Dynamics of one-pass germinal center models: Implications for affinity maturation

During an immune response, the affinity of antibodies that react with the a ntigen that triggered the response increases with time, a phenomenon known as affinity maturation. The molecular basis of affinity maturation has been partially elucidated. It involves the somatic mutation of immunoglobulin V -region genes within antigen-stimulated germinal center B cells and the sub sequent selection of high affinity variants. This mutation and selection pr ocess is extremely efficient and produces large numbers of high affinity va riants. Studies of the architecture of germinal centers suggested that B ce lls divide in the dark zone of the germinal center, then migrate to the lig ht zone, where they undergo selection based on their interaction with antig en-loaded follicular dendritic cells, after which they exit the germinal ce nter through the mantle zone. Kepler and Perelson questioned this architect urally driven view of the germinal center reaction. They, as well as others , argued that the large number of point mutations observed in germinal cent er B cell V-region genes, frequently 5 to 10 and sometimes higher, would mo st likely render cells incapable of binding the antigen, if no selection st ep was interposed between rounds of mutations. To clarify this issue, we ad dress the question of whether a mechanism in which mutants are generated an d then selected in one pass, with no post-selection amplification, can acco unt for the observed efficiency of affinity maturation. We analyse a set of one-pass models of the germinal center reaction, with decaying antigen, an d mutation occurring at transcription or at replication. We show that under all the scenarios, the proportion of high affinity cells in the output of a germinal center varies logarithmically with their selection probability. For biologically realistic parameters, the efficiency of this process is in clear disagreement with the experimental data. Furthermore, we discuss a s et of, possibly counterintuitive, more general features of one-pass selecti on models that follow from our analysis. We believe that these results may also provide useful intuitions in other cases where a population is subject ed to selection mediated by a selective force that decays over time. (C) 20 00 Society for Mathematical Biology.