Abstract
Exactly a century ago, D’Arcy Thompson set an agenda for understanding tissue development in terms of underlying biophysical, mathematically-tractable mechanisms. One such mechanism, discovered by Steinberg in the 1960s, is adhesion-mediated sorting of cell mixtures into homotypic groups. Interest in this phase separation mechanism has recently surged, partly because of its use to create synthetic biological patterning mechanisms and partly because it has been found to drive events critical to the formation of organoids from stem cells, making the process relevant to biotechnology as well as to basic development. Here, we construct quantitative model of patterning by phase separation, informed by laboratory data, and use it to explore the relationship between degree of adhesive difference and speed, type and extent of resultant patterning. Our results can be used three ways; to predict the outcome of mix-ing cells with known properties, to estimate the properties required to make some designed organoid system, or to estimate underlying cellular properties from observed behaviour.
