical reactions, especially in condensed phase, is highly desirable for improvement of efficiencies in industrial chemical processes. Here we show an approach to gaining new insights into elementary reactions in condensed phase by combining quantum chemical calculations with a single-molecule analysis. Elementary chemical reactions in liquid-phase, revealed from quantum chemical calculations, are studied by tracking the fluorescence of single dye molecules undergoing a reversible redox process. Statistical analyses of single-molecule trajectories reveal molecular reaction kinetics and dynamics of elementary reactions. The reactivity dynamic fluctuations of single molecules are evidenced and probably arise from either or both of the low-frequency approach of the molecule to the internal surface of the SiO2 nanosphere or the molecule diffusion-induced memory effect. This new approach could be applied to other chemical reactions in liquid phase to gain more insight into their molecular reaction kinetics and the dynamics of elementary steps.
Hydrolysis of Toxic Natural Glucosides Catalyzed by Cyclodextrin Dicyanohydrins
Bjerre, Jeannette; Nielsen, Erik Holm; Bols, Mikael
2008-01-01
The hydrolysis of toxic 7-hydroxycoumarin glucosides and other aryl and alkyl glucosides, catalyzed by modified a- and ß-cyclodextrin dicyanohydrins, was investigated using different UV, redox, or HPAEC detection assays. The catalyzed reactions all followed Michaelis-Menten kinetics, and an impre......The hydrolysis of toxic 7-hydroxycoumarin glucosides and other aryl and alkyl glucosides, catalyzed by modified a- and ß-cyclodextrin dicyanohydrins, was investigated using different UV, redox, or HPAEC detection assays. The catalyzed reactions all followed Michaelis-Menten kinetics......, and an impressive rate increase of up to 7569 (kcat/kuncat) was found for the hydroxycoumarin glucoside substrate 4-MUGP. Good and moderate degrees of catalysis (kcat/kuncat) of up to 1259 were found for the natural glucosides phloridzin and skimmin. By using a newly developed catechol detection UV-assay, a weak...
Diffusion Controlled Reactions, Fluctuation Dominated Kinetics, and Living Cell Biochemistry
Konkoli, Zoran
2009-01-01
In recent years considerable portion of the computer science community has focused its attention on understanding living cell biochemistry and efforts to understand such complication reaction environment have spread over wide front, ranging from systems biology approaches, through network analysis (motif identification) towards developing language and simulators for low level biochemical processes. Apart from simulation work, much of the efforts are directed to using mean field equations (equivalent to the equations of classical chemical kinetics) to address various problems (stability, robustness, sensitivity analysis, etc.). Rarely is the use of mean field equations questioned. This review will provide a brief overview of the situations when mean field equations fail and should not be used. These equations can be derived from the theory of diffusion controlled reactions, and emerge when assumption of perfect mixing is used.
Bayesian inference of chemical kinetic models from proposed reactions
Galagali, Nikhil
2015-02-01
© 2014 Elsevier Ltd. Bayesian inference provides a natural framework for combining experimental data with prior knowledge to develop chemical kinetic models and quantify the associated uncertainties, not only in parameter values but also in model structure. Most existing applications of Bayesian model selection methods to chemical kinetics have been limited to comparisons among a small set of models, however. The significant computational cost of evaluating posterior model probabilities renders traditional Bayesian methods infeasible when the model space becomes large. We present a new framework for tractable Bayesian model inference and uncertainty quantification using a large number of systematically generated model hypotheses. The approach involves imposing point-mass mixture priors over rate constants and exploring the resulting posterior distribution using an adaptive Markov chain Monte Carlo method. The posterior samples are used to identify plausible models, to quantify rate constant uncertainties, and to extract key diagnostic information about model structure-such as the reactions and operating pathways most strongly supported by the data. We provide numerical demonstrations of the proposed framework by inferring kinetic models for catalytic steam and dry reforming of methane using available experimental data.
Reaction route graphs. III. Non-minimal kinetic mechanisms.
Fishtik, Ilie; Callaghan, Caitlin A; Datta, Ravindra
2005-02-24
The concept of reaction route (RR) graphs introduced recently by us for kinetic mechanisms that produce minimal graphs is extended to the problem of non-minimal kinetic mechanisms for the case of a single overall reaction (OR). A RR graph is said to be minimal if all of the stoichiometric numbers in all direct RRs of the mechanism are equal to +/-1 and non-minimal if at least one stoichiometric number in a direct RR is non-unity, e.g., equal to +/-2. For a given mechanism, four unique topological characteristics of RR graphs are defined and enumerated, namely, direct full routes (FRs), empty routes (ERs), intermediate nodes (INs), and terminal nodes (TNs). These are further utilized to construct the RR graphs. One algorithm involves viewing each IN as a central node in a RR sub-graph. As a result, the construction and enumeration of RR graphs are reduced to the problem of balancing the peripheral nodes in the RR sub-graphs according to the list of FRs, ERs, INs, and TNs. An alternate method involves using an independent set of RRs to draw the RR graph while satisfying the INs and TNs. Three examples are presented to illustrate the application of non-minimal RR graph theory.
Stochastic reaction-diffusion kinetics in the microscopic limit
Fange, David; Berg, Otto G.; Sjöberg, Paul; Elf, Johan
2010-01-01
Quantitative analysis of biochemical networks often requires consideration of both spatial and stochastic aspects of chemical processes. Despite significant progress in the field, it is still computationally prohibitive to simulate systems involving many reactants or complex geometries using a microscopic framework that includes the finest length and time scales of diffusion-limited molecular interactions. For this reason, spatially or temporally discretized simulations schemes are commonly used when modeling intracellular reaction networks. The challenge in defining such coarse-grained models is to calculate the correct probabilities of reaction given the microscopic parameters and the uncertainty in the molecular positions introduced by the spatial or temporal discretization. In this paper we have solved this problem for the spatially discretized Reaction-Diffusion Master Equation; this enables a seamless and physically consistent transition from the microscopic to the macroscopic frameworks of reaction-diffusion kinetics. We exemplify the use of the methods by showing that a phosphorylation-dephosphorylation motif, commonly observed in eukaryotic signaling pathways, is predicted to display fluctuations that depend on the geometry of the system. PMID:21041672
Liechty, Derek S.; Lewis, Mark J.
2010-01-01
Recently introduced molecular-level chemistry models that predict equilibrium and nonequilibrium reaction rates using only kinetic theory and fundamental molecular properties (i.e., no macroscopic reaction rate information) are extended to include reactions involving charged particles and electronic energy levels. The proposed extensions include ionization reactions, exothermic associative ionization reactions, endothermic and exothermic charge exchange reactions, and other exchange reactions involving ionized species. The extensions are shown to agree favorably with the measured Arrhenius rates for near-equilibrium conditions.
王丹; 赵玲; 尹平河; 肖娟宜; 黄思明
2012-01-01
在实验室模拟条件下,以粉煤灰改性污泥为垃圾填埋场生物覆盖材料,分析了初始甲烷浓度、初始氧气浓度对甲烷氧化效率的影响,并测定了甲烷氧化动力学方程及动力学参数,旨在为材料实际工程应用提供理论依据.结果表明:初始CH4、O2浓度制约生物覆盖材料的甲烷氧化效率,初始CH4、O2浓度越高,材料甲烷氧化能力越强；甲烷氧化过程符合2级动力学方程-dV(CH4)/dt=kV(CH4)V(O2)；利用Michaelis-Menten模型得出覆盖层材料的最大氧化速率Vmax为2.54 μmol g-1h-1,半速常数Km为0.49 μmol.%In this study, laboratory-scale experiments were carried out to examine the effects of initial methane and oxygen contents on methane oxidation efficiency in landfill bio-cover sewage sludge, and the kinetic equation and corresponding parameters were also determined, aiming to provide scientific basis for the practical engineering application. The results showed that the methane and oxygen contents strongly affected the methane oxidation efficiency. The higher methane and oxygen contents resulted in stronger methane oxidation efficiency. The kinetics of methane oxidation was - dV( CH4)/di = kV{ CH4 ) V( 02) , which fit the second-order reaction. As calculated from Michaelis-Menten equation, the largest methane oxidation rate ( Kmax ) was 2. 54 μmol g ‐ 1h‐ 1, and the half saturation constant ( Km ) was found at 0. 49 μmol.
Gumowski, I
1977-01-01
A class of differential equations with pure delay and a hyperbolic nonlinearity, analogous to the Michaelis-Menten term in chemical reaction kinetics, is examined. Conditions for the existence of periodic solutions are established. The amplitude and period dependences on the equation parameters are estimated analytically. A mixed analytico-numerical approach is used in the computations, because a straightforward integration of the equations is numerically ill conditioned. (11 refs).
Manipulating single enzymes by an external harmonic force
Lomholt, Michael A; Urbakh, Michael; Metzler, Ralf
2007-01-01
We study a Michaelis-Menten reaction for a single two-state enzyme molecule, whose transition rates between the two conformations are modulated by an harmonically oscillating external force. In particular, we obtain a range of optimal driving frequencies for changing the conformation of the enzyme......, thereby controlling the enzymatic activity (i.e., product formation). This analysis demonstrates that it is, in principle, possible to obtain information about particular rates within the kinetic scheme....
Amino acid uptake and energy coupling dependent on photosynthesis in Anacystis nidulans.
Lee-Kaden, J; Simonis, W
1982-01-01
The photoautotrophic cyanobacterium Anacystis nidulans was used to investigate the membrane transport of branched-chain, neutral amino acids and its dependence on photosynthetic reactions. The uptake of alpha-amino [1-14C]isobutyric acid and L-[1-14C]leucine followed Michaelis, Menten kinetics and resulted in an energy-dependent accumulation. As in bacteria, different uptake systems for neutral amino acids were present: two DAG (D-alanine, aminoisobutyric acid, and glycine) systems responsibl...
