  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.
