Mathematical modeling of escape of HIV from cytotoxic T lymphocyte responses

Human immunodeficiency virus (HIV-1 or simply HIV) induces a persistent infection, which in the absence of treatment leads to AIDS and death in almost all infected individuals. HIV infection elicits a vigorous immune response starting about 2-3 weeks post infection that can lower the amount of virus in the body, but which cannot eradicate the virus. How HIV establishes a chronic infection in the face of a strong immune response remains poorly understood. It has been shown that HIV is able to rapidly change its proteins via mutation to evade recognition by virus-specific cytotoxic T lymphocytes (CTLs). Typically, an HIV-infected patient will generate 4-12 CTL responses specific for parts of viral proteins called epitopes. Such CTL responses lead to strong selective pressure to change the viral sequences encoding these epitopes so as to avoid CTL recognition. Indeed, the viral population "escapes" from about half of the CTL responses by mutation in the first year. Here we review experimental data on HIV evolution in response to CTL pressure, mathematical models developed to explain this evolution, and highlight problems associated with the data and previous modeling efforts. We show that estimates of the strength of the epitope-specific CTL response depend on the method used to fit models to experimental data and on the assumptions made regarding how mutants are generated during infection. We illustrate that allowing CTL responses to decay over time may improve the fit to experimental data and provides higher estimates of the killing efficacy of HIV-specific CTLs. We also propose a novel method for simultaneously estimating the killing efficacy of multiple CTL populations specific for different epitopes of HIV using stochastic simulations. Lastly, we show that current estimates of the efficacy at which HIV-specific CTLs clear virus-infected cells can be improved by more frequent sampling of viral sequences and by combining data on sequence evolution with experimentally measured CTL dynamics.