Is Cell segregation just like oil and water

Understanding the segregation of cells is crucial to answer questions about tissue formation in embryos or tumor progression. Steinberg proposed that separation of cells can be compared to the separation of two liquids. Such a separation is well described by the Cahn-Hilliard (CH) equations and the segregation indices exhibit an algebraic decay with exponent 1/3 with respect to time. However, experimental cell segregation data also reveals other scaling exponents and even slow logarithmic scaling laws. These discrepancies are commonly attributed to the effects of collective motion or velocity-dependent interactions. By using a cellular automaton (CA) model which implements a dynamic variant of the differential adhesion hypothesis, we demonstrate that it is possible to reproduce biological cell segregation experiments from Mehes et al. with just adhesive forces. The segregation in the CA model follows a logarithmic scaling, which is in contrast to the proposed algebraic scaling with exponent 1/3. However, within the less than two orders of magnitudes in time which are observable in the experiments, a logarithmic scaling may appear as a pseudo-algebraic scaling. In particular, we demonstrate that the CA model can exhibit a range of exponents $\leq$ 1/3 for such a pseudo-algebraic scaling. Additionally, we reproduce the experimental data with segregation of the CH model, although the CH model matches in an intermittent regime, where it exhibits an algebraic scaling with an exponent 1/4, which is smaller than the asymptotic exponent of 1/3. This corroborates the ambiguity of the scaling behavior, when segregation processes are only observed on short time spans.