Discrete- versus continuous-state descriptions of the F1-ATPase molecular motor

TL;DR

This paper develops a discrete-state model of the F1-ATPase motor that captures its dependence on chemical and mechanical parameters, providing insights into its kinetics and thermodynamics.

Contribution

It introduces a discrete-state model fitted to a continuous-angle model, linking chemical and mechanical control parameters for the F1-ATPase motor.

Findings

Model accurately describes rotation and ATP consumption rates.

Reveals dependence of motor behavior on mechanical parameters.

Provides thermodynamic efficiency estimates.

Abstract

A discrete-state model of the F1-ATPase molecular motor is developed which describes not only the dependences of the rotation and ATP consumption rates on the chemical concentrations of ATP, ADP, and inorganic phosphate, but also on mechanical control parameters such as the friction coefficient and the external torque. The dependence on these mechanical parameters is given to the discrete-state model by fitting its transition rates to the continuous-angle model of P. Gaspard and E. Gerritsma [J. Theor. Biol. 247 (2007) 672-686]. This discrete-state model describes the behavior of the F1 motor in the regime of tight coupling between mechanical motion and chemical reaction. In this way, kinetic and thermodynamic properties of the F1 motor are obtained such as the Michaelis-Menten dependence of the rotation and ATP consumption rates on ATP concentration and its extension in the presence of ADP and Pi, their dependences on friction and external torque, as well as the chemical and mechanical thermodynamic efficiencies.