Dynamics of Molecular Motors in Reversible Burnt-Bridge Models

TL;DR

This paper presents an exact theoretical analysis of molecular motor dynamics in reversible burnt-bridge models, revealing how bridge interactions influence motor velocity, direction, and fluctuations.

Contribution

It introduces explicit formulas for velocities and dispersions in burnt-bridge models, including reversible burning, and uncovers dynamic transitions and complex behaviors.

Findings

Reversible burning induces biased motion even in unbiased walkers.

Backward bias can be reversed under certain parameters.

Dispersion exhibits non-monotonic behavior with large fluctuations.

Abstract

Dynamic properties of molecular motors whose motion is powered by interactions with specific lattice bonds are studied theoretically with the help of discrete-state stochastic "burnt-bridge" models. Molecular motors are depicted as random walkers that can destroy or rebuild periodically distributed weak connections ("bridges") when crossing them, with probabilities $p_1$ and $p_2$ correspondingly. Dynamic properties, such as velocities and dispersions, are obtained in exact and explicit form for arbitrary values of parameters $p_1$ and $p_2$. For the unbiased random walker, reversible burning of the bridges results in a biased directed motion with a dynamic transition observed at very small concentrations of bridges. In the case of backward biased molecular motor its backward velocity is reduced and a reversal of the direction of motion is observed for some range of parameters. It is also found that the dispersion demonstrates a complex, non-monotonic behavior with large fluctuations for some set of parameters. Complex dynamics of the system is discussed by analyzing the behavior of the molecular motors near burned bridges.