Tug-of-war in motor proteins and the emergence of Levy walk

In recent experiment, transport of mRNA–protein complex in neurons has been observed to follow a truncated Levy walk behavior. We have theoretically 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 run-time distribution P(t) for unidirectional transport of a cargo can be described by a truncated Levy walk P(t) ∝ t^−3/2e^−γ_ut with γ_u being the unbinding rate of a motor protein from microtubule. The mean squared displacement of a cargo changes from super-diffusive behavior 〈X²〉 ∝ t² for t < γ_u⁻¹ to normal diffusion 〈X²〉 ∝ t for t > γ_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) ∝ t^−3/2 persists robustly against correlation simply adding a finite cutoff time γ_b/γ_c² with γ_c representing the amount of correlation.