title: 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 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 time scale below which active mechanisms must take over. We consider N independent diffusing particles in a closed domain, containing a subregion with N_{0} particles, on average. We investigate the time until the subregion 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_{0}^{2}. For the case of T-cell receptors, we find that stochastic cavitation is exceedingly slow, 10^{9}  s at physiological densities; however, it can be accelerated to occur within 5 s with only a fourfold dilution.
authors.affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, 329 Phillips Hall, Chapel Hill, North Carolina 27599, USA.
authors.forename: Jay
authors.initials: J
authors.lastname: Newby
authors.affiliation: Department of Mathematics, University of California, Irvine, 340 Rowland Hall, Irvine, California 92697, USA.
authors.forename: Jun
authors.initials: J
authors.lastname: Allard
mesh_terms: D002450:Cell Communication / Q000502:physiology*; D008024:Ligands; D008954:Models, Biological; D011948:Receptors, Antigen, T-Cell / Q000737:chemistry / Q000276:immunology / Q000378:metabolism*
chemical_list: D008024:Ligands; D011948:Receptors, Antigen, T-Cell