Affinity maturation is a complex dynamical process allowing the immune system to generate antibodies capable of recognizing antigens. We introduce a model for the evolution of the distribution of affinities across the antibody population in germinal centers. The model is amenable to detailed mathematical analysis, and gives insight on the mechanisms through which antigen availability controls the rate of maturation and the expansion of the antibody population. It is also capable, upon maximum-likelihood inference of the parameters, to reproduce accurately the distributions of affinities of IgG-secreting cells we measure in mice immunized against Tetanus Toxoid under largely varying conditions (antigen dosage, delay between injections). Both model and experiments show that the average population affinity depends non-monotonically on the antigen dosage. We show that combining quantitative modelling and statistical inference is a concrete way to investigate biological processes underlying affinity maturation (such as selection permissiveness), hardly accessible through measurements.

中文翻译：

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抗原剂量对成熟生发中心B细胞亲和力分布影响的定量建模

亲和力成熟是一个复杂的动力学过程，允许免疫系统产生能够识别抗原的抗体。我们介绍了一个模型，用于在生发中心跨越抗体群体的亲和力分布演变。该模型适用于详细的数学分析，并提供了有关抗原可利用性控制抗体成熟度和抗体种群扩展的机制的见解。根据参数的最大似然推断，它还能够准确地重现我们在很大变化的条件下（抗原剂量，注射间隔）对破伤风类毒素免疫的小鼠中测得的分泌IgG的细胞的亲和力分布。模型和实验均表明，平均群体亲和力非单调取决于抗原剂量。我们表明，将定量建模与统计推断相结合是研究亲和力成熟（例如选择容忍度）基础的生物学过程的一种具体方法，该过程很难通过测量获得。