On the Physical and Evolutionary Limits to the Rates of Enzyme-Catalyzed Reactions

Carlo Canepa

doi:10.1155/2020/2524862

Abstract

An existing model for the rate coefficients of enzyme-catalyzed processes involves the regularized gamma function of Euler replacing the exponential dependence of the rate coefficient from the reaction barrier. The application of this model to experimental data, on one hand, validates the model by correctly describing the negative curvature of Eyring plots. On the other hand, this analysis evidences that enzymes never reach the maximum theoretical efficiency, a counterintuitive fact that requires an explanation. This work interprets this evolutionary limit in terms of the necessity of living systems to achieve and maintain homeostasis. Further validation of the expression for the rate coefficients comes from the analysis of the discrepancy between the theoretically predicted energy difference between reactants and products in a chemical equilibrium and the corresponding value obtained by regression to the classical expression for the equilibrium constant. The discrepancy is resolved by making use of the proposed model.

Highlights

A functional form of the rate coefficient for enzyme-catalyzed reactions based on the coupling of the protein vibrational modes to the reaction coordinate has been proposed [1, 2]. e model was tested on a series of both catalyzed and uncatalyzed reactions, for which the temperature-dependent rate coefficients have been measured [3]. e outcome was that, in the majority of cases, the curvature of the Arrhenius plots was found to be negative, a feature that transition state theory (TST) in its various forms is not able to explain
E thermally averaged rate coefficient of a chemical reaction is expressed as the integral of the product of an energy-dependent rate coefficient kr(ε) and the classical Boltzmann distribution of low-frequency vibrational modes: kr(T)
E total number of modes s includes the subset of all the excited modes that can transfer energy to the reaction coordinate, implying (Zωi/kT) ≪ 1, and the classical expression for the vibrational density of states εs− 1 ρ (s − 1)!􏽑si 1 Zωi, (3)

Summary

Carlo Canepa

Received 30 March 2020; Revised 24 May 2020; Accepted 28 May 2020; Published 27 June 2020. An existing model for the rate coefficients of enzyme-catalyzed processes involves the regularized gamma function of Euler replacing the exponential dependence of the rate coefficient from the reaction barrier. E application of this model to experimental data, on one hand, validates the model by correctly describing the negative curvature of Eyring plots. This analysis evidences that enzymes never reach the maximum theoretical efficiency, a counterintuitive fact that requires an explanation. Further validation of the expression for the rate coefficients comes from the analysis of the discrepancy between the theoretically predicted energy difference between reactants and products in a chemical equilibrium and the corresponding value obtained by regression to the classical expression for the equilibrium constant. E discrepancy is resolved by making use of the proposed model Further validation of the expression for the rate coefficients comes from the analysis of the discrepancy between the theoretically predicted energy difference between reactants and products in a chemical equilibrium and the corresponding value obtained by regression to the classical expression for the equilibrium constant. e discrepancy is resolved by making use of the proposed model

Introduction

Journal of Chemistry s kT zv

Results and Discussion

Dihydrofolate reductase

Conclusions