A cell topography-based mechanism for ligand discrimination by the T cell receptor.

The T cell receptor (TCR) initiates the elimination of pathogens and tumors by T cells. To avoid damage to the host, the receptor must be capable of discriminating between wild-type and mutated self and nonself peptide ligands presented by host cells. Exactly how the TCR does this is unknown.

First-passage times, mobile traps, and Hopf bifurcations.

For a random walk on a confined one-dimensional domain, we consider mean first-passage times (MFPT) in the presence of a mobile trap. The question we address is whether a mobile trap can improve capture times over a stationary trap. We consider two scenarios: a randomly moving trap and an oscillating trap.

Asymptotic analysis of first passage time problems inspired by ecology.

A hybrid asymptotic-numerical method is formulated and implemented to accurately calculate the mean first passage time (MFPT) for the expected time needed for a predator to locate small patches of prey in a 2-D landscape. In our analysis, the movement of the predator can have both a random and a directed component, where the diffusivity of the predator is isotropic but possibly spatially heterogeneous. Our singular perturbation methodology, which is based on the assumption that the ratio [Formula: see text] of the radius of a typical prey patch to that of the overall landscape is asymptotically small, leads to the derivation of an algebraic system that determines the MFPT in terms of parameters characterizing the shapes of the small prey patches together with a certain Green's function, which in general must be computed numerically.