Statistical mechanics of the Huxley-Simmons model

TL;DR

This paper applies statistical mechanics to the Huxley-Simmons model, revealing its equilibrium and kinetic properties through an analogy with the Ising model, and broadening its applicability to allosteric systems.

Contribution

It introduces a statistical mechanical framework for the HS model, enabling explicit calculations of its properties and extending its relevance to various biological allosteric systems.

Findings

Explicit computation of equilibrium properties of the HS model.

Development of a master equation for kinetics under different protocols.

Formalism applicable to a broad class of allosteric systems.

Abstract

The chemomechanical model of Huxley and Simmons (HS) [A. F. Huxley and R. M. Simmons, Nature 233, 533 (1971)] provides a paradigmatic description of mechanically induced collective conformational changes relevant in a variety of biological contexts, from muscles power-stroke and hair cell gating to integrin binding and hairpin unzipping. We develop a statistical mechanical perspective on the HS model by exploiting a formal analogy with a paramagnetic Ising model. We first study the equilibrium HS model with a finite number of elements and compute explicitly its mechanical and thermal properties. To model kinetics, we derive a master equation and solve it for several loading protocols. The developed formalism is applicable to a broad range of allosteric systems with mean-field interactions.