Restricted occupancy models for neutralization of HIV virions and populations.

HIV virions infect cells by attaching to target cell receptors, fusing membranes with the cell and by finally releasing their genetic material into the target cells. Antibodies can hinder the infection by attaching to the HIV envelope glycoprotein trimers before or during attachment. The exact mechanisms and the quantitative requirements of antibody neutralization are still debated. Recently, the number of antibodies rendering one trimer non-functional, called stoichiometry of (trimer) neutralization, was studied with mathematical models. Here we extend this theoretical framework to calculate the stoichiometries of neutralizing a single virion and a whole virion population. We derive mathematical equations for antibody neutralization based on restricted occupancy theory. Additionally we simulate these processes when a direct calculation is not possible. We find that the number of trimers needed for cell entry and the number of antibodies neutralizing one trimer strongly influence the mean number of antibodies needed for virion and population neutralization. Further we show that the mean number of antibodies needed to neutralize a virion population exceeds the product of the number of virions in the population and the mean number of antibodies needed to neutralize one virion.