Mean-field computational approach to HIV dynamics on a fitness landscape

Abstract

During acute infection by the human immunodeficiency virus (HIV), the intra-host viral population accumulates mutations due to selection by host T cell responses. The timescales at which HIV mutations emerge vary widely, correlating with their diversity in the global population of hosts, and with the relative strengths at which different regions of the HIV sequence are targeted by the host. In recent years, \"fitness landscapes\" of HIV proteins have been estimated from this global diversity, capturing residue-specific fitness costs and epistatic interactions between residues, and have been shown to predict the locations and relative timescales of escape mutations arising in hosts with known T cell responses. However, existing computational approaches to HIV dynamics that make use of realistic fitness landscapes are limited to fixed-population-size stochastic simulations, and extending other dynamical approaches to capture full sequence-level detail is computationally nontrivial. In this paper, we introduce and study an alternative approach for simulating HIV dynamics given a fitness landscape, which we designate the evolutionary mean-field (EMF) method. EMF is the high-recombination-rate limit of a model of HIV replication and mutation, which we justify using methods from statistical physics. EMF outputs a set of time-dependent \"effective fitnesses\" that crucially depend on epistatic interactions and the sequence background, as well as predictions of the frequencies of mutation at each HIV residue over time. As a proof of principle, we apply this method to the dynamics of the p24 gag protein infecting a host whose T cell responses are known. Specifically, we show how fitness costs and epistatic interactions in the fitness landscape, the relative strengths of T cell responses, and the HIV sequence background, impact the locations and time course of HIV escape mutations, consistent with previous work. We also describe features of longer-term dynamics, specifically reversions, in terms of the effective fitnesses yielded by EMF, and quantify the mean fitness and entropy of the intra-host population over time. Finally, we develop a stochastic population dynamics version of EMF, extending prior stochastic approaches to a time-varying population size that crucially depends on the fitness of strains existing in the intra-host population at each time. The EMF approach offers a framework for understanding features of HIV dynamics in terms of effective fitnesses, and allows for a more detailed study of how the fitness landscape and sequence background impact both the evolutionary and population dynamics of HIV, in a computationally tractable way.\n\nAuthor summaryAs fitness landscapes of HIV proteins become more accurately known, it may become possible to more faithfully predict the locations and timescales of HIV mutations arising in a host with known immune responses, which may inform the design of vaccine immunogens. However, existing approaches for computing HIV dynamics given a fitness landscape are limited to fixed-population-size stochastic simulations. Here, we present an alternative approach that we designate the evolutionary mean-field (EMF) method. It takes as input an HIV fitness landscape and the locations and strengths of host immune responses, and outputs a set of time-dependent \"effective fitnesses\" and frequencies of mutation at each HIV residue over time. EMF is the high-recombination-rate limit of a model of HIV replication and mutation, which we derive using methods from statistical physics. We apply EMF on an example to show how fitness costs and epistatic interactions in the fitness landscape, the relative strengths of host immune responses, and the HIV sequence background, impact the locations and time course of HIV mutations. We also develop a stochastic population dynamics version of EMF where population size changes crucially depend on the fitness of strains existing in the population at each time. EMF makes quick predictions of the dynamics of HIV mutations through the effective fitnesses, crucially taking into account the fitness landscape and sequence background, and enables more detailed studies of how these affect the evolutionary and population dynamics of HIV, in a computationally tractable way.