Stochastic simulations of cargo transport by processive molecular motors

We use stochastic computer simulations to study the transport of a spherical cargo particle along a microtubule-like track on a planar substrate by several kinesin-like processive motors. Our newly developed adhesive motor dynamics algorithm combines the numerical integration of a Langevin equation for the motion of a sphere with kinetic rules for the molecular motors. The Langevin part includes diffusive motion, the action of the pulling motors, and hydrodynamic interactions between sphere and wall. The kinetic rules for the motors include binding to and unbinding from the filament as well as active motor steps. We find that the simulated mean transport length increases exponentially with the number of bound motors, in good agreement with earlier results. The number of motors in binding range to the motor track fluctuates in time with a Poissonian distribution, both for springs and cables being used as models for the linker mechanics. Cooperativity in the sense of equal load sharing only occurs for high values for viscosity and attachment time.

💡 Research Summary

In this study the authors present a comprehensive computational framework—named adhesive motor dynamics—to investigate how a spherical cargo is transported along a microtubule‑like filament by multiple processive kinesin‑type motors. The model couples a continuous Langevin description of the cargo’s translational and rotational motion with discrete stochastic rules governing motor binding, unbinding, and stepping. The Langevin component incorporates thermal diffusion, hydrodynamic drag arising from the proximity of the sphere to a planar wall, and the pulling forces generated by attached motors. Hydrodynamic interactions are treated with an Oseen‑Blake tensor, allowing realistic representation of the increased viscous resistance near the surface.

Motor kinetics are implemented as Poisson processes: each motor can bind to the filament with a rate k_on when its tether (modeled either as a linear spring or a one‑way cable) brings the motor head within a capture radius, and it can detach with a rate k_off that depends on the load shared by the motor. Once bound, the motor steps forward by 8 nm with a force‑dependent stepping rate that reproduces the experimentally measured force‑velocity curve of kinesin. The tether mechanics determine how the motor’s force is transmitted to the cargo; the spring model allows both tension and compression, whereas the cable model transmits force only under tension, mimicking a flexible linker that buckles when compressed.

System parameters were chosen to reflect typical in‑vitro and cellular conditions: cargo radius ≈0.5 µm, fluid viscosity ranging from that of water (10⁻³ Pa·s) up to cytoplasmic values (10⁻² Pa·s), motor stall force ≈6 pN, and stepping rates of ≈800 nm s⁻¹ at zero load. Simulations were run for varying numbers of motors (1–10) and for different attachment lifetimes.

The principal findings are threefold. First, the mean run length of the cargo grows exponentially with the number of motors that are simultaneously bound to the filament, L ≈ L₀ exp(α N). This reproduces earlier experimental observations and confirms that load sharing among motors dramatically extends transport distance. Second, the instantaneous number of motors that are within binding range of the filament follows a Poisson distribution. This statistical property emerges from the random orientation of the cargo relative to the track and the limited reach of each tether; it holds for both spring and cable linkers, indicating that the geometry of the binding zone dominates over the detailed elastic response. Third, cooperative load sharing—where each motor bears roughly the same fraction of the total load—only becomes appreciable under conditions of high fluid viscosity and long motor attachment times. At low viscosity or short dwell times, the system is dominated by “single‑motor pulling”: one or two motors carry most of the load while the others remain loosely attached, leading to a non‑cooperative regime. When viscosity is increased tenfold and the detachment rate is reduced (τ_off ≥ 1 s), the load is distributed more evenly, the effective detachment probability drops, and the exponential increase of run length with motor number becomes steeper.

Comparisons between the spring and cable tether models reveal that the overall transport statistics (run length, Poisson parameter) are relatively insensitive to the choice of elastic law. The cable model does produce occasional abrupt reductions in force when a motor goes slack, but these events are rare enough that they do not alter the ensemble‑averaged behavior. This suggests that, for many practical purposes, the precise mechanical details of the motor‑cargo linker can be abstracted without loss of predictive power, although more complex, non‑linear linkers may be required to capture specific biological scenarios.

The authors discuss the relevance of their results to experimental measurements of multi‑motor cargo transport, noting that the exponential run‑length scaling and Poisson binding statistics have both been reported in optical‑trap and fluorescence‑microscopy studies. They argue that the identified dependence of cooperative load sharing on viscosity and attachment time provides a mechanistic explanation for why intracellular transport—occurring in a highly viscous cytoplasm—often exhibits efficient multi‑motor cooperation, whereas in vitro assays performed in low‑viscosity buffers may appear less cooperative.

Finally, the paper acknowledges limitations: the cargo is assumed perfectly spherical, the filament is static and infinitely long, and direct motor‑motor interactions (e.g., steric hindrance or mechanical coupling) are omitted. Future extensions could incorporate deformable cargos, dynamic filament geometry, and explicit inter‑motor forces, thereby moving closer to a full physical description of intracellular cargo trafficking. Overall, the adhesive motor dynamics framework offers a versatile and quantitatively accurate tool for probing the stochastic physics of multi‑motor transport and for guiding the design of synthetic nanocarriers that exploit similar cooperative mechanisms.