The Mathematical Theory of Diffusion and Reaction in Enzymes Immoblized Artificial Membrane. The Theory of the Non-Steady State

Abstract

In this paper, mathematical model pertaining to the decomposition of enzyme-substrate complex in an artificial membrane is discussed. Here the transport through liquid membrane phases is considered. The model involves the system of non-linear reaction diffusion equations. The non-linear terms in this model are related to Michaelis-Menten reaction scheme. Approximate analytical expressions for the concentrations of substrate and product have been derived by solving the system of non-linear reaction diffusion equations using new approach of homotopy perturbation method for all values of Michaelis-Menten constant, diffusion coefficient, and rate constant. Approximate flux expression for substrate and product for non-steady-state conditions are also reported. A comparison of the analytical approximation and numerical simulation is also presented. The results obtained in this work are valid for the entire solution domain.

A New Solution for The Enzymatic Glucose Fuel Cell Model with Morrison Equation via Haar Wavelet Collocation Method

“…Then, we define the 2M operational matric of integrations P n and its element order n, index i is computed using the relation P n (i, l) = p i,n (x l ), where x l is defined in (17) For example, if J = 1 ⇒ 2M = 4, and n = 1, then from ( 22) the Haar integral matrix of first order and when n = 2, the Haar wavelet integral matrix of second order is computed by using (23) as…”

“…Rajendran [15] solved the approximate analytical solution for a mono enzymatic biosensor with the Michaelis Menten equation via the Homotopy perturbation method. Malinidevi [17] studied the reaction and diffusion of enzymes immobilized in an artificial membrane with a mathematical model. The enzymatic glucose fuel cell uses glucose as a fuel to generate electrical energy and enzymes as a biocatalyst to change chemical energy into electrical energy [14].…”