Kepler T B, Perelson A S
Santa Fe Institute, NM 87501.
J Theor Biol. 1993 Sep 7;164(1):37-64. doi: 10.1006/jtbi.1993.1139.
The vertebrate immune system generates high-affinity antibodies to external antigens through a process of somatic hypermutation that takes place in germinal centers formed in the secondary lymphoid tissues. B cells proliferating in these germinal centers experience random mutations in the genes encoding the variable region of their immunoglobulin molecules and are subsequently selected for high-affinity binding to antigen. These germinal center reactions last for only about 2 weeks, yet in that time typically produce multiple point mutations resulting in affinity increases of factors of ten to a hundred or more. We have attempted to understand this extraordinary effectiveness by causing the problem of affinity maturation as an optimization problem in which a quantity that we call the total affinity is maximized as a functional of mu(t), the mutation rate as a function of time. We have developed a single-compartment model for the process and an optimization algorithm based on the Pontryagin maximum principle. Our results show that the optimum mutation schedule is one with brief bursts of high mutation rates interspersed between periods of mutation-free growth. Though this result at first seems highly non-physiological, we show that, in fact, it provides a framework within which the anatomy and kinetics of the germinal center reaction can be understood.
脊椎动物免疫系统通过体细胞超突变过程产生针对外部抗原的高亲和力抗体，该过程发生在次级淋巴组织中形成的生发中心。在这些生发中心增殖的B细胞在编码其免疫球蛋白分子可变区的基因中经历随机突变，随后被选择用于与抗原的高亲和力结合。这些生发中心反应仅持续约2周，但在此期间通常会产生多个点突变，导致亲和力增加10到100倍或更多。我们试图通过将亲和力成熟问题作为一个优化问题来理解这种非凡的有效性，在这个问题中，我们称之为总亲和力的量作为μ(t)（突变率作为时间的函数）的函数被最大化。我们已经为该过程开发了一个单室模型和一种基于庞特里亚金极大值原理的优化算法。我们的结果表明，最佳突变时间表是在无突变生长阶段之间穿插短暂的高突变率爆发。尽管这个结果乍一看似乎非常不符合生理学，但我们表明，事实上，它提供了一个框架，在这个框架内可以理解生发中心反应的解剖结构和动力学。
