Modelling T cell proliferation: Dynamics heterogeneity depending on cell differentiation, age, and genetic background

Cell proliferation is the common characteristic of all biological systems. The immune system insures the maintenance of body integrity on the basis of a continuous production of diversified T lymphocytes in the thymus. This involves processes of proliferation, differentiation, selection, death and migration of lymphocytes to peripheral tissues, where proliferation also occurs upon antigen recognition. Quantification of cell proliferation dynamics requires specific experimental methods and mathematical modelling. Here, we assess the impact of genetics and aging on the immune system by investigating the dynamics of proliferation of T lymphocytes across their differentiation through thymus and spleen in mice. Our investigation is based on single-cell multicolour flow cytometry analysis revealing the active incorporation of a thymidine analogue during S phase after pulse-chase-pulse experiments in vivo, versus cell DNA content. A generic mathematical model of state transition simulates through Ordinary Differential Equations (ODEs) the evolution of single cell behaviour during various durations of labelling. It allows us to fit our data, to deduce proliferation rates and estimate cell cycle durations in sub-populations. Our model is simple and flexible and is validated with other durations of pulse/chase experiments. Our results reveal that T cell proliferation is highly heterogeneous but with a specific “signature” that depends upon genetic origins, is specific to cell differentiation stages in thymus and spleen and is altered with age. In conclusion, our model allows us to infer proliferation rates and cell cycle phase durations from complex experimental 5-ethynyl-2'-deoxyuridine (EdU) data, revealing T cell proliferation heterogeneity and specific signatures.细胞增殖是所有生物系统共有的特征。免疫系统通过在胸腺中持续产生多样化的T淋巴细胞（T lymphocyte），维持机体完整性。这一过程涉及淋巴细胞的增殖、分化、筛选、凋亡以及向外周组织的迁移，而淋巴细胞在外周组织中遭遇抗原识别后同样会发生增殖。对细胞增殖动力学进行定量分析，需要借助特定实验方法与数学建模手段。 本研究通过探究小鼠体内T淋巴细胞经胸腺与脾脏完成分化全过程中的增殖动力学特征，评估遗传因素与衰老对免疫系统的影响。本研究采用单细胞多色流式细胞术分析，通过体内脉冲-追踪-脉冲实验，检测S期（S phase）阶段胸腺核苷类似物的主动掺入情况，并与细胞DNA含量进行对比。 我们构建了一个通用的状态转换数学模型，通过常微分方程（Ordinary Differential Equations，ODEs）模拟不同标记时长下单细胞行为的演化过程。该模型可用于拟合实验数据，推导各细胞亚群的增殖速率并估算其细胞周期时长。本模型简洁灵活，并通过不同时长的脉冲/追踪实验完成了验证。 研究结果表明，T细胞增殖具有高度异质性，但存在特定的"特征标识"：该标识受遗传背景调控，对应胸腺与脾脏内不同的细胞分化阶段，并随衰老进程发生改变。综上，本模型可从复杂的5-乙炔基-2'-脱氧尿苷（5-ethynyl-2'-deoxyuridine，EdU）实验数据中推导出增殖速率与各细胞周期时相的时长，进而揭示T细胞增殖的异质性与特异性特征。