Estimating the Stoichiometry of Human Immunodeficiency Virus Entry

To enter target cells, human immunodeficiency virus (HIV) first attaches to the cells and fuses with the cell membrane. Attachment and fusion involve envelope glycoprotein trimers on the surface of the virion and the CD4 receptor and chemokine coreceptors on the surface of the target cell. The stoichiometry of entry, that is, the number of bonds between such trimers and CD4 that are required for infection, is unknown. Pseudotyped virions that express mixed trimers consisting of functional and nonfunctional envelope proteins have been used to study how many trimer-receptor interactions are required for virus entry. However, to extract information on the stoichiometry of entry from data generated in in vitro infectivity assays with such viruses, mathematical models are required. Here, we describe mathematical models that can be used to infer the stoichiometry of entry. By fitting our simplest model to previously published data (X. Yang, S. Kurteva, X. Ren, S. Lee, and J. Sodroski, J. Virol. 79: 12132-12147, 2005), we estimated that the number of trimer-receptor interactions required for HIV to infect a target cell is approximately eight, which is higher than previous estimates. We also consider model extensions that explain some systematic deviations of the data from the prediction of the simplest model. However, these extended models yield very different estimates of the stoichiometry of entry ranging from 2 to 19. These results strongly suggest that, based on our present knowledge of HIV entry, the stoichiometry of this process cannot be reliably estimated. Our study identifies parameters that need to be defined to render the estimation of the stoichiometry of HIV entry possible.