Maximization of Enzymic Activity under Consideration of Various Constraints

Abstract

The distribution of the kinetic parameters of a reversible enzymic reaction with an ordered mechanism is theoretically studied under the assumption that during evolution the increase of reaction rate was an important target of natural selection. The optimal individual rate constants in the steady state for fixed reactant concentrations are determined from optimization principles. The reaction rate is a homogeneous function of first degree of the elementary rate constants and the determination of states of maximal activity is only possible if constraints for the rate constants are taken into account. Besides a fixed thermodynamical equilibrium constant this concerns upper limits for the values of the individual rate constants. In extension of previous work on the optimization of enzyme kinetic parameters the influence of constraints concerning upper limits of the rate constants is analysed. Two different models are introduced: the separate limit model and the overall limit model. The concept of “evolutionary effort” is applied to derive an expression for the cost function leading to an overall upper limit for the values of the rate constants. The resulting optimization problem is solved for ordered mechanisms involving different numbers of elementary steps in dependence on the reactant concentrations and on the thermodynamical equilibrium constant.