An information-theoretic measure for patterning in epithelial tissues

We present path entropy, an information-theoretic measure that captures the notion of patterning due to phase separation in organic tissues. Recent work has demonstrated, both in silico and in vitro, that phase separation in epithelia can arise simply from the forces at play between cells with differing mechanical properties. These qualitative results give rise to numerous questions about how the degree of patterning relates to model parameters or underlying biophysical properties. Answering these questions requires a consistent and meaningful way of quantifying degree of patterning that we observe. We define a resolution-independent measure that is better suited than image-processing techniques for comparing cellular structures. We show how this measure can be usefully applied in a selection of scenarios from biological experiment and computer simulation, and argue for the establishment of a tissue-graph library to assist with parameter estimation for synthetic morphology.