Kinetic co-evolutionary models predict the temporal emergence of HIV resistance mutations under drug selection pressure

Drug resistance in human immunodeficiency virus (HIV) is a pervasive problem that affects the lives of millions of people worldwide. Although records of drug-resistant mutations (DRMs) have been extensively tabulated within public repositories, our understanding of the evolutionary kinetics of DRMs and how they evolve together remains limited. Epistasis, the interactions between a DRM and other residues in HIV protein sequences, is found to be key to the temporal evolution of drug resistance. We use a Potts sequence-covariation statistical-energy model of HIV protein fitness under drug selection pressure, which captures epistatic interactions between all positions, combined with kinetic Monte-Carlo simulations of sequence evolutionary trajectories, to explore the acquisition of DRMs as they arise in an ensemble of drug-naive patient protein sequences. We follow the time course of 52 DRMs in the enzymes protease, reverse transcriptase, and integrase, the primary targets of antiretroviral therapy (ART). The rates at which DRMs emerge are highly correlated with their observed acquisition rates reported in the literature when drug pressure is applied. This result highlights the central role of epistasis in determining the kinetics governing DRM emergence. Whereas rapidly acquired DRMs begin to accumulate as soon as drug pressure is applied, slowly acquired DRMs are contingent on accessory mutations that appear only after prolonged drug pressure. We provide a foundation for using computational methods to determine the temporal evolution of drug resistance using Potts statistical potentials, which can be used to gain mechanistic insights into drug resistance pathways in HIV and other infectious agents. SignificanceHIV affects the lives of millions of patients worldwide; cases of pan-resistant HIV are emerging. We use kinetic Monte-Carlo methods to simulate the evolution of drug resistance based on HIV patient-derived sequence data available on public databases. Our simulations capture the timeline for the evolution of DRMs reported in the literature across the major drug-target enzymes - PR, RT, and IN. The network of epistatic interactions with the primary DRMs determines the rate at which DRMs are acquired. The timeline is not explained by the overall fitness of the DRMs or features of the genetic code. This work provides a framework for the development of computational methods that forecast the time course over which drug resistance to antivirals develops in patients.