| Through mathematical modeling and analysis, we investigate T lymphocyte behavior in health and disease. We seek fundamental mechanistic rules that govern T cell mediated immune responses, and ask: What features distinguish healthy responses to pathogens from destructive autoimmune responses? A variety of experimental approaches have identified many specific details of T cell interactions for particular autoimmune disease models; however, these results often apply only to unique experimental settings. Many unanswered questions exist in the scientific literature regarding antigen presentation, T cell receptor interactions, and the functional roles of different classes of T cells. The models presented in this thesis address these issues.; We begin with an ordinary differential equation system describing T cell proliferation and retraction following viral infection. Previous modeling was based on an assumption that memory T cells arise only after the peak response time. We propose an alternative model, and argue that it offers a more robust mechanism for the generation of a stable immune memory. To capture the theory that T cell development is based on the duration of T cell receptor engagement, we introduce a model that consists of a system of partial differential equations. This model adds receptor engagement as an additional independent variable in the evolution of T cell populations in time. Our derivation, analysis and simulation results are presented in this thesis. We are able to solve specific forms of the model analytically, and find other results from numerical simulation. We also propose a simple ordinary differential equation system that reveals a switch mechanism that can prevent autoimmune reactions. In this model, we include recent theory about the role of regulatory T cells, and the activation level of the antigen presenting cells. We study inflammation in the tissue as a bifurcation parameter, and find bistability in certain parameter regimes.; The models in this thesis build on other theoretical models of T cell population dynamics and provide testable predictions for future experimental work. Our findings center around T cell interactions with antigen presenting cells of the innate immune system, that dynamically determine the type and magnitude of a response. |
