Exact solution of a linear molecular motor model driven by two-step fluctuations and subject to protein friction

TL;DR

This paper provides an exact analytical solution to a linear molecular motor model driven by two-step fluctuations and protein friction, enabling detailed insights into motor behavior and predictions of physiologically relevant velocities.

Contribution

It offers the first explicit analytical expressions for the average motion and velocity-force relationship of this molecular motor model, enhancing understanding beyond numerical methods.

Findings

Predicts physiologically reasonable load-free velocities

Derives explicit formulas for motor velocity and mobility

Provides detailed interpretation of motor dynamics

Abstract

We investigate by analytical means the stochastic equations of motion of a linear molecular motor model based on the concept of protein friction. Solving the coupled Langevin equations originally proposed by Mogilner et al. (A. Mogilner et al., Phys. Lett. {\bf 237}, 297 (1998)), and averaging over both the two-step internal conformational fluctuations and the thermal noise, we present explicit, analytical expressions for the average motion and the velocity-force relationship. Our results allow for a direct interpretation of details of this motor model which are not readily accessible from numerical solutions. In particular, we find that the model is able to predict physiologically reasonable values for the load-free motor velocity and the motor mobility.