Analytical Solutions of System of Non-Linear Differential Equations in the Single-Enzyme, Single-Substrate Reaction with Non-Mechanism-Based Enzyme Inactivation

Abstract

A closed form of an analytical expression of concentration in the single-enzyme, single-substrate system for the full range of enzyme activities has been derived. The time dependent analytical solution for substrate, enzyme-substrate complex and product concentrations are presented by solving system of non-linear differential equation. We employ He's Homotopy perturbation method to solve the coupled non-linear differential equations containing a non-linear term related to basic enzymatic reaction. The time dependent simple analytical expressions for substrate, enzyme-substrate and free enzyme concentrations have been derived in terms of dimensionless reaction diffusion parameters

Iterative approximate solutions of kinetic equations for reversible enzyme reactions

“…Straightforward methods are derived for estimating the concentrations of substrate u, product w, enzyme-substrate complex v and enzyme E. The dimensionless technique applies to reduce the non-linear system of ODE. The HPM was used for a simple enzyme reaction (1) [11,18]. We have used this method for our case study, and have obtained an analytical approximate solution.…”

“…The Michaelis -Meten equation ( 1) was applied by Kuhn in 1924 [12] to several cases of enzyme kinetics. The model of biochemical reaction was developed by Briggs and Haldane in 1925 [18]. The model of an enzyme action considers a reaction that includes a substrate [S] which binds an enzyme [E] reversibly to a substrate-enzyme [ES].…”

“…In this paper, we estimate the analytic approximate solution for a system of nonlinear ODE equations ( 15)- (18), by using the methods of (HPM) and (SIM).…”

“…Also, k 1 , k 2 and k 3 represent the reaction rate constants. By using the idea of mass action, we can describe the reaction equation (1) in terms of a system of non-linear ordinary differential equations [18].…”

“…These stages are known as the enzymatic mechanism. There are two types of mechanisms, single substrate and multiple substrate mechanisms [16,11,19,18]. An important branch of enzymology is enzyme kinetics which is used to study the rate of chemical reactions.…”