Collective transport of weakly interacting molecular motors with Langmuir kinetics

TL;DR

This paper models the collective transport of weakly interacting molecular motors on filaments using a driven lattice gas framework coupled with Langmuir kinetics, revealing complex phase behavior and validating results with simulations.

Contribution

It introduces a mean field model for molecular motor transport incorporating weak interactions and Langmuir kinetics, mapping it to a known non-conserved KLS model.

Findings

Rich phase diagram with localized shocks and inhomogeneous phases.

Good agreement between mean field theory and Monte Carlo simulations for weak interactions.

Steady state density and current profiles depend on interaction strength.

Abstract

Filament based intracellular transport involves the collective action of molecular motor proteins. Experimental evidences suggest that microtubule (MT) filament bound motor proteins such as {\it kinesins} weakly interact among themselves during transport and with the surrounding cellular environment. Motivated by these observations we study a driven lattice gas model for collective unidirectional transport of molecular motors on open filament, which incorporates the short-range interactions between the motors on filaments and couples the transport process on filament with surrounding cellular environment through adsorption-desorption Langmuir (LK) kinetics of the motors. We analyse this model within the framework of a Mean Field (MF) theory in the limit of {\it weak} interactions between the motors. We point to the mapping of this model with the non-conserved version of Katz-Lebowitz-Spohn (KLS) model. The system exhibits rich phase behavior with variety of inhomogeneous phases including localized shocks in the bulk of the filament. We obtain the steady state density and current profiles and analyse their variation as function of the strength of interaction. We compare these MF results with Monte Carlo simulations and find that the MF analysis shows reasonably good agreement as long as the motors are weakly interacting. We also construct the non-equilibrium MF phase diagram.