Random Runs on Random Networks: Trapping of Driven Cargo on Disordered Filament Arrays

Cytoskeletal networks are crucial for vesicular transport and distribution in highly extended neuronal projections. The localization of motor-driven cargos is determined not only by the kinetic parameters of transport but also by the spatial organization of the microtubules themselves. In proximal mammalian dendrites, short microtubules are distributed in parallel, unpolarized arrays, an arrangement that has been proposed to allow for broad scattering of processively moving cargos.

We consider the dynamics of particles that switch between diffusive motion and directed runs along fixed filaments randomly scattered in a linear domain. By mapping the microtubule configuration to networks of discrete milestone states, we derive the effective behavior of the cargo as it traverses the domain. In the limit of rapid attachment and detachment, the system can be mapped to a single-layer linear network, which inherently obeys detailed balance and can be described in terms of an effective energy landscape. The landscape captures exploratory dynamics of cargo discovering local traps before settling down to a steady state. Cargo distributions are found to be highly localized, particularly in the case of rapid directional switching and intermediate run velocities.

For the case of general attachment–detachment rates, the model is extended to a multi-layer network of advective and diffusive states in which cargo retains memory of the specific microtubule it is bound to, leading to cyclical fluxes that drive the steady-state cargo distribution away from its equilibrium state. Graph transformation methods are applied to solve for mean first passage times, revealing that intermediate attachment and detachment rates yield the fastest domain-crossing times.

These findings establish a quantitative link between microtubule architecture and kinetic parameters, highlighting how cargo distributions and exploratory dynamics emerge from a disordered active transport system.