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

We introduce a multi-species 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 cargoes being carried by oppositely directed molecular motors, moving on a single biofilament. Building on a totally asymmetric exclusion process (TASEP) to characterize the motion of the interacting cargoes, 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 non-equilibrium phase diagrams. The interplay of interconversion rates, which allow for flux reversal and evaporation/deposition processes introduce qualitatively new 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 {\it shocks}. Current reversals due to internal regulation emerge naturally within the framework of this model. We believe 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 {\it in-vivo} situations.

💡 Research Summary

The authors present a multi‑species lattice‑gas framework that extends the classic totally asymmetric simple exclusion process (TASEP) to capture collective vesicle transport driven by oppositely directed molecular motors on a single filament. Two particle species, denoted (+) and (–), represent vesicles propelled toward the filament’s plus‑end and minus‑end, respectively. Standard exclusion rules forbid multiple occupancy of a lattice site, and open boundary conditions allow injection (rates α₊, α₋) and extraction (rates β₊, β₋) of each species at the filament ends. The novelty lies in incorporating interconversion processes: a (+) particle can switch to (–) with rate k₊₋, and a (–) particle can switch to (+) with rate k₋₊. This captures the biological situation where a vesicle may exchange attached motor types, leading to possible reversal of its net motion. In addition, the model includes bulk attachment (adsorption) and detachment (evaporation) with rates ω_a and ω_d, representing vesicle binding to or unbinding from the filament.

Using a mean‑field continuum description together with boundary‑layer analysis, the authors derive steady‑state density profiles and flux–density relations for each species. They map out non‑equilibrium phase diagrams in the multidimensional parameter space spanned by the boundary rates, interconversion rates, and bulk exchange rates. As in the standard TASEP, low‑density (LD), high‑density (HD), and maximal‑current (MC) phases appear, but the added processes generate qualitatively new features: (i) coexistence regions where LD and HD domains are separated by a stationary shock (density discontinuity) inside the filament, (ii) three‑phase coexistence (LD/MC/HD) and even triple‑phase coexistence involving both species, (iii) re‑entrant behavior where a given phase reappears upon varying a single control parameter, and (iv) flux reversal driven solely by the balance of interconversion rates. The shock position is tunable by the relative injection/extraction rates and by the conversion asymmetry, providing a mechanism for spatial polarization of vesicles observed in vivo.

Monte‑Carlo simulations corroborate the analytical predictions, showing excellent agreement for phase boundaries, shock locations, and current magnitudes across a wide range of parameters. Systematic scans reveal that increasing the conversion asymmetry (k₊₋ ≠ k₋₊) biases the net transport direction, while symmetric conversion can lead to a balanced bidirectional flow that is highly sensitive to small changes in ω_a/ω_d or α/β. High bulk detachment (large ω_d) suppresses overall density and expands the MC region, whereas strong adsorption (large ω_a) promotes crowding and stabilizes HD domains.

The study highlights how internal regulation—through motor composition changes, ATP‑dependent activity, or accessory proteins that modulate attachment/detachment—can dynamically reshape transport patterns without altering filament geometry. By providing a minimal yet analytically tractable model, the work offers a conceptual bridge between microscopic motor dynamics and macroscopic vesicle distribution patterns such as homogeneous spreading, polarized accumulation, or shock‑mediated segregation. The authors argue that this framework can be extended to more realistic cellular contexts (multiple filaments, cargo size heterogeneity, load‑dependent stepping) and can serve as a quantitative baseline for interpreting experimental data on bidirectional organelle transport in neurons, immune cells, and other systems where opposing motor teams cooperate and compete.