AN EVOLUTIONARY APPROACH TO ENZYME-KINETICS - OPTIMIZATION OF ORDEREDMECHANISMS

A theoretical investigation is presented which allows the calculation of rate constants and phenomenological parameters in states of maximal reaction rates for unbranched enzymic reactions. The analysis is base d on the assumption that an increase in reaction rates was an importan t characteristic of the evolution of the kinetic properties of enzymes . The corresponding nonlinear optimization problem is solved taking in to account the constraint that the rate constants of the elementary pr ocesses do not exceed certain upper limits. One-substrate-one-product reactions with two, three and four steps are treated in detail. Genera lizations concern ordered uni-uni-reactions involving an arbitrary num ber of elementary steps. It could be shown that depending on the subst rate and product concentrations different types of solutions can be fo und which are classified according to the number of rate constants ass uming in the optimal state submaximal values. A general rule is derive d concerning the number of possible solutions of the given optimizatio n problem. For high values of the equilibrium constant one solution al ways applies to a very large range of the concentrations of the reacta nts. This solution is characterized by maximal values of the rate cons tants of all forward reactions and by non-maximal values of the rate c onstants of all backward reactions. Optimal kinetic parameters of orde red enzymic mechanisms with two substrates and one product (bi-uni-mec hanisms) are calculated for the first time. Depending on the substrate and product concentrations a complete set of solutions is found. In a ll cases studied the model predicts a matching of the concentrations o f the reactants and the corresponding Michaelis constants, which is in good accordance with the experimental data. It is discussed how the m odel can be applied to the calculation of the optimal kinetic design o f real enzymes.