Evolutionary optimization of enzyme kinetic parameters; effect of constraints.

The distribution of the kinetic parameters of enzymic reactions is theoretically studied, on the assumption that, during evolution, the increase of reaction rates was an important target of natural selection. In extension of previous work on the optimization of enzyme kinetic parameters, the influence of constraints concerning upper limits of the individual rate constants is analyzed. 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. It is shown that the optimum for the enzyme kinetic parameters strongly depends on the concentrations of the reactants. Low reactant concentrations lead generally to a tight binding of the reactants, while high concentrations result in a weak binding, favouring the rate constants of the other steps. In particular, states of maximum activity are not always characterized by maximal values of second-order rate constants. The results support the hypothesis that there is a mutual adaptation of Michaelis constants and reactant concentrations in an evolutionary timescale. In the limit of infinite values of the exponent of the cost function the results of the present "overall limit model" turn into the results of a model which takes into account individual upper limits for rate constants ("separate limit model"). The distributions of optimal rate constants are discussed in terms of free-energy profiles. The model is applied to the interpretation of the kinetic data of triosephosphate isomerase and inorganic pyrophosphatase.