A random walker on a ratchet

TL;DR

This paper models a two-footed walker on a ratchet potential, inspired by motor proteins, revealing how coupling dynamics influence walking styles and transport efficiency.

Contribution

Introduces a nonlinear bistable coupling model for a walker on a ratchet, capturing alternating and non-alternating walking behaviors similar to motor proteins.

Findings

Maximum current occurs when the equilibrium distance is an integer multiple of the ratchet period.

Bistable coupling allows for alternating and non-alternating walking modes.

Transport efficiency depends on the coupling and distance parameters.

Abstract

We analyze a model for a walker moving on a ratchet potential. This model is motivated by the properties of transport of motor proteins, like kinesin and myosin. The walker consists of two feet represented as two particles coupled nonlinearly through a bistable potential. In contrast to linear coupling, the bistable potential admits a richer dynamics where the ordering of the particles can alternate during the walking. The transitions between the two stable states on the bistable potential correspond to a walking with alternating particles. We distinguish between two main walking styles: alternating and no alternating, resembling the hand-over-hand and the inchworm walking in motor proteins, respectively. When the equilibrium distance between the two particles divided by the periodicity of the ratchet is an integer, we obtain a maximum for the current, indicating optimal transport.