title: 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.
  
  
  OBJECTIVE
  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 is the number of susceptible cells available for virus replication. How does the number of susceptible cells influence the growth potential of the virus? Besides the importance of such information for clinical responses, a thorough understanding of this is also important for the prediction of virus levels in patients and the estimation of crucial patient parameters through the use of mathematical models. This paper investigates the relationship between target cell availability and the virus growth potential with a combination of experimental and mathematical approaches and provides significant new insights.
authors.affiliation: Department of Ecology and Evolutionary Biology, University of California, Irvine, California, USA Department of Mathematics, University of California, Irvine, California, USA.
authors.forename: Dominik
authors.initials: D
authors.lastname: Wodarz
authors.affiliation: Department of Basic Science, New York University College of Dentistry, New York, New York, USA.
authors.forename: Chi N
authors.initials: CN
authors.lastname: Chan
authors.affiliation: Department of Basic Science, New York University College of Dentistry, New York, New York, USA.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Trinité
authors.affiliation: Department of Ecology and Evolutionary Biology, University of California, Irvine, California, USA Department of Mathematics, University of California, Irvine, California, USA.
authors.forename: Natalia L
authors.initials: NL
authors.lastname: Komarova
authors.affiliation: Department of Basic Science, New York University College of Dentistry, New York, New York, USA dnlevy@nyu.edu.
authors.forename: David N
authors.initials: DN
authors.lastname: Levy
mesh_terms: D015497:HIV-1 / Q000254:growth & development*; D006801:Humans; D019169:Jurkat Cells; D008962:Models, Theoretical; D013601:T-Lymphocytes / Q000821:virology*