Biological organisms are complex systems characterized by collective behaviour emerging out of the interaction of a large number of components (molecules and cells). In complex systems, even if the basic and local interactions are perfectly known, it is possible that the global (collective) behaviour can not be obviously extrapolated from the individual properties. Collective dynamics of migrating and interacting cell populations drive key processes in tissue formation and maintenance under normal and diseased conditions. For revealing the principles of tissue organization, it is fundamental to analyze the tissue-scale consequences of intercellular interaction. Only an understanding of the dynamics of collective effects at the molecular and cellular scale allows answering biological key questions such as: what enables ensembles of molecules to organize themselves into cells? How do ensembles of cells create tissues and whole organisms? What is different in diseased tissues as malignant tumors? Mathematical models for spatio-temporal pattern formation can contribute to answer these questions. The first models of spatio-temporal pattern formation focused on the dynamics of diffusible morphogen signals and have been formulated as partial differential equations (e.g.). In addition to diffusible molecular signals, the role of cells in morphogenesis can not be neglected. Living cells possess migration strategies that go beyond the merely random displacements of non-living molecules (diffusion). More and more evidence exists about how the self-organization of interacting and migrating cells contributes to the formation of order in a developing organism. Thereby, both the particular type of cell interaction and migration are crucial and suitable combinations allow for a wide range of patterns. The question is: What are appropriate mathematical models for analyzing organization principles of moving and interacting cells cells?
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