Single-enzyme kinetics with branched pathways: exact theory and series expansion

TL;DR

This paper develops an exact theoretical framework and series expansion methods to analyze how enzyme and molecular motor dwell time distributions depend on substrate or ATP concentration, especially considering branched pathways.

Contribution

It introduces a novel series expansion approach for dwell time distributions in enzymes and motors with branched pathways, extending previous linear pathway models.

Findings

Derived approximate series expansions for [ATP]-dependence of dwell time moments

Compared branched pathway results with linear models, revealing pathway effects

Provided insights into the general [S]-dependence of enzymatic and motor kinetics

Abstract

The progress of the successive rounds of catalytic conversion of substrates into product(s) by a single enzyme is characterized by the distribution of turnover times. Establishing the most general form of dependence of this distribution on the substrate concentration [S] is one of the fundamental challenges in single molecule enzymology. The distribution of the times of dwell of a molecular motor at the successive positions on its track is an analogous quantity. We derive approximate series expansions for the [ATP]-dependence of the first two moments of the dwell time distributions of motors that catalyze hydrolysis of ATP to draw input energy. Comparison between our results for motors with branched pathways and the corresponding expressions reported earlier for linear enzymatic pathways provides deep insight into the effects of the branches. Such insight is likely to help in discovering the most general form of [S]-dependence of these fundamental distributions.