Mathematical modeling in cellular immunology: T cell activation and parameter estimation

A critical step in mounting an immune response is antigen rec ognition by T cells. This step proceeds by productive interactions between T cell receptors (TCR) on the s urface of T cells and foreign antigen, in the form of peptide-major-histocompatibility-complexes (pMHC), on the surface of antigen-presenting-cells (APC). Antigen recognition is exceedingly difficult to understand beca use the vast majority of pMHC on APCs are derived from self-proteins. Nevertheless, T cells have been shown t be exquisitely sensitive, responding to as few as 10 antigenic pMHC in an ocean of tens of thousands of self pMHC. I n addition, T cells are extremely specific and respond only to a small subset of pMHC by virtue of their speci fic TCR. To explain the sensitivity of T cells to pMHC it has been propo sed that a single pMHC may serially bind multiple TCRs. Integrating present knowledge on the spatial-t emporal dynamics of TCR/pMHC in the T cell-APC contact interface, we have constructed mathematical model s to investigate the degree of TCR serial engagements by pMHC. In addition to reactions within clusters, the model s capture the formation and mobility of TCR clusters. We find that a single pMHC serially binds a substantial number of TCRs in a TCR cluster only if the TCR/pMHC bond is stabilized by coreceptors and/or pMHC dimerization . I a separate study we propose that serial engagements can explain T cell specificity. Using Monte Carlo s imulations, we show that the stochastic nature of TCR/pMHC interactions means that multiple binding events a re needed for accurate detection of foreign pMHC. Critical to our studies are estimates of TCR/pMHC reaction r ates and mobilities. In the second half of the thesis, we show that Fluorescence Recovery After Photoblea ching (FRAP) experiments can reveal effective diffusion coefficients. We then show, using asymptotic analysis a nd model fitting, that FRAP experiments can be used to estimate reaction rates between cell surface proteins, l ike TCR/pMHC. Lastly, we use FRAP experiments to investigate how the actin cytoskeleton modulates TCR mobil ity and report effective reaction rates between TCR and the cytoskeleton.