A model for bidirectional traffic of cytoskeletal motors

We introduce a stochastic lattice gas model including two particle species and two parallel lanes. One lane with exclusion interaction and directed motion and the other lane without exclusion and unbiased diffusion, mimicking a micotubule filament and the surrounding solution. For a high binding affinity to the filament, jam-like situations dominate the system’s behaviour. The fundamental process of position exchange of two particles is approximated. In the case of a many-particle system, we were able to identify a regime in which the system is rather homogenous presenting only small accumulations of particles and a regime in which an important fraction of all particles accumulates in the same cluster. Numerical data proposes that this cluster formation will occur at all densities for large system sizes. Coupling of several filaments leads to an enhanced cluster formation compared to the uncoupled system, suggesting that efficient bidirectional transport on one-dimensional filaments relies on long-ranged interactions and track formation.

💡 Research Summary

The paper presents a stochastic lattice‑gas framework designed to capture the collective dynamics of bidirectional cytoskeletal motor traffic. Two particle species—representing plus‑directed (e.g., kinesin) and minus‑directed (e.g., dynein) motors—move on two parallel one‑dimensional lanes. Lane 1 mimics a microtubule filament: particles experience hard‑core exclusion and a fixed drift direction (rightward for one species, leftward for the other). Lane 2 represents the surrounding cytosol, where particles diffuse unbiasedly without exclusion. Motors can bind to the filament (transition from lane 2 to lane 1) and unbind (the reverse) with rates that are controlled by a binding‑affinity parameter κ. High κ corresponds to strong filament attachment, a regime relevant for many intracellular transport processes.

The authors first develop a mean‑field description of the elementary exchange event in which two oppositely moving particles meet on the filament and swap positions. This approximation yields an analytical expression for the current‑density relation (the fundamental diagram) under various κ values. To test and extend the theory, extensive Monte‑Carlo simulations are performed for a broad range of global densities ρ, system lengths L, and κ values.

Two distinct dynamical regimes emerge. In the low‑affinity regime (small κ), most motors reside in the diffusive lane; the filament is sparsely populated, and the system remains essentially homogeneous, with only minor local density fluctuations. In the high‑affinity regime (large κ), motors accumulate on the filament, and exclusion prevents easy overtaking. As a result, “jam‑like” configurations appear. For sufficiently large L and moderate to high ρ, a macroscopic cluster forms: a single, dense aggregation of motors occupies a finite fraction of the filament, while the remaining sites contain a dilute background. Finite‑size scaling analysis indicates that the cluster‑formation threshold shifts toward lower densities as L increases, suggesting that in the thermodynamic limit (L → ∞) clustering occurs at any non‑zero density.

The study is then extended to multiple coupled filaments. Inter‑filament hopping is allowed, which models the physical proximity of neighboring microtubules in a cell. Coupling amplifies the clustering phenomenon: a cluster on one filament can nucleate or absorb particles from adjacent filaments, leading to larger, more persistent aggregates. This cooperative effect implies that simple one‑dimensional transport on isolated filaments may be insufficient for efficient bidirectional cargo delivery; instead, long‑range interactions or the formation of multi‑filament tracks appear necessary to alleviate jams.

In the discussion, the authors relate their findings to experimental observations of motor traffic, such as the formation of “traffic jams” on axonal microtubules and the role of microtubule bundles in sustaining robust transport. They argue that the model captures essential physics—exclusion, bidirectional drift, binding/unbinding dynamics—and provides a quantitative baseline for interpreting in‑vivo data. The conclusion emphasizes that efficient intracellular bidirectional transport likely relies on mechanisms that suppress macroscopic clustering, such as regulatory proteins that modulate binding affinity, motor coordination, or the spatial organization of the filament network.

Overall, the paper delivers a comprehensive theoretical and computational analysis of how motor binding affinity, particle density, system size, and filament coupling govern the emergence of homogeneous flow versus large‑scale clustering. It offers valuable insights for biophysicists studying intracellular logistics and for the design of synthetic nanotransport systems that must avoid congestion on one‑dimensional tracks.