Mathematically Capturing HIV: Quantifying CTL killing of HIV-infected cells using mathematical models

Abstract

The dynamics of HIV infected cells are of the utmost important in understanding the disease, and mathematical modeling can help us quantify and understand the processes at work. One parameter that is heavily debated is the contribution of CD8+ T cells in the killing of HIV infected cells; some attribute a negligible role to CD8+ T cells in this respects, others an indispensable role. Moreover, CD8+ T cell mediated killing can take place at different stages in the cycle of HIV infected cells. Here, we used a two-stage mathematical model, distinguishing between non-productively and productively infected cells. The killing rates were estimated in two ways. First, the viral replication rate was calculated based on six different studies using CD8+ depletion studies. From this replication rate, we then calculated the killing rates for the early, late, and equal killing scenarios. An interesting, novel finding on the side is that the viral replication rate of elite controller rhesus monkeys is higher than that of progressor monkeys, corresponding to a higher killing rate in the former group. Secondly, we fitted our mathematical model to a dataset of an experiment using adoptive transfer of CD8+ T cells using a script written in R. These fits were done with fully free, partially fixed, and mostly fixed parameters. Both estimation methods suggest that the role of CD8+ T cells in the killing of HIV infected cells is crucial and not negligible.