A novel method for analyzing enzyme kinetic systems (original) (raw)

Application of computer algebra techniques to enzyme kinetics

Applied Mathematics and Computation, 1998

It is possible to write the equations governing a one-stage enzyme-catalysed reaction (according to Michaelis±Menten kinetics) quite easily, and deduce information about the steady-state¯ux in such a system. The situation is somewhat more complicated if several such reactions form a linear chain. We have applied Gr obner-basis techniques to solve such systems and hence demonstrate the use of computer algebra as a powerful technique in enzyme kinetic analysis. Ó 1998 Elsevier Science Inc. All rights reserved.

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

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.

Parameter estimation of an enzyme kinetic system using computer algebra techniques

Applied Mathematics and Computation, 1999

A procedure for fitting enzyme kinetic data directly to the flux equation was described. It involves choosing parameters that minimize the sum of the squares of deviations due to errors in s, the substrate concentration at time t. Estimates of the standard errors of the parameters are provided using computer algebra and numerical analysis techniques.

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.

Metabolic control analysis in enzymes kinetics

2012

Mathematical modelling of metabolic pathway provides us a wide variety of information about behaviour of the system. The kinetic approach to the modelling of the systems is sometimes hampered by the fact that kinetic properties are imperfectly know that makes the structural approach more attractive. In order to make kinetic analysis of a metabolic pathway, construction of mathematical model describing its kinetics is a major part of the work. In the framework of metabolic kinetic theory, it is assumed that the rate of changes in the concentration i x of a metabolite i X is the sum of the r reaction rates, each weighted by corresponding stoichiometric coefficient of i X . Using v and x to denote the rate vector and concentration vector respectively, mathematical model for kinetics of a system can be written as dx Nv dt = where N is stoichiometric matrix which represents how the metabolites involved in the system combine. Derivation of conservation relationship which mainly depends on...

Enzyme Kinetics: Theory and Practice Reaction Rates and Reaction Order

Enzymes, like all positive catalysts, dramatically increase the rate of a given reaction. Enzyme kinetics is principally concerned with the measurement and mathematical description of this reaction rate and its associated constants. For many steps in metabolism, enzyme kinetic properties have been determined, and this information has been collected and organized in publicly available online databases (www.brenda.uni-koeln.de). In the first section of this chapter, we review the fundamentals of enzyme kinetics and provide an overview of the concepts that will help the metabolic modeler make the best use of this resource. The techniques and methods required to determine kinetic constants from purified enzymes have been covered in detail elsewhere and are not discussed here. In the second section, we will describe recent advances in the high throughput, high sensitivity measurement of enzyme activity, detail the methodology, and discuss the use of high throughput techniques for profiling large numbers of samples and providing a first step in the process of identifying potential regulatory candidates.

A program for the numerical integration of enzyme kinetic equations using small computers

International journal of bio-medical computing, 1984

A simple program to integrate differential equations is given. The program is written in BASIC and has been devised to be used on small computers. The program has been used to integrate the differential equations corresponding to a single reaction-single enzyme, a bireaction-single enzyme and a four reaction-four substrate-single enzyme mechanism; it has been used also for studying the interconversions among various molecular forms of a single enzyme, viz. monomer -dimertrimer -tetramer. The program has proven to be very effective in these models and its time consumption comparable with that of other longer programs.

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...