Estimating the Stoichiometry of HIV Neutralization

HIV-1 virions infect target cells by first establishing contact between envelope glycoprotein trimers on the virion's surface and CD4 receptors on a target cell, recruiting co-receptors, fusing with the cell membrane and finally releasing the genetic material into the target cell. Specific experimental setups allow the study of the number of trimer-receptor-interactions needed for infection, i.e., the stoichiometry of entry and also the number of antibodies needed to prevent one trimer from engaging successfully in the entry process, i.e., the stoichiometry of (trimer) neutralization. Mathematical models are required to infer the stoichiometric parameters from these experimental data. Recently, we developed mathematical models for the estimations of the stoichiometry of entry [1]. In this article, we show how our models can be extended to investigate the stoichiometry of trimer neutralization. We study how various biological parameters affect the estimate of the stoichiometry of neutralization. We find that the distribution of trimer numbers—which is also an important determinant of the stoichiometry of entry—influences the estimated value of the stoichiometry of neutralization. In contrast, other parameters, which characterize the experimental system, diminish the information we can extract from the data about the stoichiometry of neutralization, and thus reduce our confidence in the estimate. We illustrate the use of our models by re-analyzing previously published data on the neutralization sensitivity [2], which contains measurements of neutralization sensitivity of viruses with different envelope proteins to antibodies with various specificities. Our mathematical framework represents the formal basis for the estimation of the stoichiometry of neutralization. Together with the stoichiometry of entry, the stoichiometry of trimer neutralization will allow one to calculate how many antibodies are required to neutralize a virion or even an entire population of virions.Author Summary: A large part of the research on the Human Immunodeficiency Virus focuses on how virus particles attach and enter their target cells, and how entry can be inhibited by antibodies or antiretroviral drugs. Because virus particles are too small to be observed in action the inference of the details of HIV entry has to be indirect—involving the genetic manipulation of virions, and often mathematical modeling. It is known that virus particles establish contact to their target cells with spikes on their surface, and antibodies binding to these spikes can inhibit virus entry. It is not known, however, how many antibodies are needed to neutralize a spike. In this article, we develop a mathematical framework to estimate this number, called the stoichiometry of neutralization, from data obtained in experiments with genetically engineered virions. An estimate of the stoichiometry of neutralization for different antibodies is important, as it will allow us to calculate the amount of antibodies required to abrogate virus replication.