2012-01-01
chloroethene mineralization under nomi- nally anoxic conditions can exhibit saturation type ( Michaelis - Menten ) kinetics over the range of environmentally...relevant concentrations. The Michaelis - Menten parameters, Vmax and ks, are sensitive to a number of environmental factors and vary according to in
Assessment and kinetics of soil phosphatase in Brazilian Savanna systems
ADÃO S. FERREIRA
2016-06-01
Full Text Available The activity and kinetics of soil phosphatases are important indicators to evaluate soil quality in specific sites such as the Cerrado (Brazilian Savanna. This study aimed to determine the activity and kinetic parameters of soil phosphatase in Cerrado systems. Soil phosphatase activity was assessed in samples of native Cerrado (NC, no-tillage (NT, conventional tillage (CT and pasture with Brachiaria brizantha (PBb and evaluated with acetate buffer (AB, tris-HCl buffer (TB, modified universal buffer (MUB and low MUB. The Michaelis-Menten equation and Eadie-Hofstee model were applied to obtain the kinetic parameters of soil phosphatase using different concentrations of p-nitrophenol phosphate (p-NPP. MUB showed the lowest soil phosphatase activity in all soils whereas AB in NC and NT presented the highest. Low MUB decreased interferences in the assessment of soil phosphatase activity when compared to MUB, suggesting that organic acids interfere on the soil phosphatase activity. In NC and NT, soil phosphatase activity performed with TB was similar to AB and low MUB. Km values from the Michaels-Menten equation were higher in NC than in NT, which indicate a lower affinity of phosphatase activity for the substrate in NC. Vmax values were also higher in NC than in NT. The Eadie-Hofstee model suggests that NC had more phosphatase isoforms than NT. The study showed that buffer type is of fundamental importance when assessing soil phosphatase activity in Cerrado soils.
Statistical theory for the kinetics and dynamics of roaming reactions.
Klippenstein, Stephen J; Georgievskii, Yuri; Harding, Lawrence B
2011-12-22
We present a statistical theory for the effect of roaming pathways on product branching fractions in both unimolecular and bimolecular reactions. The analysis employs a separation into three distinct steps: (i) the formation of weakly interacting fragments in the long-range/van der Waals region of the potential via either partial decomposition (for unimolecular reactants) or partial association (for bimolecular reactants), (ii) the roaming step, which involves the reorientation of the fragments from one region of the long-range potential to another, and (iii) the abstraction, addition, and/or decomposition from the long-range region to yield final products. The branching between the roaming induced channel(s) and other channels is obtained from a steady-state kinetic analysis for the two (or more) intermediates in the long-range region of the potential. This statistical theory for the roaming-induced product branching is illustrated through explicit comparisons with reduced dimension trajectory simulations for the decompositions of H(2)CO, CH(3)CHO, CH(3)OOH, and CH(3)CCH. These calculations employ high-accuracy analytic potentials obtained from fits to wide-ranging CASPT2 ab initio electronic structure calculations. The transition-state fluxes for the statistical theory calculations are obtained from generalizations of the variable reaction coordinate transition state theory approach. In each instance, at low energy the statistical analysis accurately reproduces the branching obtained from the trajectory simulations. At higher energies, e.g., above 1 kcal/mol, increasingly large discrepancies arise, apparently due to a dynamical biasing toward continued decomposition of the incipient molecular fragments (for unimolecular reactions). Overall, the statistical theory based kinetic analysis is found to provide a useful framework for interpreting the factors that determine the significance of roaming pathways in varying chemical environments.
Wang, Zhican; Wong, Timothy; Hashizume, Takanori; Dickmann, Leslie Z; Scian, Michele; Koszewski, Nicholas J; Goff, Jesse P; Horst, Ronald L; Chaudhry, Amarjit S; Schuetz, Erin G; Thummel, Kenneth E
2014-06-01
25-Hydroxyvitamin D3 (25OHD3) is used as a clinical biomarker for assessment of vitamin D status. Blood levels of 25OHD3 represent a balance between its formation rate and clearance by several oxidative and conjugative processes. In the present study, the identity of human uridine 5'-diphosphoglucuronyltransferases (UGTs) capable of catalyzing the 25OHD3 glucuronidation reaction was investigated. Two isozymes, UGT1A4 and UGT1A3, were identified as the principal catalysts of 25OHD3 glucuronidation in human liver. Three 25OHD3 monoglucuronides (25OHD3-25-glucuronide, 25OHD3-3-glucuronide, and 5,6-trans-25OHD3-25-glucuronide) were generated by recombinant UGT1A4/UGT1A3, human liver microsomes, and human hepatocytes. The kinetics of 25OHD3 glucuronide formation in all systems tested conformed to the Michaelis-Menten model. An association between the UGT1A4*3 (Leu48Val) gene polymorphism with the rates of glucuronide formation was also investigated using human liver microsomes isolated from 80 genotyped livers. A variant allele dose effect was observed: the homozygous UGT1A4*3 livers (GG) had the highest glucuronidation activity, whereas the wild type (TT) had the lowest activity. Induction of UGT1A4 and UGT1A3 gene expression was also determined in human hepatocytes treated with pregnane X receptor/constitutive androstane receptor agonists, such as rifampin, carbamazepine, and phenobarbital. Although UGT mRNA levels were increased significantly by all of the known pregnane X receptor/constitutive androstane receptor agonists tested, rifampin, the most potent of the inducers, significantly induced total 25OHD3 glucuronide formation activity in human hepatocytes measured after 2, but not 4 and 24 hours, of incubation. Finally, the presence of 25OHD3-3-glucuronide in both human plasma and bile was confirmed, suggesting that the glucuronidation pathway might be physiologically relevant and contribute to vitamin D homeostasis in humans.
Stepwise kinetic equilibrium models of quantitative polymerase chain reaction
Cobbs Gary
2012-08-01
Full Text Available Abstract Background Numerous models for use in interpreting quantitative PCR (qPCR data are present in recent literature. The most commonly used models assume the amplification in qPCR is exponential and fit an exponential model with a constant rate of increase to a select part of the curve. Kinetic theory may be used to model the annealing phase and does not assume constant efficiency of amplification. Mechanistic models describing the annealing phase with kinetic theory offer the most potential for accurate interpretation of qPCR data. Even so, they have not been thoroughly investigated and are rarely used for interpretation of qPCR data. New results for kinetic modeling of qPCR are presented. Results Two models are presented in which the efficiency of amplification is based on equilibrium solutions for the annealing phase of the qPCR process. Model 1 assumes annealing of complementary targets strands and annealing of target and primers are both reversible reactions and reach a dynamic equilibrium. Model 2 assumes all annealing reactions are nonreversible and equilibrium is static. Both models include the effect of primer concentration during the annealing phase. Analytic formulae are given for the equilibrium values of all single and double stranded molecules at the end of the annealing step. The equilibrium values are then used in a stepwise method to describe the whole qPCR process. Rate constants of kinetic models are the same for solutions that are identical except for possibly having different initial target concentrations. Analysis of qPCR curves from such solutions are thus analyzed by simultaneous non-linear curve fitting with the same rate constant values applying to all curves and each curve having a unique value for initial target concentration. The models were fit to two data sets for which the true initial target concentrations are known. Both models give better fit to observed qPCR data than other kinetic models present in the
Doktorov, Alexander B.; Kipriyanov, Alexander A.; Kipriyanov, Alexey A.
2010-05-01
Using an modern many-particle method for the derivation of non-Markovian binary kinetic equations, we have treated theoretically the applicability of the encounter theory (ET) (the prototype of the collision theory) concepts to the widely known diffusion assisted irreversible bulk reaction A +A→product (for example, radical reaction) in dilute solutions. The method shows that the agreement with the ET is observed when the familiar integral ET is employed which in this method is just a step in the derivation of kinetic equations. It allows for two-particle correlations only, but fails to take account of correlation of reactant simultaneously with the partner of the encounter and the reactant in the bulk. However, the next step leading to the modified ET under transformation of equations to the regular form both extends the time range of the applicability of ET rate equation (as it was for reactions proceeding with one of the reactants in excess), and gives the equation of the generalized ET. In full agreement with physical considerations, this theory reveals macroscopic correlations induced by the encounters in the reservoir of free walks. This means that the encounters of reactants in solution are correlated on a rather large time interval of the reaction. Though any nonstationary (non-Markovian) effects manifest themselves rather weakly in the kinetics of the bimolecular reaction in question, just the existence of the revealed macroscopic correlations in the binary theory is of primary importance. In particular, it means that the well-known phenomena which are generally considered to be associated solely with correlation of particles on the encounter (for example, chemically induced dynamic nuclear polarization) may be induced by correlation in the reservoir of free random walks of radicals in solution.
Doktorov, Alexander B; Kipriyanov, Alexander A; Kipriyanov, Alexey A
2010-05-28
Using an modern many-particle method for the derivation of non-Markovian binary kinetic equations, we have treated theoretically the applicability of the encounter theory (ET) (the prototype of the collision theory) concepts to the widely known diffusion assisted irreversible bulk reaction A+A-->product (for example, radical reaction) in dilute solutions. The method shows that the agreement with the ET is observed when the familiar integral ET is employed which in this method is just a step in the derivation of kinetic equations. It allows for two-particle correlations only, but fails to take account of correlation of reactant simultaneously with the partner of the encounter and the reactant in the bulk. However, the next step leading to the modified ET under transformation of equations to the regular form both extends the time range of the applicability of ET rate equation (as it was for reactions proceeding with one of the reactants in excess), and gives the equation of the generalized ET. In full agreement with physical considerations, this theory reveals macroscopic correlations induced by the encounters in the reservoir of free walks. This means that the encounters of reactants in solution are correlated on a rather large time interval of the reaction. Though any nonstationary (non-Markovian) effects manifest themselves rather weakly in the kinetics of the bimolecular reaction in question, just the existence of the revealed macroscopic correlations in the binary theory is of primary importance. In particular, it means that the well-known phenomena which are generally considered to be associated solely with correlation of particles on the encounter (for example, chemically induced dynamic nuclear polarization) may be induced by correlation in the reservoir of free random walks of radicals in solution.
Thermochemistry, reaction paths, and kinetics on the tert-isooctane radical reaction with O2.
