A short recursive procedure for evaluating effectiveness factors for immobilized enzymes with reversible Michaelis–Menten kinetics

A short recursive procedure for calculating the effectiveness factor for enzymes immobilized in porous spherical particles is presented. The method is mathematically simple and very precise; it is valid for reversible Michaelis–Menten kinetics including, as particular situations, simple Michaelis–Menten and product competitive inhibition kinetics.The procedure is a modification of the two-parameter model previously published by the authors. The definition of an auxiliary dimensionless concentration leads to a recursive equation which simplifies the resolution of the model by means of elementary numerical methods. The solution algorithm has been transformed into a computer program, whose source code is appended.The exact values of the effectiveness factors for zero and first order kinetics, as a function of the Thiele module, were compared with those obtained with the numerical procedure proposed in this work. The good agreement between both results demonstrates the validity of the method.