First-Passage Time to Clear the Way for Receptor-Ligand Binding in a Crowded Environment

Abstract

Certain biological reactions, such as receptor-ligand binding at cellcell 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 N0 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 subexponential, T ∝ e N 0 /N 2 0 . 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.Diffusion drives many biological processes, both positively, by delivering cargo to a target, and negatively, by removal of cargo from a region of interest (ROI). While the temporal dynamics of diffusional delivery have been extensively studied [5,4,24,12], diffusion-driven removal has been less characterized experimentally or theoretically [3]. Removal is of particular interest in the crowded environment of cells, where large biomolecules and cellular structures require the displacement of smaller molecules, a phenomenon we term stochastic cavitation.A specific example arises in the study of cell-cell interfaces including the T-cell/antigen-presenting-cell interface [22,2,29,8] (see Fig. 1). A fundamental question for all cell-cell interfaces is how receptors and ligands come into

Simulation of receptor triggering by kinetic segregation shows role of oligomers and close-contacts

“…We confirm mathematical estimates that, at physiological concentrations, spontaneous evacuation is extremely rare [12]. We find that dimerization decreases the timescale of evacuation for even weak bi- molecular interaction by several orders of magnitude.…”

“…Estimate of physiological density of CD45 assuming an ROI of ~ 100nm in radius and ~ 9 × 10 -4 molecules per nm 2 (see main text) marked with a vertical line. Evacuation times from WE for domain size L = 5 (blue) agree with brute force simulations (red) at low ρ and with an asymptotic (infinite domain) approximation at low to intermediate ρ [12]. (Both the asymptotics and WE overestimate the evacuation times at very low ρ ).…”

“…In the base case, we assume motion is purely diffusive with coefficient D (which could be thermal or include active, random forces [27]). Note that previous work [12] has shown that diffusion alone is too slow to be consistent with experimental data, giving MFPTs of ~ 10 10 s whereas triggering can occur in reality within seconds [28, 29]. That is, the simultaneous evacuation of all molecules from the ROI by simple diffusion, given physiological surface density and ROI size, is a rare event.…”

“…Various mechanisms for this evacuation process have been proposed. These include: simple Brownian motion of CD45 in the plasma membrane [12]; oligomerization reactions between the molecules [13, 14] shown schematically in Fig. 1B; and mechanical compression by a nearby surface, such as that of the cell presenting the antigen.…”

Molecular mechanisms of T cell sensitivity to antigen

“…How long would it take for CD45 to be passively (ie, spontaneously) segregated from a small 100 nm membrane patch? This calculation was recently performed showing that at physiological densities of CD45, it would take an astronomical period of time (10 9 seconds) . A recent in vitro reconstitution of passive CD45 segregation showed that it would require approximately 15 minutes to first observe short receptor/ligand interactions .…”