Overdamped thermal ratchets in one and more dimensions. Kinesin transport and protein folding

TL;DR

This paper revisits overdamped thermal ratchets driven by external noise, analyzing their behavior in multiple dimensions with applications to kinesin transport and protein folding, highlighting conditions for current and potential biological mechanisms.

Contribution

It introduces multidimensional ratchet models applicable to biological systems like kinesin movement and protein folding, expanding understanding of non-periodic, unbounded ratchet dynamics.

Findings

Current can be generated without stationary states in unbounded ratchets.

A 2D model of kinesin on microtubules demonstrates directed transport.

A multidimensional ratchet model suggests a mechanism for protein folding.

Abstract

The overdamped thermal ratchet driven by an external (Orstein-Uhlenbeck) noise is revisited. The ratchet we consider is unbounded in space and not necessarily periodic . We briefly discuss the conditions under which current is obtained by analyzing the corresponding Fokker-Planck equation and its lack of stationary states. Next, two examples in more than one dimension and related to biological systems are presented. First, a two-dimensional model of a ``kinesin protein'' on a ``microtubule'' is analyzed and, second, we suggest that a ratchet mechanism may be behind the folding of proteins; the latter is elaborated with a multidimensional ratchet model.