Enzyme membrane model systems and their implication in biological research

Abstract

Summary A theoretical analysis of the kinetic behavior of artificial enzyme membranes was carried out. The analysis allowed deduction of the magnitude and direction of flows of substrate and product as well as their concentration profiles within the membranes. It was possible to predict the local pH values within an enzyme membrane in which acid or base are formed as the result of the enzymic reaction. The theoretical treatment was extended to include effects of the Nernst diffusion layer on the kinetic behavior of enzyme membranes. The existence of an unstirred layer (Nernst diffusion layer) at the interface leads to the formation of substrate and product concentration gradients across the layer. The concentration of substrate at the outer surfaces of the membrane, So, is thus a function of the thickness of the diffusion layer, as well as the parameters of the enzyme-membrane-substrate system. It could be shown for hypothetical enzyme-membrane systems that the presence of an unstirred layer will markedly affect the kinetic behavior of enzyme membranes possessing high catalytic activity and low Michaelis-Menten constants. The main theoretical conclusions were experimentally verified in studies employing papain- collodion and alkaline phosphatase-collodion membranes. A combination of the calculated relation between the overall reaction rate, V, and So and an experimentally obtained relation of V as a function of substrate concentration in the bulk solution enabled the estimation of the thickness of the unstirred layer of alkaline phosphatase-collodion membranes. The kinetic behavior of a two-enzyme membrane carrying out two consecutive reactions has also been analysed and compared to that of an analogous system consisting of the two enzymes in solution. The analysis of the immobilized enzyme system is based on the assumption that a quasi-stationary state is established within the unstirred layer, i.e. the rate of flow of the product formed by the first enzyme into the bulk of the solution. equals the difference between the rate of its production and the rate of its consumption by the second enzyme. The effect of the kinetic parameters and of the physical characteristics of the system on its kinetic behavior under simplifying boundary conditions, were examined. It was shown that in the immobilized systems the concentrations of products of both enzymes in the bulk of the solution increase linearly with time while in the corresponding homogeneous systems there is an initial lag period in the production of the second product and the concentration does not increase in a linear rate. The initial rate of production of the end product is markedly higher in the immobilized enzyme system than that predicted for a corresponding homogeneous system. Experimental findings with systems of enzymes immobilized on synthetic or biological matrices in accord with the predictions derived from theory are discussed.