Random Walk by Majority Rule and L\'evy walk

TL;DR

This study models cargo transport as a Levy walk influenced by motor protein dynamics, revealing a transition from super-diffusive to normal diffusion and demonstrating robustness of Levy walk behavior under correlated motor binding.

Contribution

The paper introduces a novel random walk model based on majority rule and motor protein interactions, showing Levy walk characteristics in cargo transport and analyzing effects of motor binding correlations.

Findings

Cargo run time follows a Levy walk distribution for short times.

Mean squared displacement transitions from super-diffusive to diffusive behavior.

Levy walk behavior remains robust under correlated motor binding effects.

Abstract

We have studied a random walk model based on majority rule. At a given instant, the moving direction of a cargo is determined by motor coordination mediated by a tug-of-war mechanism between two kinds of competing motor proteins. We have demonstrated that the probability distribution $P(t)$ for unidirectional run time $t$ of a cargo can be remarkably described by Levy walk for $t<\gamma_u^{-1}$ as $P(t)\propto t^{-3/2} e^{-\gamma_u t}$ with $\gamma_u$ being the unbinding rate of a motor protein from microtubule. The mean squared displacement of a cargo changes from super-diffusive behavior $\langle X^2\rangle\propto t^2$ for $t<\gamma_u^{-1}$ to normal diffusion $\langle X^2\rangle\propto t$ for $t>\gamma_u^{-1}$. By considering the correlation effect in binding of a motor protein to microtubule, we have shown that Levy walk behavior of $P(t)\propto t^{-{3/2}}$ persists robustly against correlations only adding an effective cutoff time $\gamma_b/\gamma_c^2$ with $\gamma_c$ representing the amount of correlations.