Properties of modified periodic one-dimensional hopping model

TL;DR

This paper analyzes a modified one-dimensional hopping model for microscopic particles, incorporating new jump possibilities observed in light-driven molecular motors, and derives key dynamical properties verified through application to synthetic motors.

Contribution

It introduces a generalized periodic hopping model allowing jumps of multiple steps, providing analytical expressions for velocity, diffusion, and dwell time.

Findings

Derived formulas for mean velocity and diffusion constant.

Validated model with synthetic rotary molecular motors.

Enhanced understanding of motor protein dynamics.

Abstract

One-dimensional hopping model is useful to describe the motion of microscopic particle in thermal noise environment, such as motor proteins. Recent experiments about the new generation of light-driven rotary molecular motors found that, the motor in state i can jump forward to state i+1 or i+2, or backward to state i-1 or i-2 directly. In this paper, such modified periodic one-dimensional hopping model of arbitrary period N is studied mathematically. The mean velocity, effective diffusion constant, and mean dwell time in one single cycle are obtained. Corresponding results are illustrated and verified by being applied to a type of synthetic rotary molecular motors.