Evolution of drug resistance and antigenic escape: alternative models

Igor M. Rouzine¹* and John M. Coffin^1,2. ¹Department of Microbiology and Molecular Biology, Tufts University, Boston, Massachussetts 02111; ²HIV Drug resistance program, National Cancer Institute, Frederick, Maryland 21702 (USA).

Background: Drug-resistant and antigenic escape mutations are among mechanisms by which HIV persists in the face of functional immune responses, antiretroviral therapy, and therapeutic vaccination. Even very small mutation cost of a potentially-resistant mutation affects its concentration in population. Among other important factors affecting success of therapy are random drift, linkage of sites in DNA, and recombination. Because these factors present a serious mathematical challenge, their role, in quantitative terms, is poorly understood. In this work, we compare predictions of several models of evolution of drug-resistant and escape mutations before and after start of a therapy, and in the presence of immune response. Material and Methods: We use the analytic method of “solitary wave” we have developed recently to describe evolution of weakly deleterious mutations in the presence of random drift, selection, linkage, and recombination. Selection of strongly advantageous mutations under therapy or immune response is described deterministically but with random initial conditions. Additional methods are used to describe a continuous antigenic escape in the presence of diversifying immune response. Results: Recently, we have confirmed the qualitative prediction that linkage greatly enhances accumulation of weakly deleterious mutations in asexual population and slows down fixation of better-fit variants, as compared to unlinked sites. We obtained general expressions for the rates of these processes at different population sizes. Now we incorporate recombination into the model to describe the continuous transition between the asexual and the strong-recombination limit. We find out that even very infrequent recombination (<1 crossover/genome/generation) is able to counteract effects of linkage. However, at small population sizes expected during antiretroviral therapy, linkage remains important. Regarding the antigenic escape of HIV under immune pressure, we focus on the observed difference between the cases of CTL and antibody (Ab) response. While Ab cannot keep up with rapidly evolving virus population and poorly neutralize virus sampled at the same time, CTL recognize the concurrent virus that evolves slowly at CTL epitopes. We develop two alternative models, assuming a slow and a fast immune response relative to the rate of virus evolution, and estimate the critical response rate. The slower response rate (due to glycosylation, CD4 cell depletion), as well as a smaller epitope number, explain why the evolving virus escapes from Ab more successfully than from CTL.