The cellular basis of cell sorting kinetics

Cell sorting is a dynamical cooperative phenomenon that is fundamental for tissue morphogenesis and tissue homeostasis. According to Steinberg's differential adhesion hypothesis, the structure of sorted cell aggregates is determined by physical characteristics of the respective tissues, the tissue surface tensions. Steinberg postulated that tissue surface tensions result from quantitative differences in intercellular adhesion. Several experiments in cell cultures as well as in developing organisms support this hypothesis. The question of how tissue surface tension might result from differential adhesion was addressed in some theoretical models. These models describe the cellular interdependence structure once the temporal evolution has stabilized. In general, these models are capable of reproducing sorted patterns. However, the model dynamics at the cellular scale are defined implicitly and are not well-justified. The precise mechanism describing how differential adhesion generates the observed sorting kinetics at the tissue level is still unclear. It is necessary to formulate the concepts of cell level kinetics explicitly. Only then it is possible to understand the temporal development at the cellular and tissue scales. Here we argue that individual cell mobility is reduced the more the cells stick to their neighbors. We translate this assumption into a precise mathematical model which belongs to the class of stochastic interacting particle systems. Analyzing this model, we are able to predict the emergent sorting behavior at the population level. We describe qualitatively the geometry of cell segregation depending on the intercellular adhesion parameters. Furthermore, we derive a functional relationship between intercellular adhesion and surface tension and highlight the role of cell mobility in the process of sorting. We show that the interaction between the cells and the boundary of a confining vessel has a major impact on the sorting geometry.