Snitsiriwat, Suarwee; Bozzelli, Joseph W
2014-07-03
Thermochemical properties of tert-isooctane hydroperoxide and its radicals are determined by computational chemistry. Enthalpies are determined using isodesmic reactions with B3LYP density function and CBS QB3 methods. Application of group additivity with comparison to calculated values is illustrated. Entropy and heat capacities are determined using geometric parameters and frequencies from the B3LYP/6-31G(d,p) calculations for the lowest energy conformer. Internal rotor potentials are determined for the tert-isooctane hydroperoxide and its radicals in order to identify isomer energies. Recommended values derived from the most stable conformers of tert-isooctane hydroperoxide of are -77.85 ± 0.44 kcal mol(-1). Isooctane is a highly branched molecule, and its structure has a significant effect on its thermochemistry and reaction barriers. Intramolecular interactions are shown to have a significant effect on the enthalpy of the isooctane parent and its radicals on peroxy/peroxide systems, the R• + O2 well depths and unimolecular reaction barriers. Bond dissociation energies and well depths, for tert-isooctane hydroperoxide → R• + O2 are 33.5 kcal mol(-1) compared to values of ∼38 to 40 kcal mol(-1) for the smaller tert-butyl-O2 → R• + O2. Transition states and kinetic parameters for intramolecular hydrogen atom transfer and molecular elimination channels are characterized to evaluate reaction paths and kinetics. Kinetic parameters are determined versus pressure and temperature for the chemically activated formation and unimolecular dissociation of the peroxide adducts. Multifrequency quantum RRK (QRRK) analysis is used for k(E) with master equation analysis for falloff. The major reaction paths at 1000 K are formation of isooctane plus HO2 followed by cyclic ether plus OH. Stabilization of the tert-isooctane hydroperoxy radical becomes important at lower temperatures.
Database of atomistic reaction mechanisms with application to kinetic Monte Carlo.
Terrell, Rye; Welborn, Matthew; Chill, Samuel T; Henkelman, Graeme
2012-07-07
Kinetic Monte Carlo is a method used to model the state-to-state kinetics of atomic systems when all reaction mechanisms and rates are known a priori. Adaptive versions of this algorithm use saddle searches from each visited state so that unexpected and complex reaction mechanisms can also be included. Here, we describe how calculated reaction mechanisms can be stored concisely in a kinetic database and subsequently reused to reduce the computational cost of such simulations. As all accessible reaction mechanisms available in a system are contained in the database, the cost of the adaptive algorithm is reduced towards that of standard kinetic Monte Carlo.
Zahra Ghobadi Nejad
2014-01-01
Full Text Available Due to great commercial application of protease, it is necessary to study kinetic characterization of this enzyme in order to improve design of enzymatic reactors. In this study, mathematical modeling of protease enzyme production kinetics which is derived from Bacillus licheniformis BBRC 100053 was studied (at 37°C, pH 10 after 73 h in stationary phase, and 150 rpm. The aim of the present paper was to determine the best kinetic model and kinetic parameters for production of protease and calculating Ki (inhibition constant of different inhibitors to find the most effective one. The kinetic parameters Km (Michaelis-Menten constant and Vm (maximum rate were calculated 0.626 mM and 0.0523 mM/min. According to the experimental results, using DFP (diisopropyl fluorophosphate and PMSF (phenylmethanesulfonyl fluoride as inhibitors almost 50% of the enzyme activity could be inhibited when their concentrations were 0.525 and 0.541 mM, respectively. Ki for DFP and PMSF were 0.46 and 0.56 mM, respectively. Kinetic analysis showed that the Lineweaver-Burk model was the best fitting model for protease production kinetics DFP was more effective than PMSF and both of them should be covered in the group of noncompetitive inhibitors.
A biological interpretation of transient anomalous subdiffusion. II. Reaction kinetics.
Saxton, Michael J
2008-02-01
Reaction kinetics in a cell or cell membrane is modeled in terms of the first passage time for a random walker at a random initial position to reach an immobile target site in the presence of a hierarchy of nonreactive binding sites. Monte Carlo calculations are carried out for the triangular, square, and cubic lattices. The mean capture time is expressed as the product of three factors: the analytical expression of Montroll for the capture time in a system with a single target and no binding sites; an exact expression for the mean escape time from the set of lattice points; and a correction factor for the number of targets present. The correction factor, obtained from Monte Carlo calculations, is between one and two. Trapping may contribute significantly to noise in reaction rates. The statistical distribution of capture times is obtained from Monte Carlo calculations and shows a crossover from power-law to exponential behavior. The distribution is analyzed using probability generating functions; this analysis resolves the contributions of the different sources of randomness to the distribution of capture times. This analysis predicts the distribution function for a lattice with perfect mixing; deviations reflect imperfect mixing in an ordinary random walk.
Non-steady state population kinetics of intravenous phenytoin.
Frame, B; Beal, S L
1998-08-01
This observational study explored the effects of demographics, sickness, and polypharmacy on the non-steady state population pharmacokinetics of intravenous phenytoin. One hundred fifteen patients were studied. Models were developed using the NONMEM program with hybrid first-order conditional estimation. A Michaelis-Menten model with delayed induction was preferred over a Michaelis-Menten model without induction, a Michaelis-Menten model with immediate induction, or a linear model with delayed induction. When the data were fit to a Michaelis-Menten model with delayed induction, the volume of distribution (Vd) was found to depend on weight and serum albumin. The Vd was estimated to be 0.95 l/kg, assuming an albumin level of 3 g/dl. The Michaelis-Menten constant (km) was estimated to be 7.9 mg/l. The baseline maximum metabolic rate was 580 mg/day for a 70-kg patient. The average time to onset of induction was 59.5 hours. If a fever developed after induction began, it increased the extent of induction. This model was evaluated retrospectively in 26 additional patients, yielding a mean prediction error of -0.4 mg/l (-3.0-2.2 mg/l) and a mean absolute prediction error of 4.7 mg/l (3.2-6.2 mg/l) based on two-level feedback. Given the large interindividual variances in maximum metabolic rate, phenytoin levels should be measured frequently.
Chlorination of parabens: reaction kinetics and transformation product identification.
Mao, Qianhui; Ji, Feng; Wang, Wei; Wang, Qiquan; Hu, Zhenhu; Yuan, Shoujun
2016-11-01
The reactivity and fate of parabens during chlorination were investigated in this work. Chlorination kinetics of methylparaben (MeP), ethylparaben (EtP), propylparaben (PrP), and butylparaben (BuP) were studied in the pH range of 4.0 to 11.0 at 25 ± 1 °C. Apparent rate constants (k app) of 9.65 × 10(-3) M(-0.614)·s(-1), 1.77 × 10(-2) M(-1.019)·s(-1), 2.98 × 10(-2) M(-0.851)·s(-1), and 1.76 × 10(-2) M(-0.860)·s(-1) for MeP, EtP, PrP, and BuP, respectively, were obtained at pH 7.0. The rate constants depended on the solution pH, temperature, and NH4(+) concentration. The maximum k app was obtained at pH 8.0, and the minimum value was obtained at pH 11.0. The reaction rate constants increased with increasing temperature. When NH4(+) was added to the solution, the reaction of parabens was inhibited due to the rapid formation of chloramines. Two main transformation products, 3-chloro-parabens and 3,5-dichloro-parabens, were identified by GC-MS and LCMS-IT-TOF, and a reaction pathway was proposed. Dichlorinated parabens accumulated in solution, which is a threat to human health and the aqueous environment.
Lopes, Fernanda Cristina Rezende; Tannous, Katia; Rueda-Ordóñez, Yesid Javier
2016-11-01
This work aims the study of decomposition kinetics of guarana seed residue using thermogravimetric analyzer under synthetic air atmosphere applying heating rates of 5, 10, and 15°C/min, from room temperature to 900°C. Three thermal decomposition stages were identified: dehydration (25.1-160°C), oxidative pyrolysis (240-370°C), and combustion (350-650°C). The activation energies, reaction model, and pre-exponential factor were determined through four isoconversional methods, master plots, and linearization of the conversion rate equation, respectively. A scheme of two-consecutive reactions was applied validating the kinetic parameters of first-order reaction and two-dimensional diffusion models for the oxidative pyrolysis stage (149.57kJ/mol, 6.97×10(10)1/s) and for combustion stage (77.98kJ/mol, 98.611/s), respectively. The comparison between theoretical and experimental conversion and conversion rate showed good agreement with average deviation lower than 2%, indicating that these results could be used for modeling of guarana seed residue. Copyright © 2016 Elsevier Ltd. All rights reserved.
Gargano, Immacolata; Olivieri, Giuseppe; Spasiano, Danilo; Andreozzi, Roberto; Pollio, Antonino; Marotta, Raffaele; Ambrosio, D' Nicola; Marzocchella, Antonio
2015-01-01
The kinetic characterization of the photosynthetic activity in autotrophic microalgae plays a key role in the design of optimized photobioreactors. This paper presents a procedure to assess kinetic parameters of a three-state photosynthetic reaction centres model. Four kinetic parameters of the
许志锋; 文戈; 邝代治; 张复兴; 王剑秋; 李俊华
2011-01-01
The applications of molecularly imprinted polymers(MIPs) in synthesis and catalysis are being increasingly investigated. Conventional bulk polymerization often produces the polymer materials exhibiting low binding capacity, binding sites heterogeneity, and poor site accessibility. The use of nano-sized MIPs is expected to overcome these problems because nano-sized materials have a small dimension with high surface-tovolume ratio. The objective of this study is to construct molecular imprinting microreactor( MIM ) in nanomaterials. In the first step, alkenyl multiwalled carbon nanotubes(MWCNTs) were prepared by esterification reaction of hydroxyl group of MWCNTs and methacryloyl chloride. Then, the molecular imprinted catalyst for Diels-Alder cycloaddition was fabricated on MWCNTs using alkenyl-MWCNTs as matrix, Diels-Alder cycloaddition product of anthracene and maleic acid as template molecule, methacrylic acid(MAA) and ethylene glycol dimethacrylate(EDMA) as functional monomer and cross-linker, respectively. The molecular imprinted catalyst exhibited catalytic activity for the cycloaddition reaction of anthracene and maleic acid. Compared with the uncatalyzed reaction, a rate enhancement of 1.77 fold was obtained. Plots of initial velocities of the cycioaddition versus substrate concentration showed typical Michaelis-Menten kinetics. In addition, the Michaelis constant(Km ) and maximal rate(vmmax ) were calculated from Lineweaver-Burk plots to be 17735.24 μmoL/L and 0. 713 μ.moi/(L · s), respectively.%通过多壁碳纳米管(MWCNTs)上羟基的酯化反应在碳纳米管表面接枝双键,以蒽和马来酸的加成反应产物为模板分子,甲基丙烯酸(MAA)为功能单体,乙二醇二甲基丙烯酸酯(EDMA)为交联刺,通过微波辐射聚合在碳纳米管表面接枝一层厚度约为30 nm的分子印迹催化剂.该催化剂对蒽和马来酸的加成反应具有明显的催化作用,反应开始后的180 min内,催化反应速率是
王周俊; 李翔; 王琛琛; 唐颐; 张亚红
2011-01-01
通过在毛细管内层层组装纳米沸石并固定脂肪酶来构建纳米沸石修饰的固定化酶微反应器通道,将纳米沸石良好的生物相容性和高的酶固定能力与微反应器反应效率高和扩散传质快等优点相结合,以对硝基苯棕榈酸酯的水解作为探针反应,对该微反应器内固定化酶催化水解反应动力学进行了研究和计算,并与普通反应器内同样的反应进行比较.通过对比米氏方程参数,证实在微反应器内酶催化水解反应效率比普通反应器内提高3倍以上,并可提高酶和反应底物的亲和能力.%Nanozeolite modified microchannel reactors were constructed by assembling zeolite nanocrystals into capillary using layer-by-layer assemble method. And then lipase CRL was immobilized on the nanozeolites assembled in the microreactors. The nanozeolite modified microreactors could incorporate excellent biocaptibility and large external area of nanozeolites and high efficiency and fast mass diffusion of microreactors together.Hydrolysis of 4-nitrophenyl palmitate (4-NPP) was carried out as a probe reaction to study the hydrolysis kinetics catalyzed by immobilized CRL in the microreactors. By comparing the characteristic parameters (Km and Vmax) of Michaelis-Menten equation, it is found that efficiency of enzymatic hydrolysis in such nanozeolite modified microchannel reactors could be 3 or more times higher than that of the same reaction in conventional reactors. In addition, affinity between enzyme and substrates is also enhanced in the nanozeolite modified microchannel reactors.
