de Boer, R. J.,Perelson, A. S.

Many HIV-1-infected patients evolve broadly neutralizing antibodies (bnAbs). This evolutionary process typically takes several years and is poorly understood as selection taking place in germinal centers occurs on the basis of antibody affinity. B cells with the highest-affinity receptors tend to acquire the most antigen from the follicular dendritic cell (FDC) network and present the highest density of cognate peptides to follicular helper T (Tfh) cells, which provide survival signals to the B cell. bnAbs are therefore expected to evolve only when the B cell lineage evolving breadth is consistently capturing and presenting more peptides to Tfh cells than other lineages of more specific B cells. Here we develop mathematical models of Tfh cells in germinal centers to explicitly define the mechanisms of selection in this complex evolutionary process. Our results suggest that broadly reactive B cells presenting a high density of peptides bound to major histocompatibility complex class II molecules (pMHC) are readily outcompeted by B cells responding to lineages of HIV-1 that transiently dominate the within host viral population. Conversely, if broadly reactive B cells acquire a large variety of several HIV-1 proteins from the FDC network and present a high diversity of several pMHC, they can be rescued by a large fraction of the Tfh cell repertoire in the germinal center. Under such circumstances the evolution of bnAbs is much more consistent. Increasing either the magnitude of the Tfh cell response or the breadth of the Tfh cell repertoire markedly facilitates the evolution of bnAbs. Because both the magnitude and breadth can be increased by vaccination with several HIV-1 proteins, this calls for experimental testing. IMPORTANCE Many HIV-infected patients slowly evolve antibodies that can neutralize a large variety of viruses. Such broadly neutralizing antibodies (bnAbs) could in the future become therapeutic agents. bnAbs appear very late, and patients are typically not protected by them. At the moment, we fail to understand why this takes so long and how the immune system selects for broadly neutralizing capacity. Typically, antibodies are selected based on affinity and not on breadth. We developed mathematical models to study two different mechanisms by which the immune system can select for broadly neutralizing capacity. One of these is based upon the repertoire of different follicular helper T (Tfh) cells in germinal centers. We suggest that broadly reactive B cells may interact with a larger fraction of this repertoire and demonstrate that this would select for bnAbs. Intriguingly, this suggests that broadening the Tfh cell repertoire by vaccination may speed up the evolution of bnAbs.