Transport by molecular motors in the presence of static defects

The transport by molecular motors along cytoskeletal filaments is studied theoretically in the presence of static defects. The movements of single motors are described as biased random walks along the filament as well as binding to and unbinding from the filament. Three basic types of defects are distinguished, which differ from normal filament sites only in one of the motors’ transition probabilities. Both stepping defects with a reduced probability for forward steps and unbinding defects with an increased probability for motor unbinding strongly reduce the velocities and the run lengths of the motors with increasing defect density. For transport by single motors, binding defects with a reduced probability for motor binding have a relatively small effect on the transport properties. For cargo transport by motors teams, binding defects also change the effective unbinding rate of the cargo particles and are expected to have a stronger effect.

💡 Research Summary

The paper presents a theoretical investigation of how static defects on cytoskeletal filaments affect the transport of molecular motors. Motors are modeled as biased random walkers that can bind to, step along, and unbind from a one‑dimensional lattice representing a filament. Three distinct defect types are introduced, each altering a single transition probability while leaving the others unchanged: (i) stepping defects reduce the forward stepping probability, (ii) unbinding defects increase the probability of detachment, and (iii) binding defects lower the probability of re‑attachment from the solution. The defects are distributed randomly with a density ρ.

Using a master‑equation framework, the authors derive analytical expressions for the steady‑state average velocity ⟨v⟩ and run length ⟨λ⟩ of a single motor. For low defect densities a perturbative expansion yields linear corrections for stepping defects (⟨v⟩≈v₀(1‑αρ)) and exponential damping for unbinding defects (⟨λ⟩≈λ₀ e⁻ᵝρ). Binding defects have only a minor impact on single‑motor dynamics because the bound‑state residence time is dominated by the stepping and unbinding rates. Numerical Monte‑Carlo simulations confirm these analytical results and reveal strong non‑linear effects at higher ρ.

The study then extends the model to cargo transport by multiple motors. In this case, the effective detachment rate of the cargo depends on the collective binding probability of all attached motors. Consequently, binding defects, which scarcely affect a solitary motor, become significant for cargo: a reduction in the on‑rate (γ<1) effectively raises the cargo’s unbinding rate, dramatically shortening cargo run lengths and increasing transport times.

Key insights include: (1) stepping defects primarily slow down motor velocity in a proportional manner; (2) unbinding defects cause a dramatic loss of processivity, even at modest defect densities; (3) binding defects are largely irrelevant for single‑motor transport but can dominate cargo dynamics when multiple motors cooperate. The authors discuss biological relevance, noting that microtubule post‑translational modifications, drug‑induced protein binding, or disease‑related filament damage can be mapped onto these defect categories. For example, neurodegenerative diseases that destabilize microtubules may act as unbinding defects, explaining observed transport deficits.

Overall, the paper provides a unified, quantitative framework for assessing how static heterogeneities on filaments modulate motor‑driven intracellular transport. It highlights the importance of defect type and density, and it suggests that cells may mitigate adverse effects by employing motor teams, selecting defect‑free filament tracks, or regulating binding affinities. Future work is proposed to incorporate dynamic (time‑varying) defects, cooperative motor interactions, and experimental validation using in‑vitro reconstituted systems.