IJERT-A Proposal for Reversible Enzymatic Inhibition Applied to the Michaelis-Menten Model in the Transient State (original) (raw)
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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.
Journal of Mathematical Chemistry, 2007
This work presents an alternative analysis of the integrated rate equations corresponding to the simple Michaelis-Menten mechanism without product inhibition. The suggested new results are reached under a minimal set of assumptions and include, as a particular case, the classical integrated Michaelis-Menten equation. Experimental designs and a kinetic data analysis are suggested to the estimation of the maximum steady-state rate, V max , the Michaelis-Menten constant, K m , the initial enzyme * Corresponding author. 789 0259-9791/07/1100-0789/0 © 2006 Springer Science+Business Media, Inc. R. Varón et al. / Integrated form of the Michaelis-Menten Equation concentration, [E] 0 , and the catalytic constant, k 2 . The goodness of the analysis is tested with simulated time progress curves obtained by numerical integration.
Extending the kinetic solution of the classic Michaelis–Menten model of enzyme action
Journal of Mathematical Chemistry
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 of enzyme catalysis was undertaken by Briggs–Haldane (Biochem J 19:338, 1925). These authors proposed the steady-state treatment, since its applicability was constrained to this condition. The present work describes an extending solution of the Michaelis–Menten model without the need for such a steady-state restriction. We provide the first analysis of all of the individual reaction constants calculated analytically. Using this approach, it is possible to accurately predict the results under new experimental conditions and to characterize and optimize industrial processes in the fields of chemical and food engineering, pharmaceuticals and biotechnology.
Computers & Chemical Engineering, 2016
One essential engineering problem when developing an industrial enzymatic process concerns the model-based design and optimal operation of the enzymatic reactor based on the process and enzyme inactivation kinetics. For a complex enzymatic system, the "default" used first-order enzyme deactivation model has been proved to lead to inadequate process design or sub-optimal operating policies. The present study investigates if a complex enzyme deactivation can be approximated with simple 1st, 2nd, or a novel proposed model with variable deactivation constant. The approached complex enzymatic system is those of the oxidation of d-glucose to 2-keto-d-glucose in the presence of pyranose 2-oxidase. The necessary "simulated experimental data" have been generated by means of an extended kinetic model from literature used to simulate a batch reactor under well-defined nominal conditions. The proposed enzyme deactivation model has been found to be the best lumping alternative, presenting several advantages: simplicity, flexibility, and a very good adequacy.
An analysis of the kinetics of unstable enzymatic systems using MAPLE
Applied Mathematics and Computation, 2000
In this paper, we presented a general kinetic analysis of the reversible enzymatic system for the case in which the substrate, the enzyme±substrate complex and the product are all unstable. Using computer algebra technique, we solve the system of ordinary dierential equations symbolically under the assumption [E] ) [S]. Since this condition satis®ed inside the cells, it can be more relevant to physiological problems. Then using numerical values, simulation progress curves for the concentration of all species are obtained. Ó 0096-3003/00/$ -see front matter Ó 2000 Elsevier Science Inc. All rights reserved. PII: S 0 0 9 6 -3 0 0 3 ( 9 9 ) 0 0 0 3 4 -X
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 with the mathematical technique known as quasi-steady-state approximation. In the second part of the paper an exact one-dimensional formulation of HMM kinetics is considered. The whole problem is condensed in a single one-variable evolution equation that is a second-order non-linear autonomous differential equation, and the control parameters are reduced to three dimensionless quantities: enzyme efficiency, substrate reduced initial concentration, and enzyme reduced initial concentration. The exact solution of HMM kinetics is obtained as a set of Maclaurin series. From the same equation, a number of approximate solutions, some known, some new, are derived in a systematic way that allows a precise evaluation of the respective level of approximation and conditions of validity. The evolution equation obtained is also shown to be well suited for the numerical computation of the concentrations of all species as a function of time for any given combination of parameters.
17 Alternative Perspectives of Enzyme Kinetic Modeling
2012
The basis of enzyme kinetic modelling was established during the early 1900’s when the work of Leonor Michaelis and Maud Menten produced a pseudo-steady state equation linking enzymatic catalytic rate to substrate concentration (Michaelis & Menten, 1913). Building from the Michaelis-Menten equation, other equations used to describe the effects of modifiers of enzymatic activity were developed based on their effect on the catalytic parameters of the Michaelis-Menten equation. Initially, inhibitors affecting the substrate affinity were deemed competitive and inhibitors affecting the reaction rate were labelled non-competitive (McElroy 1947). These equations have persisted as the basis for inhibition studies and can be found in most basic textbooks dealing with the subject of enzyme inhibition. Here the functionality of the competitive and non-competitive equations are examined to support the development of a unified equation for enzymatic activity modulation. From this, a modular appr...
Modeling of enzymatic protein hydrolysis
Process Biochemistry, 1999
Studies on proteolysis of hemoglobin by Alcalase 0.6L are described. Trials were conducted in a batch reactor at different operating conditions. Degrees of hydrolysis in the proteolysates were determined and kinetics of the reaction was considered in detail in relation to substrate concentration, enzyme concentration, temperature, degree of hydrolysis and reaction time. From the results a general kinetic equation for the enzymic hydrolysis of proteins is suggested. The proposed kinetic model allows an easier determination of kinetic parameters using only a few experiments.
Modeling of enzyme production kinetics
Applied Microbiology and Biotechnology, 2006
Models of single cells, cell populations, and cultures can be most useful in organizing information in a comprehensive system description, as well as in optimizing and controlling actual production operations. Models discussed in this article are of various degrees of biological structure and mathematical complexity. The models are developed based on the biomass formation, substrate consumption, and product formation. The potentials and the limitations of all the models have been reported. The parameter estimation by different methods has been discussed in this communication. These parameters will be helpful to explore the areas where future-modeling studies may be especially valuable.
Novel modeling methodology for the characterization of enzymatic hydrolysis of proteins
A novel methodology for the modeling and characterization of the enzymatic hydrolysis of proteins is proposed. The hydrolysis time course can be predicted at different operating conditions for protein concentration , enzyme concentration and temperature. The hydrolysis kinetics of salmon muscle proteins and whey protein isolate by Alcalase were studied using a central composite design. A combination of the logarithmic equation P = 1/bln (abt + 1) to model the hydrolysis time course with the response surface methodology to correlate the kinetic constants a and b with the operating conditions: protein concentration , enzyme concentration and temperature were achieved. The logarithmic equation was a very good fit with the hydrolysis time courses, with both substrates achieving R 2 > 0.995. The kinetic constants a and b were significantly affected by the operating conditions. Empirical models were obtained for a and b as functions of operating conditions. The kinetic constant values were predicted, and a strong correlation between predicted and experimental values was obtained for a (R 2 = 0.949) and b (R 2 = 0.945). The predicted and experimental time courses resulted in good correlation for both salmon muscle proteins (R 2 > 0.987) and whey protein isolate (R 2 > 0.978). The model allowed calculation of the hydrolysis time course of proteins from a given set of operating conditions with good predictability. This methodology can be used with different sources of proteins and enzymes to test the susceptibility of proteins to hydrolysis as well as the catalytic efficiency of proteases. Additionally, the combined model can be used as a design and optimization function.