Metabolic control analysis in enzymes kinetics (original) (raw)

Mathematical Modeling to Optimize the Product in Enzyme Kinetics

2013

Optimization of product in enzyme kinetics is successful by the showers of mathematical analysis with control measures. Enzymes are an important functional aspects of all biochemical processes, as they catalyze numerous reaction taking place within living organisms. With this view, optimization and quantification of product is stressed upon and in such a context, optimal control approaches have been applied in our study. In this article, we have formulated a mathematical model of enzymatic system dynamics with control measures with a view to optimize the product as well as process conditions. Here, Pontryagin Minimum Principle is used for determination of optimal control with the help of Hamiltonian. We discuss the relevant numerical solutions for the concentration of substrate, enzyme, complex and product with respect to a specified time interval by varying control factors.

A novel method for analyzing enzyme kinetic systems

Applied Mathematics and Computation, 1997

The rate law governing the kinetics of a Single enzyme mediated reaction may be derived relatively easily by hand, given knowledge of the enzyme's mechanism. Such rate lows are typically non-linear in the concentrations of metabolites involved. When a number of enzymes interact, the composite rate law for the complete System involves the simultaneous Solution of the individual enzyme rate laws. We show how Computer algebra tan be used to solve this previously intractable Problem, using the method of Gröbner Bsses. We present an experimental example where kinetic Parameters for individual enzymes arc measured by making observations of a multi-enzyme System, and fitting these data to the rate law for the complete System.

Symbolic and Numeric Computations in Kinetic Analysis of Multi Enzyme Systems in Biochemistry

Although kinetics of coupled enzymatic systems are important from the biochemical point of view only single substrat enzyme kinetic problems are investigated until Computer Algebra Systems are developed. [1]. In this study, kinetics analysis of coupled enzymatic systems including three enzymes of creatine kinase, hexokinase and glucose 6-fosphate dehydrogenase have been performed using both symbolic and numeric methods. Three kinetic parameters that control the flux of the system had been determined, then the parameters have been estimated using experimental data. These parameters are

Application of computer algebra-techniques to metabolic control analysis

Computational Biology and Chemistry / Computers & Chemistry, 2003

For practical purposes the calculation of rate constants is not particularly valuable, since their physical significance is not clear. Of greater practical use are metabolic control coefficients and elasticities. Given the definition of the flux control coefficients CEJ, concentration control coefficient CEX and elasticity εXv1. We can calculate symbolic formulae for these using computer algebra-techniques. These are then functions of Vmax, Km, Ki enzyme and concentrations. Having derived estimates of Vmax, Km, Ki using the fitting method we can then calculate values of the control coefficients and elasticities. Furthermore we can calculate the metabolic control parameters using symbolic values for the conventional kinetic parametrs. Using these we have verified the summation and connectivity theorems. This is a useful cross check on the reliability of the calculations.

On the Numerical Computation of Enzyme Kinetic Parameters

Biomath Communications, 2014

We consider the enzyme kinetic reaction scheme originally proposed by V. Henri of single enzyme-substrate dynamics where two fractions of the enzyme-free and bound-are involved. Henri's scheme involves four concentrations and three rate constants and via the mass action law it is translated into a system of four ODEs. In two case studies we demonstrate how the rate constants can be computed whenever time course experimental data are available. The obtained results are compared with analogous results implied by the classical Michaelis-Menten model. Our approach focuses on the uncertainties in the experimental data, as well as on the use of contemporary computational tools such as CAS Mathematica.

Some Mathematical and Statistical Aspects of Enzyme Kinetics

Most calculus or differential equations courses utilize examples taken from physics, often discussing them in great detail. Chemistry, however, is seldom utilized to illustrate mathematical concepts. This tendency should be reversed because chemistry, especially chemical kinetics, provides the opportunity to apply mathematics readily. We will analyze some basic ideas behind enzyme kinetics, which allow us to deal with separable and linear differential equations as well as realize the need to use power series to approximate x e and) 1 ln(x close to the origin, and to apply the recently defined Lambert W function. The models studied in this context require the estimation of parameters based on experimental data, which in turn allows us to discuss simple and multiple linear regression, transformations and non-linear regression and their implementation using statistical software.

On a general model structure for macroscopic biological reaction rates

Journal of Biotechnology, 2007

Macroscopic modelling of bioprocesses requires the determination of a biological reaction scheme and a kinetic model. The a priori selection of an appropriate kinetic model structure is usually made difficult by the lack of detailed bioprocess knowledge and the profusion of apparently similar biological kinetic laws. Moreover, parameter identification is made arduous and time-consuming by the strong non-linearities involved in kinetic laws. In most cases, these kinetic structures are non-linearizable and no first parameter estimation can be deduced easily. In order to avoid such identification problems, Bogaerts et al. . A general mathematical modelling technique for bioprocesses in engineering applications. Syst. Anal. Model. Simul. 35, have developed a general linearizable kinetic structure which allows the representation of activation and/or inhibition effects of each component in the culture. This paper further generalizes this structure in order to improve the way saturation effects are taken into account, and in turn, improve the biological interpretation of the model parameters. The main advantage of the proposed structure lies in an associated systematic estimation procedure. The usefulness of the proposed model is tested with simulated as well as with experimental data.

Simplifying principles for chemical and enzyme reaction kinetics

Biophysical Chemistry, 1983

Tihonov's Theorems for systems of first-order ordinary diffrxential equations containing small Parameters in the derivativea. which form the mathematical foundation of the stendy-state approximation, are restated. A general procedure for simplifying chemical and enzyme reaction kinetics. based on the difference of characteristic time scales. is presented. Korzuhin's Theorem. which makes it possible to approximate any kinetic sysrem by il closed chemical system. is also reported. The notions and theorrms are illustrated with examples of Michnehs-Menten enzyme kinetics and of a simple autocatalytic system. Another example illustrates how the differences in the rate constants of different elementary reactions may be exploited 10 simplify reaction kinetics by using Tihonov's Theorem. AI1 necessary mathematical notions are explained in the appendices. The most simple formulation of Tihonov's 1st Theorem 'for beginners' is also given. In different sources the name of A.N. Tihonov is often written as Tikhonov, Tichonov. Tichonoff. Tychonoff. etc. W Klonolvski/SimpIifyi,tg reaction kinetics 75