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

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.