A stochastic spatio-temporal (SST) model to study cell-to-cell variability in HIV-1 infection.

Although HIV viremia in infected patients proceeds in a manner that may be accounted for by deterministic mathematical models, single virus-cell encounters following initial HIV exposure result in a variety of outcomes, only one of which results in a productive infection. The development of single molecule tracking techniques in living cells allows studies of intracellular transport of HIV, but it remains less clear what its impact may be on viral integration efficiency. Here, we present a stochastic intracellular mathematical model of HIV replication that incorporates microtubule transport of viral components. Using this model, we could study single round infections and observe how viruses entering cells reach one of three potential fates - degradation of the viral RNA genome, formation of LTR circles, or successful integration and establishment of a provirus. Our model predicts global trafficking properties, such as the probability and the mean time for a HIV viral particle to reach the nuclear pore. Interestingly, our model predicts that trafficking determines neither the probability or time of provirus establishment - instead, they are a function of vRNA degradation and reverse transcription reactions. Thus, our spatio-temporal model provides novel insights into the HIV infection process and may constitute a useful tool for the identification of promising drug targets.