On the laws of virus spread through cell populations

The dynamics of viral infections have been investigated extensively, often with a combination of experimental and mathematical approaches. Mathematical descriptions of virus spread through cell populations are well established in the literature and have yielded important insights, yet the formulation of certain fundamental aspects of virus dynamics models remains uncertain and untested. Here, we investigate the process of infection and, in particular, the effect of varying the target cell population size on the number of productively infected cells generated. Using an in vitro single-round HIV-1 infection system, we find that the established modeling framework cannot accurately fit the data. If the model is fit to data with the lowest number of cells and is used to predict data generated with larger cell populations, the model significantly overestimates the number of productively infected cells generated. Interestingly, this deviation becomes stronger under experimental conditions that promote mixing of cells and viruses. The reason for the deviation is that the standard model makes certain oversimplifying assumptions about the fate of viruses that fail to find a cell in their immediate proximity. We derive from stochastic processes a different model that assumes simultaneous access of the virus to multiple target cells. In this scenario, if no cell is available to the virus at its location, it has a chance to interact with other cells, a process that can be promoted by mixing of the populations. This model can accurately fit the experimental data and suggests a new interpretation of mass action in virus dynamics models.