Model and simulation for spatial cell fate pattering in mouse blastocysts based on an advection-diffusion mechanism for intercellular signalling

在哺乳动物着床前发育过程中，细胞间信号传导控制着多系诱导干细胞的分化。产生的细胞命运排列有序，为研究细胞命运规范的空间协调性提供了信息。我们关注细胞间信号的活动范围，并研究其与细胞分裂和细胞分选的相互作用。受成纤维细胞生长因子（FGF）信号通路调控小鼠胚胎原始内胚层和外胚层分化的激励，我们开发了一个具有可调信号范围的数学模型框架。我们的目的是表明平流扩散机制可以为实现不同的信号活动范围提供物理解释。我们将细胞分裂和细胞分选纳入模型，假设这三种机制是并行的。对相关函数的实现有助于将模拟结果与来自三个不同实验室的四个已发表的实验数据集的至少590个生物样品进行定量比较。这将告诉我们这三种机制是否确实是并行的，或者我们是否必须让它们重叠，甚至是连续地工作。因此，作为最终结果，我们将获得细胞信号传导、细胞分裂和细胞分选的特征和时间。我们的工作对现有小鼠囊胚发育模型的关键补充是引入基于信号分子物理学的信号范围；并通过与三维空间实验数据的全面比较，详细分析了信号传导、细胞分裂和细胞分选的相对贡献。我们的方法在本质上故意是通用的，以便于扩展到其他哺乳动物物种。

During mammalian preimplantation development, intercellular signalling controls the differentiation of multilineage primed stem cells. The arising cell fates are arranged in ordered patterns, which contain the information for studying the spatial coordination of cell fate specification. We focus on the activity range of the intercellular signalling and investigate its interplay with cell division and cell sorting. Motivated by the fibroblast growth factor (FGF) signalling pathway, which regulates primitive endoderm and epiblast differentiation in the mouse embryo, we develop a mathematical modelling framework with tuneable signalling range. We aim at showing that an advection-diffusion mechanism can provide a physical explanation for achieving different signal activity ranges. We include cell division and cell sorting in the model following the hypothesis that the three mechanisms act in parallel. Implementation of a pair correlation function facilitates a quantitative comparison of the simulation results with at least 590 biological samples from four published experimental data sets from three different laboratories. This will tell us whether the three mechanisms indeed act in parallel or whether we have to let the mechanisms overlap or even work consecutively. Hence, as a final outcome, we will obtain the characteristics and timing of cell signalling, cell division and cell sorting. The key additions of our work to existing models of mouse blastocyst development are introducing a signalling range based on the physics of the signalling molecule; and a detailed analysis of the relative contributions of signalling, cell division and cell sorting through a thorough comparison of the model with three-dimensional spatial experimental data. Our approach is deliberately general in nature to facilitate an extension to other mammalian species.