Solvent viscosity dependence for enzymatic reactions

TL;DR

This paper proposes a mechanism linking solvent viscosity to enzyme reaction rates through electric field fluctuations caused by peptide group motions, explaining experimental viscosity dependence.

Contribution

It introduces a novel model based on peptide plane rocking and electric field fluctuations to explain solvent viscosity effects on enzyme reaction rates.

Findings

The model captures the main features of the viscosity dependence.

It provides an upper limit for the fractional index of the power law.

The mechanism aligns with experimental observations.

Abstract

A mechanism for relationship of solvent viscosity with reaction rate constant at enzyme action is suggested. It is based on fluctuations of electric field in enzyme active site produced by thermally equilibrium rocking (cranckshaft motion) of the rigid plane (in which the dipole moment $\approx 3.6 D$ lies) of a favourably located and oriented peptide group (or may be a few of them). Thus the rocking of the plane leads to fluctuations of the electric field of the dipole moment. These fluctuations can interact with the reaction coordinate because the latter in its turn has transition dipole moment due to separation of charges at movement of the reacting system along it. The rocking of the plane of the peptide group is sensitive to the microviscosity of its environment in protein interior and the latter is a function of the solvent viscosity. Thus we obtain an additional factor of interrelationship for these characteristics with the reaction rate constant. We argue that due to the properties of the cranckshaft motion the frequency spectrum of the electric field fluctuations has a sharp resonance peak at some frequency and the corresponding Fourier mode can be approximated as oscillations. We employ a known result from the theory of thermally activated escape with periodic driving to obtain the reaction rate constant and argue that it yields reliable description of the preexponent where the dependence on solvent viscosity manifests itself. The suggested mechanism is shown to grasp the main feature of this dependence known from the experiment and satisfactorily yields the upper limit of the fractional index of a power in it.