First-passage time to clear the way for receptor-ligand binding in a crowded environment

TL;DR

This paper models the time for a crowded environment to clear enough molecules for receptor-ligand binding, revealing that cavitation is typically very slow but can be accelerated by dilution.

Contribution

It introduces an exact simulation and asymptotic approximation for first-passage times in crowded environments, highlighting the slow natural cavitation process and potential acceleration methods.

Findings

Mean first passage time is sub-exponential, proportional to e^{N_0}/N_0^2.

Cavitation can take up to 10^9 seconds at physiological densities.

Dilution by a factor of four reduces cavitation time to about 5 seconds.

Abstract

Certain biological reactions, such as receptor-ligand binding at cell-cell interfaces and macromolecules binding to biopolymers, require many smaller molecules crowding a reaction site to be cleared. Examples include the T cell interface, a key player in immunological information processing. Diffusion sets a limit for such cavitation to occur spontaneously, thereby defining a timescale below which active mechanisms must take over. We consider $N$ independent diffusing particles in a closed domain, containing a sub-region with $N_{0}$ particles, on average. We investigate the time until the sub-region is empty, allowing a subsequent reaction to proceed. The first passage time is computed using an efficient exact simulation algorithm and an asymptotic approximation in the limit that cavitation is rare. In this limit, we find that the mean first passage time is sub-exponential, $T \propto e^{N_{0}}/N_{0}^2$. For the case of T cell receptors, we find that stochastic cavitation is exceedingly slow, $10^9$ seconds at physiological densities, however can be accelerated to occur within 5 second with only a four-fold dilution.