Discrete kinetic models for molecular motors: asymptotic velocity and gaussian fluctuations

TL;DR

This paper develops mathematical formulas to analyze the long-term behavior of molecular motors modeled as random walks on quasi-one-dimensional lattices, simplifying calculations and correcting previous biophysical models.

Contribution

It introduces general formulas for asymptotic velocity and diffusion coefficient, reducing complex calculations to linear systems, and corrects errors in existing biophysical literature.

Findings

Derived formulas for velocity and diffusion coefficient

Simplified computation via linear systems of fundamental cells

Identified and corrected errors in biophysical models

Abstract

We consider random walks on quasi one dimensional lattices, as introduced in \cite{FS}. This mathematical setting covers a large class of discrete kinetic models for non-cooperative molecular motors on periodic tracks. We derive general formulas for the asymptotic velocity and diffusion coefficient, and we show how to reduce their computation to suitable linear systems of the same degree of a single fundamental cell, with possible linear chain removals. We apply the above results to special families of kinetic models, also catching some errors in the biophysics literature.