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

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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.