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. In resting T cells, the TCR is largely unphosphorylated due to the dominance of phosphatases over the kinases expressed at the cell surface. However, when agonist peptides are presented to the TCR by major histocompatibility complex proteins expressed by antigen-presenting cells (APCs), very fast receptor triggering, i.e., TCR phosphorylation, occurs. Recent work suggests that this depends on the local exclusion of the phosphatases from regions of contact of the T cells with the APCs. Here, we developed and tested a quantitative treatment of receptor triggering reliant only on TCR dwell time in phosphatase-depleted cell contacts constrained in area by cell topography. Using the model and experimentally derived parameters, we found that ligand discrimination likely depends crucially on individual contacts being ∼200 nm in radius, matching the dimensions of the surface protrusions used by T cells to interrogate their targets. The model not only correctly predicted the relative signaling potencies of known agonists and nonagonists but also achieved this in the absence of kinetic proofreading. Our work provides a simple, quantitative, and predictive molecular framework for understanding why TCR triggering is so selective and fast and reveals that, for some receptors, cell topography likely influences signaling outcomes.

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. The expected error in approximating the MFPT by our semi-analytical procedure is smaller than any power of [Formula: see text], so that our approximation of the MFPT is still rather accurate at only moderately small prey patch radii. Overall, our hybrid approach has the advantage of eliminating the difficulty with resolving small spatial scales in a full numerical treatment of the partial differential equation (PDE). Similar semi-analytical methods are also developed and implemented to accurately calculate related quantities such as the variance of the mean first passage time (VMFPT) and the splitting probability. Results for the MFPT, the VMFPT, and splitting probability obtained from our hybrid methodology are validated with corresponding results computed from full numerical simulations of the underlying PDEs.

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. In both cases, we find that a stationary trap actually performs better (in terms of reducing expected capture time) than a very slowly moving trap; however, a trap moving sufficiently fast performs better than a stationary trap. We explicitly compute the thresholds that separate the two regimes. In addition, we find a surprising relation between the oscillating trap problem and a moving-sink problem that describes reduced dynamics of a single spike in a certain regime of the Gray-Scott model. Namely, the above-mentioned threshold corresponds precisely to a Hopf bifurcation that induces oscillatory motion in the location of the spike. We use this correspondence to prove the uniqueness of the Hopf bifurcation.