Analysis of diffusional effects in immobilized two-enzyme systems

Abstract

The effect of diffusional resistances (both inter- and intramembrane) on the kinetic behaviour of an immobilised two-enzyme system carrying out a consecutive sequence of reactions S → P₁→P₂ is analysed for the case in which the intrinsic kinetics can be considered to be first order. The method of solution consists in first representing the diffusion-reaction equations in matrix notation and applying the similarity transformation to reduce the equations to a set of uncoupled equations in pseudoconcentrations. The set of uncoupled equations are solved analytically for the appropriate boundary conditions. The solution to the original problem is then recovered by applying the reverse transformation. Two geometries have been treated, the spherical capsule and the flat plate membrane. The diffusional resistances may be described adequately by two dimensionless numbers, the Thiele modulus and modified Sherwood number. The influence of these parameters on the concentration profiles and "effectiveness factors" have been presented graphically. The analysis is also extended to the prediction of the performance of a packed bed enzyme reactor.