Enzyme kinetics determined by single-injection isothermal titration calorimetry.
Transtrum, Mark K; Hansen, Lee D; Quinn, Colette
2015-04-01
The purposes of this paper are (a) to examine the effect of calorimeter time constant (τ) on heat rate data from a single enzyme injection into substrate in an isothermal titration calorimeter (ITC), (b) to provide information that can be used to predict the optimum experimental conditions for determining the rate constant (k2), Michaelis constant (KM), and enthalpy change of the reaction (ΔRH), and (c) to describe methods for evaluating these parameters. We find that KM, k2 and ΔRH can be accurately estimated without correcting for the calorimeter time constant, τ, if (k2E/KM), where E is the total active enzyme concentration, is between 0.1/τ and 1/τ and the reaction goes to at least 99% completion. If experimental conditions are outside this domain and no correction is made for τ, errors in the inferred parameters quickly become unreasonable. A method for fitting single-injection data to the Michaelis-Menten or Briggs-Haldane model to simultaneously evaluate KM, k2, ΔRH, and τ is described and validated with experimental data. All four of these parameters can be accurately inferred provided the reaction time constant (k2E/KM) is larger than 1/τ and the data include enzyme saturated conditions. Copyright © 2014 Elsevier Inc. All rights reserved.
Kinetics of the Reaction of CO2 with Aqueous Potassium Salt of Taurine and Glycine
Kumar, P.S.; Hogendoorn, J.A.; Versteeg, G.F.; Feron, P.H.M.
2003-01-01
The kinetics of the reaction between CO2 and aqueous potassium salts of taurine and glycine was measured at 295 K in a stirred-cell reactor with a flat gas–liquid interface. For aqueous potassium taurate solutions, the temperature effect on the reaction kinetics was measured at 285 and 305 K. Unlike
Reaction Kinetics in cw Rare-Gas Halogen Lamps
Salvermoser, M.; Murnick, D. E.; Ulrich, A.; Wieser, J.
1999-10-01
Pumping with a continuous low energy (excimer gas mixtures, the reaction kinetics leading to efficient vuv emission from ArF and F2 at 193nm and 157nm respectively has been studied. The scaling of the pumping power density with energy to the inverse 2.5 power and cube of the pressure allows a wide range of pumping rates to be considered. And, by studying the spectrum and yield as a function of pressure and gas mixture, optimum conditions for vuv emission can be determined and specific formation and quenching channels can be isolated. Energy transfer efficiency near 10% has been obtained at 193nm for neon-argon-fluorine (1:0.008:0.0004) mixtures and at 157nm for neon-fluorine (1:0.002) at two to three bar pressure. Lamps emitting tens of milliwatts light output from a 0.8mm diameter point have been stable for tens of hours. Scaling to at least 10W/cm^2str continuous output is possible.
2005-01-01
International audience; This article, the second in the series, presents kinetic and photochemical data evaluated by the IUPAC Subcommittee on Gas Kinetic Data Evaluation for Atmospheric Chemistry. It covers the gas phase and photochemical reactions of Organic species, which were last published in 1999, and were updated on the IUPAC website in late 2002. The article consists of a summary sheet, containing the recommended kinetic parameters for the evaluated reactions, and eight appendices con...
Enzyme-catalyzed and binding reaction kinetics determined by titration calorimetry.
Hansen, Lee D; Transtrum, Mark K; Quinn, Colette; Demarse, Neil
2016-05-01
Isothermal calorimetry allows monitoring of reaction rates via direct measurement of the rate of heat produced by the reaction. Calorimetry is one of very few techniques that can be used to measure rates without taking a derivative of the primary data. Because heat is a universal indicator of chemical reactions, calorimetry can be used to measure kinetics in opaque solutions, suspensions, and multiple phase systems and does not require chemical labeling. The only significant limitation of calorimetry for kinetic measurements is that the time constant of the reaction must be greater than the time constant of the calorimeter which can range from a few seconds to a few minutes. Calorimetry has the unique ability to provide both kinetic and thermodynamic data. This article describes the calorimetric methodology for determining reaction kinetics and reviews examples from recent literature that demonstrate applications of titration calorimetry to determine kinetics of enzyme-catalyzed and ligand binding reactions. A complete model for the temperature dependence of enzyme activity is presented. A previous method commonly used for blank corrections in determinations of equilibrium constants and enthalpy changes for binding reactions is shown to be subject to significant systematic error. Methods for determination of the kinetics of enzyme-catalyzed reactions and for simultaneous determination of thermodynamics and kinetics of ligand binding reactions are reviewed. Copyright © 2015 Elsevier B.V. All rights reserved.
Chemical Reactions and Kinetics of the Carbon Monoxide Coupling in the Presence of Hydrogen
Fandong Meng; Genhui Xu; Zhenhua Li; Pa Du
2002-01-01
The chemical reactions and kinetics of the catalytic coupling reaction of carbon monoxide to diethyl oxalate were studied in the presence of hydrogen over a supported palladium catalyst in the gaseous phase at the typical coupling reaction conditions. The experiments were performed in a continuous flow fixed-bed reactor. The results indicated that hydrogen only reacts with ethyl nitrite to form ethanol, and kinetic studies revealed that the rate-determining step is the surface reaction of adsorbed hydrogen and the ethoxy radical (EtO-). A kinetic model is proposed and a comparison of the observed and calculated conversions showed that the rate expressions are of rather high confidence.
Christensen, Hege; Mathiesen, Liv; Postvoll, Lillian W; Winther, Bjørn; Molden, Espen
2009-01-01
In vitro drug metabolism techniques with human CYP c-DNA expressed systems are frequently used to predict human drug metabolism in vivo. The aim of this study was to compare midazolam enzyme kinetics in recombinant expressed CYP3A4 microsomes from human and insect cells. The amounts of 1'- hydroxymidazolam and 4-hydroxymidazolam formed in CYP3A4 microsomes from transfected human liver epithelial cells (T5-3A4 microsomes) and baculovirus-infected insect cells (with and without coexpressed cytochrome b(5)) were analysed by LC-MS. Enzyme kinetic parameters were estimated by nonlinear regression. Mean K(m) for the formation of 1'-hydroxymidazolam was 3- and 4-fold higher in T5-3A4 microsomes than in insect microsomes (pmicrosomes was reflected by significantly lower Cl(int) compared to insect microsomes (pmicrosomes displayed Michaelis-Menten kinetics, while insect microsomes showed substrate inhibition kinetics. The different enzyme kinetics of midazolam observed in recombinant CYP3A4 microsomes from human and insect sources, especially the substantially higher K(m) obtained in human microsomes compared to insect microsomes, should be further evaluated since it may have implications for correlations to in vivo situation.
A simple theory of motor protein kinetics and energetics. II.
Qian, H
2000-01-10
A three-state stochastic model of motor protein [Qian, Biophys. Chem. 67 (1997) pp. 263-267] is further developed to illustrate the relationship between the external load on an individual motor protein in aqueous solution with various ATP concentrations and its steady-state velocity. A wide variety of dynamic motor behavior are obtained from this simple model. For the particular case of free-load translocation being the most unfavorable step within the hydrolysis cycle, the load-velocity curve is quasi-linear, V/Vmax = (cF/Fmax-c)/(1-c), in contrast to the hyperbolic relationship proposed by A.V. Hill for macroscopic muscle. Significant deviation from the linearity is expected when the velocity is less than 10% of its maximal (free-load) value--a situation under which the processivity of motor diminishes and experimental observations are less certain. We then investigate the dependence of load-velocity curve on ATP (ADP) concentration. It is shown that the free load Vmax exhibits a Michaelis-Menten like behavior, and the isometric Fmax increases linearly with ln([ATP]/[ADP]). However, the quasi-linear region is independent of the ATP concentration, yielding an apparently ATP-independent maximal force below the true isometric force. Finally, the heat production as a function of ATP concentration and external load are calculated. In simple terms and solved with elementary algebra, the present model provides an integrated picture of biochemical kinetics and mechanical energetics of motor proteins.
Kinetics of platelet 5-hydroxytryptamine uptake in headache patients.
Hannah, P; Jarman, J; Glover, V; Sandler, M; Davies, P T; Clifford Rose, F
1991-07-01
Platelet 5-hydroxytryptamine (5-HT) uptake was measured in asymptomatic headache patients attending a specialist migraine clinic, and in hospital staff who did not suffer from regular or severe headache. Current levels of anxiety and depression were assessed in all subjects using the Hospital Anxiety and Depression (HAD) scale and their possible influence on the uptake kinetics taken into account during the analysis of results. The Michaelis-Menten constant (Km) was significantly raised in common migraine and tension headache compared with controls (p less than 0.001 and p less than 0.01, respectively), but not in classical migraine or cluster headache. The increase remained significant after adjusting for differences in age, sex, presence of anxiety or depression (HAD sub-scale score greater than or equal to 8), drug intake during the week before testing, time elapsed since last attack and time of assay (am or pm). No differences were observed between patients and controls in the maximal rate of uptake (Vmax) or platelet count, and previous reports of a reduction in Vmax in patients experiencing attack within 5 days prior to testing could not be confirmed. The cause and significance of an increased Km are not clear, but plasma factors acting as competitive inhibitors for the uptake site or an alteration in the configuration of the uptake site are possible explanations. If confirmed, the shared biochemical abnormality may suggest that common migraine and tension headache have a common pathogenesis.
