Dynamics of One-Pass Germinal Center Models: Implications for Affinity Maturation

During an immune response the affinity of antibodies that react with the antigen 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 immunoglobin V-region genes within antigen stimulated germinal center B cells and the subsequent selection of high affinity variants. This mutation and selection process is extremely efficient and produces large numbers of high affinity variants. The mechanisms responsible for the efficiency of the process are insufficiently understood. Kepler and Perelson proposed that there are multiple rounds of expansion, mutation and selection, with the cells surviving one round, allowed to expand, mutate and undergo selection again. This suggestion has been controversial. Here we examine the opposing hypothesis. We address the question of whether a mechanism in which mutants are generated and then selected in one pass, with no post-selection amplification of the surviving mutants, can account for the observed efficiency of affinity mutation. We analyze a set of one-pass models of the germinal center reaction, with decaying antigen, and mutation occurring at transcription or at replication. We show that under all such scenarios, the proportion of high affinity cells in the output of a germinal center varies logarithmically with the selection probability. For biologically realistic parameters, the efficiency of this process is unacceptably low. Furthermore, we discuss a set of, possibly counterintuitive, more general features of one-pass selection models that follow from our analysis. We believe that these results may also provide uselful intuitions in other cases where a population is subjected to a selective filter mediated by a selective agent that decays over time.