Quenched disorder in the environment can fundamentally alter transport dynamics in both active and passive systems. We explore how disordered arrays of filaments govern the distribution of intermittently moving particles which switch between diffusive and processive transport. Motivated by the mixed-polarity arrangements of parallel microtubules observed in mammalian dendrites, we show that such arrays tend to result in localization of particles at regions of convergent filament orientation. In the rapid attachment-detachment limit, the disordered system can be described by a noisy one-dimensional effective energy landscape, whose structure is approximated by a random walk. The depth and width of wells on this landscape are expressed as a function of the transport kinetics and system geometry. Localization is shown to be strongest at intermediate run lengths, where biased transport persists long enough to sense the quenched filament polarity but not so long as to facilitate escape from local traps. These results demonstrate robust localization of particles moving on random filament networks, highlighting the emergent spatial organization that arises from an interplay of active transport and quenched disorder.

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• Intracellular transport
• Localization
• Cytoskeleton
• Random & disordered media