Complex kinetics of a Landolt-type reaction: the later phase of the thiosulfate-iodate reaction.
Varga, Dénes; Nagypál, István; Horváth, Attila K
2010-05-13
The thiosulfate-iodate reaction has been studied spectrophotometrically in slightly acidic medium at 25.0 +/- 0.1 degrees C in acetate/acetic acid buffer by monitoring the absorbance at 468 nm at the isosbestic point of iodine-triiodide ion system. The formation of iodine after the Landolt time follows a rather complex kinetic behavior depending on the pH and on the concentration of the reactants as well. It is shown that the key intermediate of the reaction is I(2)O(2), its equilibrium formation from the well-known Dushman reaction along with their further reactions followed by subsequent reactions of HOI, HIO(2), S(2)O(3)OH(-), and S(2)O(3)I(-) adequately accounts for all the experimentally measured characteristics of the kinetic curves. A 19-step kinetic model is proposed and discussed with 13 fitted and 7 fixed parameters in detail.
2017-01-01
The specific consumption rate of substrate, as well as the associated specific growth rate, is an essential parameter in the mathematical description of substrate-limited microbial growth. In this paper we develop a completely new kinetic model of substrate transport, based on recent knowledge on the structural biology of transport proteins, which correctly describes very accurate experimental results at near-zero substrate concentration values found in the literature, where the widespread Michaelis-Menten model fails. Additionally, our model converges asymptotically to Michaelis-Menten predictions as substrate concentration increases. Instead of the single active site enzymatic reaction of Michaelis-Menten type, the proposed model assumes a multi-site kinetics, simplified as an apparent all-or-none mechanism for the transport, which is controlled by means of the local substrate concentration in the close vicinity of the transport protein. Besides, the model also assumes that this local concentration is not equal to the mean substrate concentration experimentally determined in the culture medium. Instead, we propose that it fluctuates with a mostly exponential distribution of Weibull type. PMID:28187189
Gonze, Didier; Abou-Jaoudé, Wassim; Ouattara, Djomangan Adama; Halloy, José
2011-01-01
The recent advance of genetic studies and the rapid accumulation of molecular data, together with the increasing performance of computers, led researchers to design more and more detailed mathematical models of biological systems. Many modeling approaches rely on ordinary differential equations (ODE) which are based on standard enzyme kinetics. Michaelis-Menten and Hill functions are indeed commonly used in dynamical models in systems and synthetic biology because they provide the necessary nonlinearity to make the dynamics nontrivial (i.e., limit-cycle oscillations or multistability). For most of the systems modeled, the actual molecular mechanism is unknown, and the enzyme equations should be regarded as phenomenological. In this chapter, we discuss the validity and accuracy of these approximations. In particular, we focus on the validity of the Michaelis-Menten function for open systems and on the use of Hill kinetics to describe transcription rates of regulated genes. Our discussion is illustrated by numerical simulations of prototype systems, including the Repressilator (a genetic oscillator) and the Toggle Switch model (a bistable system). We systematically compare the results obtained with the compact version (based on Michaelis-Menten and Hill functions) with its corresponding developed versions (based on "elementary" reaction steps and mass action laws). We also discuss the use of compact approaches to perform stochastic simulations (Gillespie algorithm). On the basis of these results, we argue that using compact models is suitable to model qualitatively biological systems.
Zhang, Fan [ORNL; Yeh, Gour-Tsyh [University of Central Florida, Orlando; Parker, Jack C [ORNL; Brooks, Scott C [ORNL; Pace, Molly [ORNL; Kim, Young Jin [ORNL; Jardine, Philip M [ORNL; Watson, David B [ORNL
2007-01-01
This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing NE equilibrium reactions and a set of reactive transport equations of M-NE kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.
Zhang, Fan; Yeh, Gour-Tsyh; Parker, Jack C.; Brooks, Scott C.; Pace, Molly N.; Kim, Young-Jin; Jardine, Philip M.; Watson, David B.
2007-06-01
This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing NE equilibrium reactions and a set of reactive transport equations of M- NE kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.
Kinetic modelling of GlmU reactions - prioritization of reaction for therapeutic application.
Vivek K Singh
Full Text Available Mycobacterium tuberculosis(Mtu, a successful pathogen, has developed resistance against the existing anti-tubercular drugs necessitating discovery of drugs with novel action. Enzymes involved in peptidoglycan biosynthesis are attractive targets for antibacterial drug discovery. The bifunctional enzyme mycobacterial GlmU (Glucosamine 1-phosphate N-acetyltransferase/ N-acetylglucosamine-1-phosphate uridyltransferase has been a target enzyme for drug discovery. Its C- and N- terminal domains catalyze acetyltransferase (rxn-1 and uridyltransferase (rxn-2 activities respectively and the final product is involved in peptidoglycan synthesis. However, the bifunctional nature of GlmU poses difficulty in deciding which function to be intervened for therapeutic advantage. Genetic analysis showed this as an essential gene but it is still unclear whether any one or both of the activities are critical for cell survival. Often enzymatic activity with suitable high-throughput assay is chosen for random screening, which may not be the appropriate biological function inhibited for maximal effect. Prediction of rate-limiting function by dynamic network analysis of reactions could be an option to identify the appropriate function. With a view to provide insights into biochemical assays with appropriate activity for inhibitor screening, kinetic modelling studies on GlmU were undertaken. Kinetic model of Mtu GlmU-catalyzed reactions was built based on the available kinetic data on Mtu and deduction from Escherichia coli data. Several model variants were constructed including coupled/decoupled, varying metabolite concentrations and presence/absence of product inhibitions. This study demonstrates that in coupled model at low metabolite concentrations, inhibition of either of the GlmU reactions cause significant decrement in the overall GlmU rate. However at higher metabolite concentrations, rxn-2 showed higher decrement. Moreover, with available intracellular
Kinetics of phosphorus uptake and root morphology of local and improved varieties of maize
Machado Cynthia Torres de Toledo
2004-01-01
Full Text Available Interspecific and intraspecific differences in the efficiency of utilization of soil phosphorus (P are explained, in part, by plant morphological and physiological variations, which characterize the plant for nutrient acquisition. As part of a study on maize genotypes characterization for P-uptake and use efficiency, kinetic parameters of P uptake and root morphological characters were evaluated for six local and improved maize varieties, grown in nutrient solution. The kinetic parameters related to P influx were: maximal transport rate (Vmax, the Michaelis-Menten constant (Km, and the external concentration when net uptake is zero (Cmin. Measured root morphological characters were: root length, radius, and surface area. Shoot and root dry matter yield and the P content in these parts were also determined. Diferences among varieties were observed in the kinetic parameters Vmax and Km, root length and in root/shoot dry matter ratio. Lower Km values were better indicatives of P uptake ability of the varietes and were significantly correlated to higher dry matter production and P-efficiency index.
Root Morphology and Zn2+ Uptake Kinetics of the Zn Hyperaccumulator of Sedum alfredii Hance
Ting-Qiang LI; Xiao-E YANG; Zhen-Li HE; Jin-Yan YANG
2005-01-01
Root morphology and Zn2+ uptake kinetics of the hyperaccumulating ecotype (HE) and nonhyperaccumulating ecotype (NHE) of Sedum alfredii Hance were investigated using hydroponic methods and the radiotracer flux technique. The results indicate that root length, root surface area, and root volume of NHE decreased significantly with increasing Zn2+ concentration in growth media, whereas the root growth of HE was not adversely affected, and was even promoted, by 500 μmol/L Zn2+. The concentrations of Zn2+ in both ecotypes of S. alfredii were positively correlated with root length, root surface area and root volumes, but no such correlation was found for root diameter. The uptake kinetics for 65Zn2+ in roots of both ecotypes of S. alfredii were characterized by a rapid linear phase during the first 6 h and a slower linear phase during the subsequent period of investigation. The concentration-dependent uptake kinetics of the two ecotypes of S. alfredii could be characterized by the Michaelis-Menten equation, with the Vmax for 65Zn2+ influx being threefold greater in HE compared with NHE, indicating that enhanced absorption into the root was one of the mechanisms involved in Zn hyperaccumulation. A significantly larger Vmax value suggested that there was a higher density of Zn transporters per unit membrane area in HE roots.
L.R.B. Gonçalves
1997-12-01
Full Text Available In this work the effects of diffusion on the hydrolysis of maltose using glucoamylase immobilized on macroporous silica at 30o C are studied. Two different kinds of experimental assays are carried out: one using free enzyme and the other using an enzyme covalently linked to macroporous silica, preactivated with glutaraldehyde. Free enzyme assays are used to estimate the kinetic parameters for hydrolysis of maltose at 30ºC, according to a Michaelis-Menten equation, with inhibition by the product. Runs with the immobilized enzyme enable us to estimate dextrin diffusivities in silica, assuming that the inherent kinetic parameters are equal to the intrinsic ones. The values of kinetic and mass transfer parameters are: K3 = 0.90x10-5 g/U.s, Km = 0.61x10-3 g/ml, Ki = 1.23x10-1 g/ml, DMs = 0.50x10-6 cm2 /s and DGs = 0.55x10-6 cm2 /s
Effect of diet-induced obesity on kinetic parameters of amino acid uptake by rat erythrocytes.
Picó, C; Pons, A; Palou, A
1992-11-01
The effects of cafeteria diet-induced obesity upon in vitro uptake of L-Alanine, Glycine, L-Lysine, L-Glutamine, L-Glutamic acid, L-Phenylalanine and L-Leucine by isolated rat erythrocytes have been studied. The total Phe and Leu uptakes followed Michaelis-Menten kinetics. The Glu uptake was fitted to diffusion kinetics. The uptakes of Ala, Gly, Lys and Gln were best explained by a two-component transport: one saturable and one diffusion. Obesity increased the Km value for Ala, Gln and Leu, and the Vmax value for Ala, but decreased the Vmax for Lys. Kinetic parameters of Phe uptake were unaffected by obesity. In addition, the pseudo-first order rate constant (Vmax/Km) for Ala, Gly, Gln, Lys and Leu uptake decreased as a result of cafeteria diet-induced obesity. The Kd value for Ala, Gly, Gln and Glu decreased and that of Lys increased as result of obesity. These adaptations could, at least in part, explain alterations in amino acid distribution between blood cells and plasma related to overfeeding or obesity.
