In preimplantation mammalian embryos, the second cell fate decision introduces spatial patterns of embryonic and extra-embryonic precursor cells. The transcription factors NANOG and GATA6 are the earliest markers for the two cell types and interact between cells via the fibroblast growth factor signaling pathway. Computational models have been used to mimic the patterns and cell type proportions found in experimental studies. However, these models are always phenomenological in nature and lack a proper physical explanation. We derive a cell fate decision model motivated by the ideas of statistical mechanics. The model incorporates intra-and intercellular interactions of NANOG and GATA6. A detailed mathematical analysis on the resulting dynamical system is presented. We find that our model is capable of generating tissue wide spatial patterns of the two cell types. Its advantages are revealed in the simple physical and biological interpretation of the parameters and their interactions. In numerical simulations, we showcase the ability to replicate checkerboard patterns of different cell type proportions varying only a single parameter. The tight control of the system as well as the ease of use and the direct expandability to other signaling types provide solid reasons for the continued use of our model. We are convinced that our approach presents an exciting perspective in relation to cell fate decisions. Moreover, the concepts are generalizable to questions regarding cell signaling beyond the mammalian embryo.

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During development, cell fates are determined through a combination of intracellular transcriptional regulations and extracellular signaling. As a result, spatial patterns of different cell types arise. We investigate the decision between epiblast and primitive endoderm cells in the inner cell mass of the preimplantation mouse embryo. Our computational model uses global cell signaling for the pattern formation. By varying the signal dispersion, cell type arrangements ranging from a checkerboard to an engulfing pattern can be generated. Pair correlation functions provide a well-suited way of characterizing the model output. With these, we established a quantitative comparison between the simulation results and experimental data of inner cell mass organoids. We obtained an astonishing agreement. Thus, our model proves its capability to replicate the cell differentiation patterns, making global signaling a strong contender to explain pattern formation in the preimplantation embryo.