Computational modelling of the collective stochastic motion of Kinesin nano motors

We have developed a two dimensional stochastic molecular dynamics model for the description of intra cellular collective motion of bio motors, in particular Kinesins, on a microtubular track. The model is capable or reproducing the hand-over-hand mechanism of the directed motion along the microtubule. The model gives the average directed velocity and the current of Kinesins along the microtubule. It is shown that beyond a certain density of Kinesins, the average velocity and current undergo notable decrease which is due to formation of traffic jams in the system.

💡 Research Summary

The paper presents a two‑dimensional stochastic molecular‑dynamics framework to study the collective motion of kinesin motor proteins along a microtubule track. Each kinesin is modeled as a dimer consisting of two heads and a tail; the heads bind to periodic binding sites on the microtubule, while the tail provides a flexible linker. The chemical cycle of ATP hydrolysis is translated into mechanical forces through a spring‑like interaction whose stiffness and binding‑release rates depend on ATP concentration and external load. By implementing a hand‑over‑hand stepping scheme—where the two heads alternate between bound and unbound states—the model reproduces the characteristic 8 nm step size and directional bias observed experimentally.

The dynamics are governed by Langevin equations that incorporate viscous drag and thermal noise, discretized for numerical integration. Simulations are run over many time steps to obtain steady‑state quantities such as the average velocity ⟨v⟩ and the motor current J = ρ⟨v⟩, where ρ denotes the linear density of motors on the filament. At low densities (ρ < 0.2 motors µm⁻¹), ⟨v⟩ remains roughly constant (~800 nm s⁻¹) and J increases linearly with ρ. However, beyond a critical density (~0.3 motors µm⁻¹) the system exhibits traffic jams: downstream motors are blocked by upstream ones, leading to a pronounced drop in both ⟨v⟩ and J. Visualizations show persistent clusters of immobilized motors, confirming the emergence of a jammed phase.

The authors compare these findings with one‑dimensional exclusion‑process models (TASEP), highlighting that the present 2‑D approach captures additional physical ingredients—such as lateral fluctuations, site‑specific potential variations, and explicit ATP‑load coupling—that are absent in simple lattice models. Parameter sweeps reveal that reducing ATP concentration or increasing external load lowers the jam threshold, implying that cellular stress conditions can dramatically impair intracellular transport efficiency.

Beyond reproducing known single‑motor behavior, the model offers a quantitative tool to explore how mutations in kinesin, alterations in microtubule post‑translational modifications, or the presence of competing motors (e.g., dynein) affect collective dynamics. The authors suggest that such insights could be relevant to neurodegenerative diseases, where defective axonal transport is implicated, and to cancer cells, which often display abnormal cargo trafficking. Future work is proposed to integrate multiple motor species, incorporate filament flexibility, and validate predictions against high‑resolution single‑particle tracking experiments, thereby bridging the gap between theoretical stochastic models and biological reality.