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Formation and maintenance of complex tissues results from cellular and intracellular processes. Much is known about intracellular signaling and its connection to regulated gene expression for various cell types. Furthermore, the interaction between cells that are in direct physical contact or located within close distance of each other has also been subject of many elaborate studies. However, when cells react to their surrounding - neighboring cells as well as extracellular matrix and other environmental influences - with type-specific differences, what are the emergent properties for the whole tissue? It is a great challenge to understand which details at the molecular or cellular scale control the macroscopic behavior at the tissue scale. Predicting the dynamics of the whole cell population based on the knowledge of intercellular interactions is an important topic in cell biology. To adress this problem, the model class of interacting cell systems (ICSs) is introduced. In ICS models, cell-cell interactions are described explicitly and the finite size of cells as well as excluded volume effects are taken into account. ICS can be applied to study specific problems of spatio-temporal pattern formation during biological development. At the same time they are amenble to a variaty of analytical tools. With the help of an ICS model, we analyze the process of cell sorting, which is a dynamical cooperative phenomenon that is fundamental for the formation of tissues in biological development and the maintenance of tissue boundaries. According to Steinberg's Differential Adhesion Hypothesis, the structure of sorted cell aggregates is determined by the relations between physical characteristics of the respective tissues, the tissue surface tensions, which in turn are known to be the higher the more the cells of the particular type stick to each other. Various models have been suggested that phenomenologically reproduce experimental behaviors. But the precise mechanism how the dynamical behavior of individual cells generates the observed kinetics of de-mixing on the level of tissues is still unclear. Here we argue that individual cell motility is reduced the more the cells stick to their neighbors and 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 and to qualitatively describe the geometry of cell segregation depending on the intercellular adhesion parameters. In particular we are able to identify previously unnoted factors that determine which cell type sorts into the center of an aggregate. |
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