Inferring latent gene regulatory network kinetics
González, Javier; Vujačić, Ivan; Wit, Ernst
2013-01-01
Regulatory networks consist of genes encoding transcription factors (TFs) and the genes they activate or repress. Various types of systems of ordinary differential equations (ODE) have been proposed to model these networks, ranging from linear to Michaelis-Menten approaches. In practice, a serious d
Some kinetics aspects of chlorine-solids reactions
Kanari, N.
2010-02-01
Full Text Available The present paper describes detailed kinetics investigations on some selected chlorine-solid reactions through thermogravimetric measurements. The solids studied in this article include chemical pure oxides and sulfides as well as their natural bearing materials. The chlorinating agents employed are gaseous mixtures of Cl_{2}+N_{2} (chlorination, Cl_{2}+O_{2} (oxychlorination, and Cl_{2}+CO (carbochlorination. Results are presented as effects of various parameters on the reaction rate of these solids with these chlorinating agents. It was observed that the reactivity of these solids towards different chlorinating agents varied widely. Sulfides could be chlorinated at room temperature, while carbochlorination of chromium (III oxide was possible only above 500 °C. The variation of the chlorination rate of these complex materials with respect to gas velocity, composition and temperature enabled us to focus some light on the plausible reaction mechanisms and stoichiometries. The obtained results were used for selective removal of iron from chromite concentrates, extraction of valuable metals from sulfide materials, purification of MgO samples, etc.
Este trabajo describe detalladas investigaciones cinéticas en algunas reacciones seleccionadas de cloro-sólido a través de medidas termogravimétricas. Los sólidos estudiados en este artículo incluyen óxidos químicos puros y sulfuros, así como sus materiales naturales de soporte. Los agentes de cloración empleados son mezclas de gases de Cl_{2}+N_{2} (cloración, Cl_{2}+O_{2} (oxicloración y Cl_{2}+O_{2} (carbocloración. Los resultados se presentan como efecto de varios parámetros en el porcentaje de reacción de estos sólidos con los agentes de cloración. Se ha observado que la reactividad de estos sólidos a través de diferentes agentes de cloración varía ampliamente. Los sulfuros se pudieron
QIN Yan; LIU Haihua; HUANG Zhixiong; MEI Qilin
2007-01-01
Several kinetic models for unsaturated polyester cure reaction and some existing parameter estimation techniques of these models were introduced. Correlated kinetic parameters and kinetic equations of the autocatalytic empirical kinetic model of LPSMC system were determined by using isothermal DSC to scan the system which was thickened by crystalline polymer (PEG-MAH). Through using a serial curing degree of the system to validate the model, the experimental results were basically identical with the predictions of the autocatalytic empirical kinetic model. This model could provide a theoretical reference to the determination of molding techniques of low pressure SMC.
Farias, Daniel L; Lucena, Malson N; Garçon, Daniela P; Mantelatto, Fernando L; McNamara, John C; Leone, Francisco A
2017-08-24
We provide a kinetic characterization of (Na(+), K(+))-ATPase activity in a posterior gill microsomal fraction from the semi-terrestrial mangrove crab Cardisoma guanhumi. Sucrose density gradient centrifugation reveals two distinct membrane fractions showing considerable (Na(+), K(+))-ATPase activity, but also containing other microsomal ATPases. The (Na(+), K(+))-ATPase, notably immuno-localized to the apical region of the epithelial pillar cells, and throughout the pillar cell bodies, has an M r of around 110 kDa and hydrolyzes ATP with V M = 146.8 ± 6.3 nmol Pi min(-1) mg protein(-1) and K M = 0.05 ± 0.003 mmol L(-1) obeying Michaelis-Menten kinetics. While stimulation by Na(+) (V M = 139.4 ± 6.9 nmol Pi min(-1) mg protein(-1), K M = 4.50 ± 0.22 mmol L(-1)) also follows Michaelis-Menten kinetics, modulation of (Na(+), K(+))-ATPase activity by MgATP (V M = 136.8 ± 6.5 nmol Pi min(-1) mg protein(-1), K 0.5 = 0.27 ± 0.04 mmol L(-1)), K(+) (V M = 140.2 ± 7.0 nmol Pi min(-1) mg protein(-1), K 0.5 = 0.17 ± 0.008 mmol L(-1)), and NH4(+) (V M = 149.1 ± 7.4 nmol Pi min(-1) mg protein(-1), K 0.5 = 0.60 ± 0.03 mmol L(-1)) shows cooperative kinetics. Ouabain (K I = 52.0 ± 2.6 µmol L(-1)) and orthovanadate (K I = 1.0 ± 0.05 µmol L(-1)) inhibit total ATPase activity by around 75%. At low Mg(2+) concentrations, ATP is an allosteric modulator of the enzyme. This is the first study to provide a kinetic characterization of the gill (Na(+), K(+))-ATPase in C. guanhumi, and will be useful in better comprehending the biochemical underpinnings of osmoregulatory ability in a semi-terrestrial mangrove crab.
Model for reaction kinetics in pyrolysis of wood
Ahuja, P.; Singh, P.C.; Upadhyay, S.N.; Kumar, S. [Banaras Hindu Univ., Varanasi (India)
1996-12-31
A reaction model for the pyrolysis of small and large particles of wood Is developed. The chemical reactions that take place when biomass is pyrolyzed are the devolatilization reactions (primary) and due to the vapour-solid interactions (secondary). In the case of small particles, when the volatiles are immediately removed by the purge gas, only primary reactions occur and the reaction model is described by weight loss and char forming reactions. The of heterogeneous secondary reactions occur in the case of large particles due to the interaction between the volatiles and the hot nascent primary char. A chain reaction mechanism of secondary char formation is proposed. The model takes both the volatiles retention time and cracking and repolymerization reactions of the vapours with the decomposing solid as well as autocatalysis into consideration. 7 refs., 3 figs., 2 tabs.
Model for reaction kinetics in pyrolysis of wood
Ahuja, P.; Singh, P.C.; Upadhyay, S.N.; Kuma, S. [Banaras Hindu Univ., Varanasi (India)
1996-12-31
A reaction model for the pyrolysis of small and large particles of wood is developed. The chemical reactions that take place when biomass is pyrolyzed are the devolatilization reactions (primary) and due to the vapour-solid interactions (secondary). In the case of small particles, when the volatiles are immediately removed by the purge gas, only primary reactions occur and the reaction model is described by weight loss and char forming reactions. The heterogeneous secondary reactions occur in the case of large particles due to the interaction between the volatiles and the hot nascent primary char. A chain reaction mechanism of secondary char formation is proposed. The model takes both the volatiles retention time and cracking and repolymerization reactions of the vapours with the decomposing solid as well as autocatalysis into consideration. 6 refs., 3 figs., 2 tabs.
Almagrbi Abdualnaser Muftah
2014-01-01
Full Text Available This article presents a methodology for kinetic parameter estimation which is based on standard optimization methods. The parameter estimation procedure is applied to the example of modelling of non-catalytic transesterification reaction, based on laboratory experiments performed under elevated pressure. The kinetic model employed in this study consists of three consecutive and parallel reversible reactions of the second order, with six kinetic constants. The influence of the mass transfer effects was considered as well. The best results were obtained by Genetic Algorithm method. The application of this method resulted in kinetic parameters with improved accuracy in predicting concentrations of important reaction intermediates, i.e. diglycerides and monoglycerides. Activation energies of kinetic parameters obtained by the Genetic Algorithm method are in very good agreement with theoretical values determined by molecular orbital calculations. [Projekat Ministarstva nauke Republike Srbije, br. III-45019
Li, Jianhua; Peng, Jianbiao; Zhang, Ya; Ji, Yuefei; Shi, Huanhuan; Mao, Liang; Gao, Shixiang
2016-06-05
This study investigated and compared reaction kinetics, product characterization, and toxicity variation of triclosan (TCS) removal mediated by soybean peroxidase (SBP), a recognized potential peroxidase for removing phenolic pollutants, and the commonly used horseradish peroxidase (HRP) with the goal of assessing the technical feasibility of SBP-catalyzed removal of TCS. Reaction conditions such as pH, H2O2 concentration and enzyme dosage were found to have a strong influence on the removal efficiency of TCS. SBP can retain its catalytic ability to remove TCS over broad ranges of pH and H2O2 concentration, while the optimal pH and H2O2 concentration were 7.0 and 8μM, respectively. 98% TCS was removed with only 0.1UmL(-1) SBP in 30min reaction time, while an HRP dose of 0.3UmL(-1) was required to achieve the similar conversion. The catalytic performance of SBP towards TCS was more efficient than that of HRP, which can be explained by catalytic rate constant (KCAT) and catalytic efficiency (KCAT/KM) for the two enzymes. MS analysis in combination with quantum chemistry computation showed that the polymerization products were generated via CC and CO coupling pathways. The polymers were proved to be nontoxic through growth inhibition of green alga (Scenedesmus obliquus). Taking into consideration of the enzymatic treatment cost, SBP may be a better alternative to HRP upon the removal and detoxification of TCS in water/wastewater treatment.
Complex Kinetics in the Reaction of Taurine with Aqueous Bromine ...
The reaction of chlorite and thiourea,4 for example, had shown complex ..... From an analysis of the combination of the slow reaction R4 and the very rapid reaction ..... 22 B.S. Martincigh, C. Mundoma and R. H. Simoyi, J. Phys. Chem. A, 1998,.
Kinetics and thermodynamics of chemical reactions in Li/SOCl2 cells
Hansen, Lee D.; Frank, Harvey
1987-01-01
Work is described that was designed to determine the kinetic constants necessary to extrapolate kinetic data on Li/SOCl2 cells over the temperature range from 25 to 75 C. A second objective was to characterize as far as possible the chemical reactions that occur in the cells since these reactions may be important in understanding the potential hazards of these cells. The kinetics of the corrosion processes in undischarged Li/SOCl2 cells were determined and separated according to their occurrence at the anode and cathode; the effects that switching the current on and off has on the corrosion reactions was determined; and the effects of discharge state on the kinetics of the corrosion process were found. A thermodynamic analysis of the current-producing reactions in the cell was done and is included.
