Why do many Michaelian enzymes exhibit an equilibrium constant close to unity for the interconversion of enzyme‐bound substrate and product?

Abstract

1. The idea is advanced that an evolutionary pressure in the direction of increased metabolic fluxes should lead to the selection at any evolutionary stage of enzymes which are optimally efficient considering the total evolutionary effort which has been spent on their improvement as catalysts. Relationships are derived which may be used for determination of the optimal state of operation of a Michaelian enzyme at a given total evolutionary effort as measured, for instance, by the mean magnitude of variable rate constants in the reaction mechanism. These relationships are applied to characterize the dependence on the total evolutionary effort of the optimal value of the equilibrium constant (Kin,) for the conversion of enzyme-bound substrate into enzyme-bound product.2. The results show that the optimal value of Kin, reflects primarily the magnitude of the overall equilibrium constant for the catalysed reaction, whether or not the enzyme operates close to equilibrium. When the total evolutionary effort tends towards infinitely high values, Kin, approaches unity, regardless of the magnitude of the overall equilibrium constant and of the concentrations of substrate and product. Concomitantly, the enzyme approaches its ultimate state of catalytic perfection where all variable rate constants in the mechanism tend towards infinitely high values.3. It is concluded from previously reported kinetic data that triosephosphate isomerase has been subjected to such a low total evolutionary effort that the enzyme cannot possibly have reached (or even significantly approached) the ultimate state of perfection where the Kin, value necessarily becomes close to unity. The reason why this enzyme exhibits a Kin, value relatively close to unity is that it catalyses a reaction with an equilibrium constant relatively close to unity. Evidence is presented to show that similar considerations may apply for other enzymes operating by the examined reaction mechanism.4. Analytical data are reported which indicate that Kin, ultimately approaches unity because forward and reverse rate constants for the interconversion of enzyme-bound substrate and product are equivalent with regard to the evolutionary effort required to increase their magnitude.The evolutionary development of enzymes may certainly be dependent on a multitude of factors relating to their function as biologically regulated catalysts affecting both metabolite levels and reaction fluxes in metabolic pathways. Since enzymes serve the obvious primary purpose of maintaining high reaction fluxes, however, they can be anticipated to have evolved primarily in response to a selective pressure tending to increase their catalytic efficiency. Fundamental functional properties of presently existing enzymes, therefore, may be difficult to explain unless we have a thorough knowledge of the likely effects of such a selective pressure on the catalytic reaction mechanism. In particular, it would seem important to know how enzymic reaction mechanisms should be kinetically designed in order to opti...

Evolutionary optimization of the catalytic efficiency of enzymes

“…Similar analyses, based on application of Eqn (17), were performed by Rees [8] with the assumption that C represents a fixed parameter while the magnitude of p may be evolutionarily affected.…”

“…( 1 7) From the point of view of mathematical formalism, Albery and Knowles [6] (as well as Burbaum et al [9] in their recent extension of the original theory) used Eqn (17) to substitute the variables k2 and k -, for the new variables C and K2. This is not a mathematically useful approach for the simple reason that a variable substitution does not represent any optimization constraint; the analytical solution to the optimization problem formally addressed by Knowles and coworkers is the trivial one corresponding to first-order rate constants of infinite magnitude [17].…”

“…This is not a mathematically useful approach for the simple reason that a variable substitution does not represent any optimization constraint; the analytical solution to the optimization problem formally addressed by Knowles and coworkers is the trivial one corresponding to first-order rate constants of infinite magnitude [17]. In the case that also first-order rate constants are assumed to exhibit upper limits, the solutions presented by Heinrich et al [5] apply.…”

“…This follows from the fact that Eqn (17) lacks meaning when applied to a single observation (a single pair of k2 and K, values, which cannot define the slope and intercept of a line). Eqn (17) becomes physico-chemically meaningful only when referring to a set of observations exhibiting a linear free-energy relationship, i. e. conforming to Eqn (17) for fixed values of C and j. In the context now discussed, this set of observations is given by the pairs of k2 and K2 values characterizing a certain enzyme at different time points during evolution.…”

“…Many, if not most, of these arrangements (e. g. those leading to catalysis through approximation or orientation effects, orbital steering and various kinds of nucleophilic-electrophilic transition-state stabilization [20]) serve the obvious purpose of lowering the free energy of the transition-state for the interconversion of enzymebound substrate and product. Their evolutionary introduction, therefore, must be associated with an increase in magnitude of both the forward (k,) and the reverse ( k -, ) rate constant for the substrate/product interconversion step, such that Eqns (17) and (18) cannot apply.…”