Lattice-gas model for active vesicle transport by molecular motors with opposite polarities

We introduce a multispecies lattice-gas model for motor protein driven collective cargo transport on cellular filaments. We use this model to describe and analyze the collective motion of interacting vesicle cargos being carried by oppositely directed molecular motors, moving on a single biofilament. Building on a totally asymmetric exclusion process to characterize the motion of the interacting cargos, we allow for mass exchange with the environment, input, and output at filament boundaries and focus on the role of interconversion rates and how they affect the directionality of the net cargo transport. We quantify the effect of the various different competing processes in terms of nonequilibrium phase diagrams. The interplay of interconversion rates, which allow for flux reversal and evaporation-deposition processes, introduces qualitatively unique features in the phase diagrams. We observe regimes of three-phase coexistence, the possibility of phase re-entrance, and a significant flexibility in how the different phase boundaries shift in response to changes in control parameters. The moving steady-state solutions of this model allows for different possibilities for the spatial distribution of cargo vesicles, ranging from homogeneous distribution of vesicles to polarized distributions, characterized by inhomogeneities or shocks. Current reversals due to internal regulation emerge naturally within the framework of this model. We believe that this minimal model will clarify the understanding of many features of collective vesicle transport, apart from serving as the basis for building more exact quantitative models for vesicle transport relevant to various in vivo situations.