Two-way Bayesian hierarchical phylogenetic models: An application to the co-evolution of gp120 and gp41 during and after enfuvirtide treatment

Enfuvirtide (ENF) is a fusion inhibitor that prevents the entry of HIV virions into target cells. Studying the characteristics of viral evolution during treatment and after a treatment interruption can lend insight into the mechanisms of viral evolution and fitness. Although interruption of anti-HIV therapy often results in rapid emergence of an archived "wild-type" virus population, previous work from our group indicates that when only ENF is interrupted, viral gp41 continues to evolve forward and resistance mutations are lost due to back-mutation and remodeling of the envelope protein. To examine the co-evolution of gp120 and gp41 during ENF interruption we extend the Bayesian Hierarchical Phylogenetic model (HPM). Current HPMs enforce conditional independence across all outcomes while biologically all gene regions within a patient should return the same tree unless recombination confers an evolutionary selective advantage. A two-way-interaction HPM is proposed that provides middle ground between these two extremes and allows us to test for differences in evolutionary pressures across gene regions in multiple patients simultaneously. When the model is applied to a well-characterized cohort of HIV-infected patients interrupting ENF we find that across patients, the virus continued to evolve forward in both gene regions. Overall, the hypothesis of independence over dependence between the gene regions is supported. Models that allow for the examination of co-evolution over time will be increasingly important as more therapeutic classes are developed, each of which may impact other through novel and complex mechanisms.