Inria, Centre Inria de Saclay, Université Paris-Saclay, 91120, Palaiseau, France.
PRC, INRAE, CNRS, Université de Tours, 37380, Nouzilly, France.
J Math Biol. 2024 Jun 6;89(1):9. doi: 10.1007/s00285-024-02108-6.
In this work, we introduce a compartmental model of ovarian follicle development all along lifespan, based on ordinary differential equations. The model predicts the changes in the follicle numbers in different maturation stages with aging. Ovarian follicles may either move forward to the next compartment (unidirectional migration) or degenerate and disappear (death). The migration from the first follicle compartment corresponds to the activation of quiescent follicles, which is responsible for the progressive exhaustion of the follicle reserve (ovarian aging) until cessation of reproductive activity. The model consists of a data-driven layer embedded into a more comprehensive, knowledge-driven layer encompassing the earliest events in follicle development. The data-driven layer is designed according to the most densely sampled experimental dataset available on follicle numbers in the mouse. Its salient feature is the nonlinear formulation of the activation rate, whose formulation includes a feedback term from growing follicles. The knowledge-based, coating layer accounts for cutting-edge studies on the initiation of follicle development around birth. Its salient feature is the co-existence of two follicle subpopulations of different embryonic origins. We then setup a complete estimation strategy, including the study of structural identifiability, the elaboration of a relevant optimization criterion combining different sources of data (the initial dataset on follicle numbers, together with data in conditions of perturbed activation, and data discriminating the subpopulations) with appropriate error models, and a model selection step. We finally illustrate the model potential for experimental design (suggestion of targeted new data acquisition) and in silico experiments.
在这项工作中，我们引入了一个基于常微分方程的卵巢滤泡发育的房室模型。该模型预测了不同成熟阶段的滤泡数量随年龄的变化。滤泡可能向前移动到下一个房室（单向迁移）或退化和消失（死亡）。从第一个滤泡房室的迁移对应于休眠滤泡的激活，这是导致滤泡储备逐渐耗尽（卵巢衰老）直至生殖活动停止的原因。该模型由一个嵌入在更全面的、基于知识的层中的数据驱动层组成，该层包含滤泡发育的最早事件。数据驱动层是根据现有的关于小鼠滤泡数量的最密集采样的实验数据集设计的。其显著特点是非线性的激活率公式，该公式包括来自生长滤泡的反馈项。基于知识的涂层层解释了出生前后滤泡发育启动的前沿研究。其显著特点是存在两个不同胚胎起源的滤泡亚群。然后，我们建立了一个完整的估计策略，包括结构可识别性的研究、将不同数据来源（滤泡数量的初始数据集，以及激活受到干扰的条件下的数据，以及区分亚群的数据）与适当的误差模型相结合的相关优化标准的制定，以及模型选择步骤。最后，我们说明了该模型在实验设计（建议有针对性地获取新数据）和计算机实验中的潜力。
