Dynamic Properties of Molecular Motors in Burnt-Bridge Models

TL;DR

This paper introduces a new theoretical model for molecular motors interacting with molecular tracks, revealing how their diffusion properties depend on weak link concentration and burning probability, supported by simulations.

Contribution

A novel exact theoretical approach to analyze dynamic properties of molecular motors in burnt-bridge models, including velocity and dispersion calculations.

Findings

Dispersion decreases with higher weak link concentration.

Dispersion's dependence on burning probability is complex.

A dynamic phase transition occurs at low weak link concentrations.

Abstract

Dynamic properties of molecular motors that fuel their motion by actively interacting with underlying molecular tracks are studied theoretically via discrete-state stochastic ``burnt-bridge'' models. The transport of the particles is viewed as an effective diffusion along one-dimensional lattices with periodically distributed weak links. When an unbiased random walker passes the weak link it can be destroyed (``burned'') with probability p, providing a bias in the motion of the molecular motor. A new theoretical approach that allows one to calculate exactly all dynamic properties of motor proteins, such as velocity and dispersion, at general conditions is presented. It is found that dispersion is a decreasing function of the concentration of bridges, while the dependence of dispersion on the burning probability is more complex. Our calculations also show a gap in dispersion for very low concentrations of weak links which indicates a dynamic phase transition between unbiased and biased diffusion regimes. Theoretical findings are supported by Monte Carlo computer simulations.