A model for motor-mediated bidirectional transport along an antipolar microtubule bundle

Long-distance bidirectional transport of organelles depends on the motor proteins kinesin and dynein. Using quantitative data obtained from a fungal model system, we previously developed ASEP-models of bidirectional motion of motors along unipolar microtubules (MTs) near the cell ends of the elongated hyphal cells (herein referred as “unipolar section”). However, recent quantitative live cell imaging in this system has demonstrated that long-range motility of motors and their endosomal cargo mainly occurs along extended antipolar microtubule bundles within the central part of the cell (herein referred to as “bipolar section”). Dynein and kinesin-3 motors coordinate their activity to move early endosomes (EEs) in a bidirectional fashion, with dynein mediating retrograde motility along the unipolar section near the cell poles, whereas kinesin-3 is responsible for bidirectional motions along the antipolar section. Here we extend our modelling approach to simulate bidirectional motility along an antipolar microtubule bundle. In our model, cargos (particles) change direction on each MT with a turning rate $\Omega$ and the MTs are linked to each other at the minus ends where particles can hop between MTs with a rate $q_1$ (obstacle-induced switching rate) or $q_2$ (end-induced switching rate). By numerical simulations and mean-field approximations, we investigate the distribution of particles along the MTs for different overall densities $\Theta$. We find that even if $\Theta$ is low, the system can exhibit shocks in the density profiles near plus and minus ends caused by queueing of particles. We also discuss how the switching rates $q_{1,2}$ influence the type of motor that dominates the active transport in the bundle.

💡 Research Summary

The paper extends a previously developed asymmetric simple exclusion process (ASEP) model of bidirectional motor‑driven transport from the unipolar microtubule (MT) sections at hyphal tips to the antipolar MT bundles that dominate the central region of filamentous fungi. In the biological system, early endosomes (EEs) are carried by kinesin‑3 (plus‑end directed) and dynein (minus‑end directed). Near the cell poles dynein alone drives retrograde motion, whereas within the central antipolar bundle both motors cooperate to generate frequent forward–backward switches.

Model formulation
Two parallel MTs of opposite polarity are represented as one‑dimensional lattices. Particles (cargo‑laden endosomes) hop forward with rate p⁺ (kinesin‑3) and backward with rate p⁻ (dynein), subject to hard‑core exclusion (one particle per site). While on a given MT a particle may change its direction with a “turning” rate Ω, reflecting stochastic motor exchange or ATP‑dependent detachment/attachment. The MTs are linked at their minus ends; at this junction a particle can hop laterally to the other MT either (i) because it encounters an obstacle (another particle) with rate q₁ (obstacle‑induced switching) or (ii) simply because it reaches the bundle end with rate q₂ (end‑induced switching). The overall particle density in the system is denoted by Θ.

Analytical and numerical approach
Mean‑field equations for the site‑averaged densities ρ₁(x) and ρ₂(x) are derived, incorporating the turning term Ω and the two lateral switching terms q₁, q₂. Stationary solutions are obtained by solving coupled continuity equations with appropriate boundary conditions at the plus and minus ends. Complementary Monte‑Carlo simulations (L = 500 sites, time step Δt = 0.01) explore a broad parameter space: Θ ∈