Oprea M, van Nimwegen E, Perelson A S
Department of Computer Science, University of New Mexico, Albuquerque 87131, USA.
Bull Math Biol. 2000 Jan;62(1):121-53. doi: 10.1006/bulm.1999.0144.
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 immunoglobulin 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. Studies of the architecture of germinal centers suggested that B cells divide in the dark zone of the germinal center, then migrate to the light zone, where they undergo selection based on their interaction with antigen-loaded follicular dendritic cells, after which they exit the germinal center through the mantle zone. Kepler and Perelson questioned this architecturally driven view of the germinal center reaction. They, as well as others, argued that the large number of point mutations observed in germinal center B cell V-region genes, frequently 5 to 10 and sometimes higher, would most likely render cells incapable of binding the antigen, if no selection step was interposed between rounds of mutations. To clarify this issue, we address the question of whether a mechanism in which mutants are generated and then selected in one pass, with no post-selection amplification, can account for the observed efficiency of affinity maturation. We analyse 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 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 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 useful intuitions in other cases where a population is subjected to selection mediated by a selective force that decays over time.
在免疫反应过程中，与引发该反应的抗原发生反应的抗体亲和力会随时间增加，这一现象称为亲和力成熟。亲和力成熟的分子基础已得到部分阐明。它涉及抗原刺激的生发中心B细胞内免疫球蛋白V区基因的体细胞突变以及随后对高亲和力变体的选择。这种突变和选择过程极其高效，并产生大量高亲和力变体。对生发中心结构的研究表明，B细胞在生发中心的暗区分裂，然后迁移到亮区，在那里它们基于与负载抗原的滤泡树突状细胞的相互作用进行选择，之后通过套区离开生发中心。开普勒和佩雷尔森对这种由结构驱动的生发中心反应观点提出了质疑。他们以及其他人认为，如果在多轮突变之间没有选择步骤，那么在生发中心B细胞V区基因中观察到的大量点突变（通常为5到10个，有时更多）很可能使细胞无法结合抗原。为了阐明这个问题，我们探讨了一种机制，即突变体一次性产生然后被选择，且没有选择后扩增，是否能够解释观察到的亲和力成熟效率。我们分析了一组具有衰减抗原且在转录或复制时发生突变的生发中心反应单步模型。我们表明，在所有情况下，生发中心输出中的高亲和力细胞比例与其选择概率呈对数变化。对于生物学上现实的参数，这一过程的效率与实验数据明显不符。此外，我们讨论了一组基于我们的分析得出的、可能违反直觉的单步选择模型的更一般特征。我们相信，这些结果也可能为其他情况提供有用的直觉，即在一个群体受到随时间衰减的选择力介导的选择作用的情况下。
