Exact Solutions of Burnt-Bridge Models for Molecular Motor Transport

TL;DR

This paper develops exact analytical solutions for burnt-bridge models describing molecular motor transport, revealing how bridge burning probability influences motor dynamics and providing a comprehensive theoretical framework supported by simulations.

Contribution

It introduces a new theoretical method for analyzing burnt-bridge models with arbitrary burning probability, extending previous models and enabling exact calculations of dynamic properties.

Findings

Exact solutions for p=1 case mapped to single-particle hopping

Explicit dynamic properties for p<1 derived

Theoretical predictions validated by Monte Carlo simulations

Abstract

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called ``bridges''), is investigated theoretically by analyzing discrete-state stochastic ``burnt-bridge'' models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed (``burned'') with a probability $p$, creating a biased directed motion for the particle. It is shown that for probability of burning $p=1$ the system can be mapped into one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties. For general case of $p<1$ a new theoretical method is developed, and dynamic properties are computed explicitly. Discrete-time and continuous-time dynamics, periodic and random distribution of bridges and different burning dynamics are analyzed and compared. Theoretical predictions are supported by extensive Monte Carlo computer simulations. Theoretical results are applied for analysis of the experiments on collagenase motor proteins.