Mean-field computational approach to HIV dynamics on a fitness landscape
Authors: Chen Hanrong , Kardar Mehran 
Published: January 2019

During infection by the human immunodeficiency virus (HIV), mutations accumulate in the intra-host viral population due to selection imposed by host T cell responses. The timescales at which HIV residues acquire mutations in a host range from days to years, 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 the global HIV sequence diversity, and stochastic simulations ofin silicoHIV infection, using these inferred landscapes, were shown to generate escape mutations whose locations and relative timescales correlate with those measured in patients with known T cell responses. These results suggest that the residue-specific fitness costs and epistatic interactions in the inferred landscapes encode useful information allowing for predictions of the dynamics of HIV mutations; however, currently available computational approaches to HIV dynamics that make use of realistic fitness landscapes are limited to these fixed-population-size stochastic simulations, which require many simulation runs and do not provide further insight as to why certain mutations tend to arise in a given host and for a given sequence background. In this paper, we introduce and examine an alternative approach, which we designate the evolutionary mean-field (EMF) method. EMF is an approximate high-recombination-rate model of HIV replication and mutation, in whose limit the dynamics of a large, diverse population of HIV sequences becomes computationally tractable. EMF takes as input the fitness landscape of an HIV protein, the locations and strengths of a host’s T cell responses, and the infecting HIV strain(s), and outputs a set of time-dependent “effective fitnesses” and frequencies of mutation at each HIV residue over time. Importantly, the effective fitnesses depend crucially on the fitness costs, epistatic interactions, and time-varying sequence background, thus automatically encoding how their combined effect influences the tendency for an HIV residue to mutate, in a time-dependent manner. As a proof of principle, we apply EMF to the dynamics of the p24 gag protein infecting a host whose T cell responses are known, and show how features of the fitness landscape, relative strengths of host T cell responses, and the sequence background impact the locations and time course of HIV escape mutations, which is consistent with previous work employing stochastic simulations. Furthermore, we show how features of longer-term HIV dynamics, specifically reversions, may be described in terms of these effective fitnesses, and also quantify the mean fitness and site entropy of the intra-host population over time. Finally, we introduce a stochastic population dynamics extension of EMF, where population size changes depend crucially on the fitness of strains existing in the population at each time, unlike prior stochastic simulation approaches with a fixed population size or a time-varying one that is externally defined. The EMF method offers an alternative framework for studying how genetic-level attributes of the virus and host immune response impact both the evolutionary and population dynamics of HIV, in a computationally tractable way.

Author summary

Fitness landscapes of HIV proteins have recently been inferred from HIV sequence diversity in the global population of hosts, and have been used in simulations ofin silicoHIV infection to predict the locations and relative timescales of mutations arising in hosts with known immune responses. However, computational approaches to HIV dynamics using realistic fitness landscapes are currently limited to these fixed-population-size stochastic simulations, which require many simulation runs and do not provide further insight as to why certain mutations tend to arise in a given host and for a given sequence background. Here, we introduce an alternative approach designated the evolutionary mean-field (EMF) method, which is an approximate high-recombination-rate model of HIV dynamics. It takes as input an HIV fitness landscape, the locations and strengths of a host’s immune responses, and the infecting HIV strain(s), and outputs a set of time-dependent “effective fitnesses” and frequencies of mutation at each HIV residue over time. We apply EMF on an example to show how features of the fitness landscape, relative strengths of host immune responses, and the HIV sequence background modify the effective fitnesses and hence the locations and time course of HIV mutations. We also develop a stochastic population dynamics extension of EMF where population size changes depend crucially on the fitness of strains existing in the population at each time. The EMF method enables more detailed study of how genetic-level attributes of the virus and host immune response shape the evolutionary and population dynamics of HIV, in a computationally tractable way.