Kinetics and thermodynamics of chemical reactions in Li/SOCl2 cells
Hansen, Lee D.; Frank, Harvey
1987-01-01
Work is described that was designed to determine the kinetic constants necessary to extrapolate kinetic data on Li/SOCl2 cells over the temperature range from 25 to 75 C. A second objective was to characterize as far as possible the chemical reactions that occur in the cells since these reactions may be important in understanding the potential hazards of these cells. The kinetics of the corrosion processes in undischarged Li/SOCl2 cells were determined and separated according to their occurrence at the anode and cathode; the effects that switching the current on and off has on the corrosion reactions was determined; and the effects of discharge state on the kinetics of the corrosion process were found. A thermodynamic analysis of the current-producing reactions in the cell was done and is included.
Kinetics of the intestinal uptake of zinc acexamate in normal and zinc-depleted rats.
Torres-Molina, F; Martínez-Coscollá, A; Gisbert, S; Quintana, E; Sendrós, S; Peris-Ribera, J E; Plá-Delfina, J M
1990-10-01
The uptake of zinc as acexamic acid salt in the small intestine of the anaesthetized rat was shown to be a two-phase process in normal animals. The first phase is rapid mucosal binding which satisfies the Freundlich isotherm equation and which involves about 30 per cent of the initially perfused zinc. The second phase was characterized as an apparent absorption step which obeys Michaelis-Menten and first-order combined kinetics, with the following parameters: Vm = 6.51 mg h-1; Km = 2.96 mg; ka = 0.306 h-1. In largely non-saturated conditions, an apparent global rate constant of about 2.50 h-1 was calculated. No significant interference due to endogenous zinc excretion into the small intestine was observed during the absorption period. In zinc-deficient animals, the two phases were not so well characterized. Binding was non-linear and apparent absorption efficiency was much greater at high zinc concentrations, so no evidence of saturable kinetics was found, thus confirming the hypothesis of a homeostatic zinc regulation mechanism.
Tavares, Ana P M; Silva, Cláudia G; Dražić, Goran; Silva, Adrián M T; Loureiro, José M; Faria, Joaquim L
2015-09-15
The biocatalytic performance of immobilized enzyme systems depends mostly on the intrinsic properties of both biomolecule and support, immobilization technique and immobilization conditions. Multi-walled carbon nanotubes (MWCNTs) possess unique features for enzyme immobilization by adsorption. Enhanced catalytic activity and stability can be achieved by optimization of the immobilization conditions and by investigating the effect of operational parameters. Laccase was immobilized over MWCNTs by adsorption. The hybrid material was characterized by Fourier transformed infrared (FTIR) spectroscopy, scanning and transmission electron microscopy (SEM and TEM, respectively). The effect of different operational conditions (contact time, enzyme concentration and pH) on laccase immobilization was investigated. Optimized conditions were used for thermal stability, kinetic, and storage and operational stability studies. The optimal immobilization conditions for a laccase concentration of 3.75μL/mL were a pH of 9.0 and a contact time of 30min (522 Ulac/gcarrier). A decrease in the thermal stability of laccase was observed after immobilization. Changes in ΔS and ΔH of deactivation were found for the immobilized enzyme. The Michaelis-Menten kinetic constant was higher for laccase/MWCNT system than for free laccase. Immobilized laccase maintained (or even increased) its catalytic performance up to nine cycles of utilization and revealed long-term storage stability.
Narayani, M; Vidya Shetty, K
2014-04-01
A Gram negative hexavalent chromium (Cr(VI)) reducing bacteria, Ochrobactrum sp. Cr-B4 (genbank accession number: JF824998) was isolated from the aerator water of an activated sludge process of a wastewater treatment facility of a dye and pigment based specialty chemical industry. It showed a resistance for 1000 mg L(-1) Cr(VI). It exhibited resistance against other heavy metal ions like Ni(2+) (900 mg L(-1) ), Cu(2+) (500 mg L(-1) ), Pb(2+) (800 mg L(-1) ), and Cd(2+) (250 mg L(-1) ), Zn(2+) (700 mg L(-1) ), Fe(3+) (800 mg L(-1) ), and against selected antibiotics. Cr-B4 could efficiently reduce 200 mg L(-1) Cr(VI) completely in nutrient and LB media and could convert Cr(VI) to Cr(III) efficiently. Cr(VI) reduction in nutrient media followed allosteric enzyme kinetics with Km values of 59.39 mg L(-1) and Vmax values of 47.03 mg L(-1) h(-1) . The reduction in LB media followed Michaelis-Menten kinetics with Km values of 99.52 mg L(-1) and Vmax of 77.63 mg L(-1) h(-1) . Scanning electron micrograms revealed the presence of extracellular polymeric secretions.
Investigation of Horseradish Peroxidase Kinetics in an "Organelle-Like" Environment.
Baumann, Patric; Spulber, Mariana; Fischer, Ozana; Car, Anja; Meier, Wolfgang
2017-05-01
In order to mimic cell organelles, artificial nanoreactors have been investigated based on polymeric vesicles with reconstituted channel proteins (outer membrane protein F) and coencapsulated enzymes horseradish peroxidase (HRP) along with a crowding agent (Ficoll or polyethylene glycol) inside the cavity. Importantly, the presence of macromolecules has a strong impact on the enzyme kinetics, but no influence on the integrity of vesicles up to certain concentrations. This particular design allows for the first time the determination of HRP kinetics inside nanoreactors with crowded milieu. The values of the Michaelis-Menten constant (K m ) measured for HRP in a confined space (encapsulated in nanoreactors) in the absence of macromolecules are ≈50% lower than in free conditions, and the presence of a crowding agent results in a further pronounced decrease. These results clearly suggest that activities of enzymes in confined spaces can be tuned by varying the concentrations of crowding compounds. The present investigation represents an advance in nanoreactor design by considering the influence of environmental factors on enzymatic performance, and it demonstrates that both encapsulation and the presence of a crowding environment increase the enzyme-substrate affinity. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Cybulskis, Viktor J.; Smeltz, Andrew D.; Zvinevich, Yury; Gounder, Rajamani; Delgass, W. Nicholas; Ribeiro, Fabio H.
2016-01-01
Understanding catalytic chemistry, collecting and interpreting kinetic data, and operating chemical reactors are critical skills for chemical engineers. This laboratory experiment provides students with a hands-on supplement to a course in chemical kinetics and reaction engineering. The oxidation of methane with a palladium catalyst supported on…
A kinetic model for the glucose/glycine Maillard reaction pathways
Martins, S.I.F.S.; Boekel, van M.A.J.S.
2005-01-01
A comprehensive kinetic model for the glucose/glycine Maillard reaction is proposed based on an approach called multiresponse kinetic modelling. Special attention was paid to reactants, intermediates and end products: -fructose, N-(1-deoxy--fructos-1-yl)-glycine (DFG), 1-deoxy-2,3-hexodiulose and
Koga, Nobuyoshi; Goshi, Yuri; Yoshikawa, Masahiro; Tatsuoka, Tomoyuki
2014-01-01
An undergraduate kinetic experiment of the thermal decomposition of solids by microscopic observation and thermal analysis was developed by investigating a suitable reaction, applicable techniques of thermal analysis and microscopic observation, and a reliable kinetic calculation method. The thermal decomposition of sodium hydrogen carbonate is…
Koga, Nobuyoshi; Goshi, Yuri; Yoshikawa, Masahiro; Tatsuoka, Tomoyuki
2014-01-01
An undergraduate kinetic experiment of the thermal decomposition of solids by microscopic observation and thermal analysis was developed by investigating a suitable reaction, applicable techniques of thermal analysis and microscopic observation, and a reliable kinetic calculation method. The thermal decomposition of sodium hydrogen carbonate is…
Utilization of the Recycle Reactor in Determining Kinetics of Gas-Solid Catalytic Reactions.
Paspek, Stephen C.; And Others
1980-01-01
Describes a laboratory scale reactor that determines the kinetics of a gas-solid catalytic reaction. The external recycle reactor construction is detailed with accompanying diagrams. Experimental details, application of the reactor to CO oxidation kinetics, interphase gradients, and intraphase gradients are discussed. (CS)
A kinetic study on non-catalytic reactions in hydroprocessing Boscan crude oil
A. Marafi; E. Kam; A. Stanislaus [Kuwait Institute for Scientific Research, Safat (Kuwait). Petroleum Refining Department, Petroleum Research and Studies Center
2008-08-15
Non-catalytic hydrothermal cracking reactions are known to associate with catalytic hydrocracking reactions. In a recent study on hydroprocessing of Boscan crude over a specific catalyst system containing three distinct catalysts, it was found that hydrodesulfurization (HDS) and hydrodemetallation (HDM) reactions continued even when the catalyst is severely deactivated. Since the reactor was packed with considerable amount of inert material besides the three catalysts, it will be advantage to determine if the inert materials can also facilitate hydroprocessing reactions. A series of kinetic experiments for the inert particles was undertaken under different space velocity and temperature conditions. The extent of catalytic and non-catalytic hydroprocessing reactions was assessed. Through statistical analysis, the initial reaction rate constant, reaction order and activation energy for various hydroprocessing reactions were then determined. The absolute average deviations (AAD) of the kinetics values obtained for inert materials are less than 10%. 25 refs., 7 figs., 4 tabs.
Otero, Toribio F
2017-01-18
In this perspective the empirical kinetics of conducting polymers exchanging anions and solvent during electrochemical reactions to get dense reactive gels is reviewed. The reaction drives conformational movements of the chains (molecular motors), exchange of ions and solvent with the electrolyte and structural (relaxation, swelling, shrinking and compaction) gel changes. Reaction-driven structural changes are identified and quantified from electrochemical responses. The empirical reaction activation energy (Ea), the reaction coefficient (k) and the reaction orders (α and β) change as a function of the conformational energy variation during the reaction. This conformational energy becomes an empirical magnitude. Ea, k, α and β include and provide quantitative conformational and structural information. The chemical kinetics becomes structural chemical kinetics (SCK) for reactions driving conformational movements of the reactants. The electrochemically stimulated conformational relaxation model describes empirical results and some results from the literature for biochemical reactions. In parallel the development of an emerging technological world of soft, wet, multifunctional and biomimetic tools and anthropomorphic robots driven by reactions of the constitutive material, as in biological organs, can be now envisaged being theoretically supported by the kinetic model.
