Is Cell segregation just like oil and water: A phase field approach

Understanding the segregation of cells is crucial to answer questions about tissue formation in embryos or tumour progression. According to Steinberg's differential adhesion hypothesis [1] the separation of cells can be compared to the separation of two liquids, e.g. water and oil. Specifically, it was proposed, that similarly to the demixing of fluids, differences in the strengths of the adhesive forces in homo- and heterotypic cell contact lead to all sorting. This hypothesis has been tested on the basis of cell-based models which simulate motile cells with differential adhesive interaction on the basis of probability cellular automaton models [2]. On the other hand, the segregation of fluids like water and Oil can be well described by phase-field models as the Cahn-Hilliard-equation. Here we ask, weather the two approaches can be related to each other and how under such a relation depends on the details of the cell-based model. We develop and test various order parameters which allow assuming the degree of segregation during time in both, cell-based probability cellular automaton models for cell sorting and phase-field models for the demixing of fluids. We identify typical benchmark scenarios where the agreement between both model classes shall be maximized and calibrate the phase-field model such that it best fit to in-silico data produced by specific cell-based models of sorting. We evaluate the good-ness of fit in these scenarios and relate out findings to the original differential adhesion hypothesis.