Statistical Physics, Evolutionary Dynamics of HIV, and the Adaptive Immune System

Abstract

Humans and other vertebrate hosts possess an adaptive immune system that defends the host against infection by a plethora of pathogens in a specific, targeted manner. T cells are an important arm of the adaptive immune system, and kill virus-infected host cells by recognizing virus-derived peptides presented on the surfaces of these cells. T cell specificity emerges through a process of selection in the thymus which eliminates T cells with nonfunc- tional receptors and those recognizing host-derived peptides. During infection by the human immunodeficiency virus (HIV), the virus mutates, generating variants that evade specific T cell recognition and hence overcoming T-cell–mediated immunity. The ability of HIV to escape immune responses and drug treatment is but one of many reasons why no vaccine or cure for HIV exists, but the intra-host HIV population may be most vulnerable to extinction immediately after transmission and during initial spread within the host. In this thesis, we use mathematical and computational methods drawn from statistical physics to study problems in intra-host HIV dynamics, intra-host HIV spread, and T cell selection. Can we predict the dynamics of HIV mutants that arise during intra-host infection, given host T cell responses? In Chapter 2, we develop a computational framework designated as the evolutionary mean-field (EMF) method to predict residue-specific HIV mutational dynamics given intrinsic viral fitness effects (described by recently characterized fitness landscapes of HIV proteins) and host T cell responses. A recently developed simian immunodeficiency virus (SIV) vaccine elicits unusual T cell responses in tested rhesus macaques and remarkably clears SIV infection in a fraction of these hosts. In Chapter 3, we apply the EMF method to explain this disparity in outcomes and the SIV mutational patterns observed in vaccinated but unprotected hosts. In Chapter 4, we develop a mathematical model of intra-host HIV spread to study the stochastic spread and extinction of the virus immediately after transmission to a new host. Finally, in Chapter 5, we study a model of thymic selection of T cells to relate statistical enrichment of amino acids among T cells surviving thymic selection to nonuniform contacts made by T cell receptors during the selection process.