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 can 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.

💡 Research Summary

The manuscript investigates how intermittent, motor‑driven transport influences the time it takes for two mobile intracellular particles to encounter each other. The authors first consider a minimal run‑and‑tumble (R&T) model in two dimensions: particles move at constant speed v for an exponentially distributed run time (average τrun), covering a mean run length λ = v τrun, after which they instantaneously select a new direction uniformly at random. The particles are confined to a circular domain of radius R with a “scattering” boundary that randomizes the heading upon contact.

Using both analytical calculations and extensive Brownian‑dynamics‑type simulations, the authors compute (i) the mean first‑passage time (MFPT) to a small fixed target of radius a at the domain centre, and (ii) the mean first‑encounter time (MFET) between two identical R&T particles of diameter a. They define an effective diffusivity Deff = v λ/2, which serves as the control parameter for both R&T and purely diffusive particles. For short runs (λ ≪ a) the R&T particles behave like ordinary Brownian walkers and the MFPT follows the classic diffusion result TD = R⁴/(8Deff)