Encounter times of intermittently running particles

Intracellular processes often rely on the timely encounter of mobile reaction partners, including intermittently motor-driven organelles. The underlying cytoskeletal network presents a complex landscape that both directs particle movement and introduces quenched disorder through filament organization. We investigate the mean first encounter times for pairs of intermittently processive and diffusive particles, moving in two dimensions with and without a fixed filament network. In unstructured domains, increasing particle run-length enhances exploration of the domain, but tends to slow down the encounter times compared to equivalent diffusing particles. Encounters for long-running particles occur preferentially near the periphery, contrasting with bulk encounters for the purely diffusive case. When particles are unbiased in their runs along dense filament networks, encounters are shown to be well approximated by a continuum run-and-tumble model. For biased particles, regions of convergent filament orientation serve as traps that slow the overall spatial exploration but can allow for faster encounter rates by funneling particles into regions of reduced dimensionality. These findings provide a framework for estimating intracellular encounter kinetics, highlighting the role of key physical features such as the effective diffusivity, run times, and network architecture.