Maximisation of the yield of final product on substrate in the case of sequential reactions catalysed by coimmobilised enzymes: A theoretical analysis

A theoretical procedure is reported, which aims at finding the best molar distribution of two enzymes (considered equivalent and mutually exclusive in terms of occupancy of immobilisation sites), coimmobilised in a slab-shaped porous bead, that catalyse two sequential irreversible reactions (involving an initial reactant species, an intermediate species and a final product species, at 1:1:1 stoichiometry) following Michaelis-Menten kinetics. The mathematical derivation uses as objective function maximisation of yield of the final product on the initial reactant coupled with the maximum catalyst effectiveness. The Thiele modulus was found to drop out as a relevant parameter for the determination of the optimum concentration of the intermediate (reactant) species, although it plays a role in the best distribution of enzyme within the slab. Low values of k_cat for the first enzyme and high values of surface concentration of the initial reactant lead to small Thiele moduli; such diffusional regime promotes retention of product(s) within the porous matrix, thus providing opportunities for more complete conversion to the final product. The maximum yield of the final product corresponds to immobilising most of the first enzyme in the innermost portion of the slab and most of the second enzyme in the outermost portion.