Memory, Bias and Correlations in Bidirectional Transport of Molecular Motor-driven Cargoes

TL;DR

This paper investigates the statistical properties of bidirectional cargo transport by molecular motors, revealing that such motion is generally a correlated random walk with memory effects influenced by motor number and internal states.

Contribution

It introduces a stochastic tug-of-war model to analyze memory, bias, and correlations in bidirectional transport, highlighting the non-Markovian nature arising from multiple motors and internal states.

Findings

Bidirectional cargo transport exhibits correlated random walk behavior.

Memory effects depend non-monotonically on the number of motors.

Simulations support the theoretical analysis and biological relevance.

Abstract

Molecular motors are specialized proteins which perform active, directed transport of cellular cargoes on cytoskeletal filaments. In many cases, cargo motion powered by motor proteins is found to be bidirectional, and may be viewed as a biased random walk with fast unidirectional runs interspersed with slow `tug-of-war' states. The statistical properties of this walk are not known in detail, and here, we study memory and bias, as well as directional correlations between successive runs in bidirectional transport. We show, based on a study of the direction reversal probabilities of the cargo using a purely stochastic (tug-of-war) model, that bidirectional motion of cellular cargoes is, in general, a correlated random walk. In particular, while the motion of a cargo driven by two oppositely pulling motors is a Markovian random walk, memory of direction appears when multiple motors haul the cargo in one or both directions. In the latter case, the Markovian nature of the underlying single motor processes is hidden by internal transitions between degenerate run and pause states of the cargo. Interestingly, memory is found to be a non-monotonic function of the number of motors. Stochastic numerical simulations of the tug-of-war model support our mathematical results and extend them to biologically relevant situations.