  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. 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.
