Statistical properties of multistep enzyme-mediated reactions

TL;DR

This paper develops a perturbation theory approach to analyze the statistical properties of multistep enzyme reactions, enabling discrimination of reaction schemes and estimation of kinetic rates from measurable quantities like flux and Fano factor.

Contribution

It introduces a quantum-mechanics-inspired perturbation method to compute cumulants of enzyme reaction distributions, aiding reaction scheme identification without single-molecule data.

Findings

Fano factor varies significantly between reaction types

Measuring flux and Fano factor helps distinguish reaction mechanisms

Method estimates internal kinetic rates from aggregate data

Abstract

Enzyme-mediated reactions may proceed through multiple intermediate conformational states before creating a final product molecule, and one often wishes to identify such intermediate structures from observations of the product creation. In this paper, we address this problem by solving the chemical master equations for various enzymatic reactions. We devise a perturbation theory analogous to that used in quantum mechanics that allows us to determine the first (<n>) and the second (variance) cumulants of the distribution of created product molecules as a function of the substrate concentration and the kinetic rates of the intermediate processes. The mean product flux V=d<n>/dt (or "dose-response" curve) and the Fano factor F=variance/<n> are both realistically measurable quantities, and while the mean flux can often appear the same for different reaction types, the Fano factor can be quite different. This suggests both qualitative and quantitative ways to discriminate between different reaction schemes, and we explore this possibility in the context of four sample multistep enzymatic reactions. We argue that measuring both the mean flux and the Fano factor can not only discriminate between reaction types, but can also provide some detailed information about the internal, unobserved kinetic rates, and this can be done without measuring single-molecule transition events.