黄曲霉毒素氧化酶的酶动力学研究%Enzymatic kinetics of aflatoxin oxidase
胡丽莎; 谢春芳; 刘大岭
2012-01-01
Aflatoxin oxidase ( AFO) is a protein enzyme derived from the Armillariella tabescens, and demonstrating aflatoxin degradation effect. AFO has been successfully cloned and expressed in a prokary-otic system in our previous studies. The enzymatic kinetics has been investigated by determination of the apparent reaction rate. The traditional analysis method was carried out by end point reaction, which was not suitable for the continuous monitor of enzyme reaction. The experimental process of traditional method was more cumbersome and could be influenced by many factors. Therefore, isothermal titration microcalo-ri-metry (ITC) was used to examine the enzymatic kinetics of AFO in this study through substrate titration and direct monitoring of enzyme reactions in the process of heat change. A complete Michaelis-Ment-en curve was produced by the titration, and measured by fitting analysis. The aflatoxin oxidase activity on AFB1 (KmAFB1) and the ST Michaelis-Menten constant (KmST) were found at 3. 34 x 10-7 mol/L and 1. 06 x 10-7 mol/L, respectively. AFB1 and ST conversion factors were KcatAFB1 -2. 7 min-1 and KcatST = 1.7 min-1 respectively. The combination letters were found at AHAFB1 = - 1.686 x 107 J/mol andΔH5T = -9. 092 x 106 J/mol, respectively. Compared with the traditional methods, application of ITC in enzymatic kinetics demonstrates significant advantages, due to its simpleness, speediness, accuracy and universality.%黄曲霉毒素氧化酶(AFO)是来自Armillariella tabescens的具有降解黄曲霉毒素作用的蛋白质酶.本实验室成功克隆和以原核系统表达了黄曲霉毒素氧化酶,前期的工作中用传统测量表观酶促反应速度的方法对AFO进行了酶动力学的研究,采用了在酶反应的结束点进行分析,因此不能够连续监测酶的反应过程,且实验过程较为繁琐,影响因素较多,对动力学常数的测量存在不够准确的可能.本实验使用等温滴定微量热技术对该
翟爱华; 李新华
2012-01-01
The response mechanism and kinetic behavior of bioactive peptides by protease were studied. Rice bran protein was used as raw material. Based on the classic Michaelis - Menten equation, the enzymatic kinetics of the system of rice bran protein and alkaline protease was researched by the method of mathematical derivation combined with experiment. The mechanism model of single substrate hydrolysis of protein and inactivation of protease were considered to build the kinetics model of R =aexp[ -b(DH) ] ,and the parameters "a" and "b" of the kinetics model were determined. Origin 8. 0 software was applied to fit the deduced formula and calculate related parameters of enzyme kinetic model. It was shown that the rate of hydrolysis kinetic model was R = (94. 754e0 - 0. 0597s0 ) exp [ -0. 157 (DH)] and the kinetic model of degree of hydrolysis and time of hydrolysis was DH = 6. 37× ln[1 +(14. 88e0/s0 -0. 009)t]. The kinetic constants of the system of rice bran protein and alkaline protease were fitted by experiments and the results showed that the constant K4 of enzyme inactivation was 16. 144 min-1 and the constant k2 of enzymatic reaction rate was 94. 754 min-1 .%研究蛋白酶水解制备生物活性多肽反应机制与动力学行为,基于经典的米氏方程理论,应用数学推导结合试验研究的方法,以米糠蛋白为原料,对米糠蛋白-碱性蛋白酶体系进行酶解动力学研究.考虑蛋白质单底物水解、蛋白酶失活的机理模型,构建动力学模型R=aexp[-b(DH)],其中对参数a值和b值进行确定.利用Origin 8.0软件,对推导出的公式进行拟合得到水解速率动力学模型为R=(94.754e0-0.0597s0)exp[-0.157(DH)],水解度-水解时间的动力学模型:DH =6.37ln[1+(14.88e0/s0-0.009)t].对于米糠蛋白-碱性蛋白酶模型体系,经试验拟合,并求得该体系动力学常数:酶失活常数K4为16.144 min-1,酶解反应速率常数k2为94.754 min-1.
Marcella A. A. Carneiro
2011-04-01
Full Text Available The absorption efficiency and kinetic parameters (Vmax, Ks and Vmax:Ks of the seaweed Gracilaria cervicornis for the nutrients NH4+, NO3- and PO4(3- were evaluated. Absorption efficiency was measured by monitoring nutrient concentrations for 5 h in culture media with initial concentrations of 5, 10, 20 and 30µM. Kinetic parameters were determined by using the Michaelis-Menten formula. Absorption efficiencies for this algae were greater in treatments with lower concentrations, as evidenced by a reduction of 85.3, 97.5 and 81.2% for NH4+, NO3- and PO4(3-, respectively. Kinetic parameters show that G. cervicornis exhibits greater ability to take up high concentrations of NH4+ (Vmax=158.5µM g dw-1 h-1 and low concentrations of PO4(3- (Ks=5µM and Vmax:Ks=10.3. These results suggest that this algal species has good absorption capacity for the nutrients tested and may be a promising candidate as a bioremediator of eutrophized environments.
Kinetics for the reaction of hydrogen with uranium powder
Stakebake, J.L.
1979-01-01
The reaction of hydrogen with uranium powder was investigated at 13.3 and 26.6 kPa between 50 and 250/sup 0/C. The reaction order was independent of temperature but varied from 2/3-order at 13.3 kPa to 1st-order at 26.6 kPa. Increasing temperatures resulted in decreasing reaction rates over the temperature range studied. A reaction mechanism with adsorption as the rate controlling step is proposed to explain the temperature behavior. Decomposition of the hydride was found to follow a zero-order rate process.
2014-04-04
were determined by Michaelis - Menten steady state kinetics using Prism Graphpad (Irvine, CA). Kinetic data for CMP hydrolysis was used as a metric to...against CMP, paraoxon and phenyl acetate versus G3C9 expression in E. coli (Table 1). A closer examination of the Michaelis - Menten parameters reveals...0.05% BSA 1.09 ± 0.06 45 ± 9 24 ± 5 Table 2. Michaelis - Menten parameters for G3C9 CMP hydrolysis. G3C9 expressed in mammalian cells displayed
The kinetic resolution of enantiomers by means of enzymatic reactions
Otto, P.P.H.L.
1990-01-01
For conversions involving a single enzyme, and under certain limiting conditions, the process of kinetic resolution can be described with five variables, which can be determined experimentally. Their quantitative relations have been derived. If any three of these variables are known the other two ca
1D to 3D diffusion-reaction kinetics of defects in crystals
Trinkaus, H.; Heinisch, H.L.; Barashev, A.V.
2002-01-01
Microstructural features evolving in crystalline solids from diffusion-reaction kinetics of mobile components depend crucially on the dimension of the underlying diffusion process which is commonly assumed to be three-dimensional (3D). In metals, irradiation-induced displacement cascades produce ...... and 3D limiting cases. The analytical result is fully confirmed by kinetic Monte Carlo simulations.......Microstructural features evolving in crystalline solids from diffusion-reaction kinetics of mobile components depend crucially on the dimension of the underlying diffusion process which is commonly assumed to be three-dimensional (3D). In metals, irradiation-induced displacement cascades produce...
Bahr, J.M.
1990-01-01
This paper extends a four-step derivation procedure, previously presented for cases of transport affected by surface reactions, to transport problems involving homogeneous reactions. Derivations for these classes of reactions are used to illustrate the manner in which mathematical differences between reaction classes are reflected in the mathematical derivation procedures required to identify kinetically influenced terms. Simulation results for a case of transport affected by a single solution phase complexation reaction and for a case of transport affected by a precipitation-dissolution reaction are used to demonstrate the nature of departures from equilibrium-controlled transport as well as the use of kinetically influenced terms in determining criteria for the applicability of the local equilibrium assumption. A final derivation for a multireaction problem demonstrates the application of the generalized procedure to a case of transport affected by reactions of several classes. -from Author
Li, Jianhua; Peng, Jianbiao [State Key Laboratory of Pollution Control and Resource Reuse, School of the Environment, Nanjing University, Nanjing 210023 (China); Zhang, Ya [Nanjing Institute of Environmental Sciences, Ministry of Environmental Protection of the People’s Republic of China, Nanjing 210042 (China); Ji, Yuefei [College of Resources and Environmental Science, Nanjing Agricultural University, Nanjing 210095 (China); Shi, Huanhuan; Mao, Liang [State Key Laboratory of Pollution Control and Resource Reuse, School of the Environment, Nanjing University, Nanjing 210023 (China); Gao, Shixiang, E-mail: ecsxg@nju.edu.cn [State Key Laboratory of Pollution Control and Resource Reuse, School of the Environment, Nanjing University, Nanjing 210023 (China)
2016-06-05
Highlights: • Enzymatic treatment of triclosan in water by soybean and horseradish peroxidases. • pH, H{sub 2}O{sub 2} concentration and enzyme dosage affected the removal efficiency of TCS. • The removal of TCS by SBP was more efficient than that of HRP. • K{sub CAT} and K{sub CAT}/K{sub M} values for SBP toward TCS were much higher than those for HRP. • Polymers formed via radical coupling mechanism were nontoxic to the growth of alga. - Abstract: This study investigated and compared reaction kinetics, product characterization, and toxicity variation of triclosan (TCS) removal mediated by soybean peroxidase (SBP), a recognized potential peroxidase for removing phenolic pollutants, and the commonly used horseradish peroxidase (HRP) with the goal of assessing the technical feasibility of SBP-catalyzed removal of TCS. Reaction conditions such as pH, H{sub 2}O{sub 2} concentration and enzyme dosage were found to have a strong influence on the removal efficiency of TCS. SBP can retain its catalytic ability to remove TCS over broad ranges of pH and H{sub 2}O{sub 2} concentration, while the optimal pH and H{sub 2}O{sub 2} concentration were 7.0 and 8 μM, respectively. 98% TCS was removed with only 0.1 U mL{sup −1} SBP in 30 min reaction time, while an HRP dose of 0.3 U mL{sup −1} was required to achieve the similar conversion. The catalytic performance of SBP towards TCS was more efficient than that of HRP, which can be explained by catalytic rate constant (K{sub CAT}) and catalytic efficiency (K{sub CAT}/K{sub M}) for the two enzymes. MS analysis in combination with quantum chemistry computation showed that the polymerization products were generated via C−C and C−O coupling pathways. The polymers were proved to be nontoxic through growth inhibition of green alga (Scenedesmus obliquus). Taking into consideration of the enzymatic treatment cost, SBP may be a better alternative to HRP upon the removal and detoxification of TCS in water