Contingency and Entrenchment of Drug-Resistance Mutations in HIV Viral Proteins

The
ability of HIV-1 to rapidly mutate leads to antiretroviral
therapy (ART) failure among infected patients. Drug-resistance mutations
(DRMs), which cause a fitness penalty to intrinsic viral fitness,
are compensated by accessory mutations with favorable epistatic interactions
which cause an evolutionary trapping effect, but the kinetics of this
overall process has not been well characterized. Here, using a Potts
Hamiltonian model describing epistasis combined with kinetic Monte
Carlo simulations of evolutionary trajectories, we explore how epistasis
modulates the evolutionary dynamics of HIV DRMs. We show how the occurrence
of a drug-resistance mutation is contingent on favorable epistatic
interactions with many other residues of the sequence background and
that subsequent mutations entrench DRMs. We measure the time-autocorrelation
of fluctuations in the likelihood of DRMs due to epistatic coupling
with the sequence background, which reveals the presence of two evolutionary
processes controlling DRM kinetics with two distinct time scales.
Further analysis of waiting times for the evolutionary trapping effect
to reverse reveals that the sequences which entrench (trap) a DRM
are responsible for the slower time scale. We also quantify the overall
strength of epistatic effects on the evolutionary kinetics for different
mutations and show these are much larger for DRM positions than polymorphic
positions, and we also show that trapping of a DRM is often caused
by the collective effect of many accessory mutations, rather than
a few strongly coupled ones, suggesting the importance of multiresidue
sequence variations in HIV evolution. The analysis presented here
provides a framework to explore the kinetic pathways through which
viral proteins like HIV evolve under drug-selection pressure.