HIV

There is an increasing body of evidence that describes the acquisition and loss of HIV cytotoxic T-lymphocyte (CTL) escape mutants.  The rates at which different epitopes escape and revert within individuals has implications for the evolution of HIV at the population level and for vaccine design.  Here we give a summary of escape and reversion rates estimated from the literature.  We also present a novel mathematical model and show how it can be used to predict the prevalence of escape mutants in HLA matched and mis-matched individuals.

Figure 1 is a summary of results from various published longitudinal studies showing how long after infection it took for wildtype epitope sequences to be replaced by escape variants. It suggests that escape occurs rapidly after infection - 80% of epitopes had an average time to escape of less than 2 years.

We are developing mathematical models of the selection, transmission and reversion of CTL escape mutants.  The simplest of these describes what happens at a single epitope and considers three processes: selection of CTL escape mutants in hosts that restrict the epitope; transmission of those mutants to new hosts; and reversion of mutants in hosts who do not restrict the epitope.  Our basic model is summarized in figure 2.

Using this model we are able to calculate how the prevalence of an escape mutant in HLA matched and mismatched hosts will vary over the course of the epidemic.  When escape and reversion are fast, these prevalences reach temporarily stable values early in the epidemic which can be analytically determined (Figure 3).

Kaplan-Meier survival plot of the proportion of hosts without escape versus time since infection. Includes epitopes with data from two or more patients.

Estimated time from infection to escape for epitopes with data from only one patient.

Figure 1. Estimated times from infection to escape for different viral epitopes. 80% of epitopes had an average time to escape of less than 2 years. (a) Kaplan-Meier survival plot of the proportion of hosts without escape versus time since infection.  Includes epitopes with data from two or more patients.  (b) Estimated time from infection to escape for epitopes with data from only one patient.

Model of within-host evolution and between-host transmission of CTL escape mutants

Figure 2. Model of within-host evolution and between-host transmission of CTL escape mutants
Prevalence of escape mutants in HLA matched & mismatched hosts. Notice how, as escape gets slower, escape mutant prevalence, in both matched and mis-matched hosts, gets lower.

Figure 3. Prevalence of escape mutants in HLA matched & mismatched hosts. Notice how, as escape gets slower, escape mutant prevalence, in both matched and mis-matched hosts, gets lower.