Effective rates from thermodynamically consistent coarse-graining of models for molecular motors with probe particles

TL;DR

This paper introduces a thermodynamically consistent coarse-graining method for molecular motor models with probe particles, enabling effective one-particle descriptions that preserve key thermodynamic properties and reveal dependencies on probe size.

Contribution

The authors develop a novel coarse-graining approach that accurately maps two-degree-of-freedom motor-probe models to effective one-particle models while maintaining thermodynamic consistency.

Findings

Coarse-grained rates obey local detailed balance.

Entropy production and efficiency are invariant under coarse-graining.

Probe size influences stall force in multicyclic motors.

Abstract

Many single molecule experiments for molecular motors comprise not only the motor but also large probe particles coupled to it. The theoretical analysis of these assays, however, often takes into account only the degrees of freedom representing the motor. We present a coarse-graining method that maps a model comprising two coupled degrees of freedom which represent motor and probe particle to such an effective one-particle model by eliminating the dynamics of the probe particle in a thermodynamically and dynamically consistent way. The coarse-grained rates obey a local detailed balance condition and reproduce the net currents. Moreover, the average entropy production as well as the thermodynamic efficiency is invariant under this coarse-graining procedure. Our analysis reveals that only by assuming unrealistically fast probe particles, the coarse-grained transition rates coincide with the transition rates of the traditionally used one-particle motor models. Additionally, we find that for multicyclic motors the stall force can depend on the probe size. We apply this coarse-graining method to specific case studies of the F1-ATPase and the kinesin motor.