When our immune system encounters foreign antigens (i.e., from pathogens), the B cells that produce our antibodies undergo a cyclic process of proliferation, mutation, and selection, improving their ability to bind to the specific antigen. Immunologists have recently developed powerful experimental techniques to investigate this process in mouse models. In one such experiment, mice are engineered with a monoclonal B-cell precursor and immunized with a model antigen. B cells are sampled from sacrificed mice after the immune response has progressed, and the mutated genetic loci encoding antibodies are sequenced. This experiment allows parallel replay of antibody evolution, but produces data at only one time point; we are unable to observe the evolutionary trajectories that lead to optimized antibody affinity in each mouse. To address this, we model antibody evolution as a multitype branching process and integrate over unobserved histories conditioned on phylogenetic signal in sequence data, leveraging parallel experimental replays for parameter inference. We infer the functional relationship between B-cell fitness and antigen binding affinity in a Bayesian framework, equipped with an efficient likelihood calculation algorithm and Markov chain Monte Carlo posterior approximation. In a simulation study, we demonstrate that a sigmoidal relationship between fitness and binding affinity can be recovered from realizations of the branching process. We then perform inference for experimental data from 52 replayed B-cell lineages sampled 15 days after immunization, yielding a total of 3,758 sampled B cells. The recovered sigmoidal curve indicates that the fitness of high-affinity B cells is over six times larger than that of low-affinity B cells, with a sharp transition from low to high fitness values as affinity increases.

翻译：当免疫系统遭遇外来抗原（如病原体抗原）时，产生抗体的B细胞会经历增殖、突变和选择的循环过程，从而提升其与特定抗原的结合能力。免疫学家近期开发了强大的实验技术，可在小鼠模型中研究这一过程。在此类实验中，通过基因工程使小鼠携带单克隆B细胞前体，并用模型抗原进行免疫。在免疫反应进程结束后，从处死的小鼠中采集B细胞样本，并对编码抗体的突变基因位点进行测序。该实验实现了抗体演化的并行重演，但仅能获得单一时间点的数据；我们无法观测每只小鼠中导致抗体亲和力优化的演化轨迹。为解决此问题，我们将抗体演化建模为多类型分支过程，并基于序列数据中的系统发育信号对未观测历史进行积分，利用并行实验重演实现参数推断。我们在贝叶斯框架下推断B细胞适应度与抗原结合亲和力之间的函数关系，并采用高效似然计算算法和马尔可夫链蒙特卡洛后验近似方法。通过模拟研究，我们证明可以从分支过程的实现中恢复适应度与结合亲和力之间的S型关系。随后，我们对免疫后15天采集的52个重演B细胞谱系实验数据进行推断，共包含3,758个采样B细胞。恢复的S型曲线表明，高亲和力B细胞的适应度比低亲和力B细胞高出六倍以上，且随着亲和力增加，适应度值呈现从低到高的急剧转变。