On the Laws of Virus Spread through Cell Populations

Abstract

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. IMPORTANCE Understanding the principles of virus growth through cell populations is of fundamental importance to virology. It helps us make informed decisions about intervention strategies aimed at preventing virus growth, such as drug treatment or vaccination approaches, e.g., in HIV infection, yet considerable uncertainty remains in this respect. An important variable in this context Studying the dynamics of virus replication has generated important insights into several human infections, including those caused by human immunodeficiency virus (HIV) as well as hepatitis B and C viruses (1-6). Mathematical modeling of viral dynamics has played a crucial role in this research, allowing the estimation of critical replication parameters in order to obtain a better understanding of viral evolution, the interactions between viruses and the immune system, and the response of viral infections to antiviral drug therapy. The accuracy with which virus dynamics are described and, more importantly, predicted depends on various simplifying assumptions underlying the model; these have been discussed, e.g., in reference 7. Here we investigate the fundamental structure of the infection term, that is, the overall rate at which target cells in a population become infected in the presence of the virus. We specifically discover how the number of target cells available to the virus influences the number of...

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