Analysis of the subunit stoichiometries in viral entry

Virions of the Human Immunodeficiency Virus (HIV) infect cells by first attaching with their surface spikes to the CD4 receptor on target cells. This leads to conformational changes in the viral spikes, enabling the virus to engage a coreceptor, commonly CCR5 or CXCR4, and consecutively to insert the fusion peptide into the cellular membrane. Finally, the viral and the cellular membranes fuse. The HIV spike is a trimer consisting of three identical heterodimers composed of the gp120 and gp41 envelope proteins. Each of the gp120 proteins in the trimer is capable of attaching to the CD4 receptor and the coreceptor, and each of the three gp41 units harbors a fusion domain. It is still under debate how many of the envelope subunits within a given trimer have to bind to the CD4 receptors and to the coreceptors, and how many gp41 protein fusion domains are required for fusion. These numbers are referred to as subunit stoichiometries. We present a mathematical framework for estimating these parameters individually by analyzing infectivity assays with pseudotyped viruses. We find that the number of spikes that are engaged in mediating cell entry and the distribution of the spike number play important roles for the estimation of the subunit stoichiometries. Our model framework also shows why it is important to subdivide the question of the number of functional subunits within one trimer into the three different subunit stoichiometries. In a second step, we extend our models to study whether the subunits within one trimer cooperate during receptor binding and fusion. As an example for how our models can be applied, we reanalyze a data set on subunit stoichiometries. We find that two envelope proteins have to engage with CD4-receptors and coreceptors and that two fusion proteins must be revealed within one trimer for viral entry. Our study is motivated by the mechanism of HIV entry but the experimental technique and the model framework can be extended to other viral systems as well.