Collective dynamics and pattern formation in systems of communicating cells: Theory and Simulations

How a system of genetically identical biological cells organizes into spatially heterogeneous tissues is a central question in biology. Even when the molecular and genetic underpinnings of cell-cell interactions are known, how these lead to multicellular patterns is often poorly understood. Of particular interest are dynamic patterns such as traveling waves, which confer spatiotemporal control over key developmental processes such as differentiation, segmentation and cell division. Theoretical approaches based on mathematical descriptions of underlying physical and chemical processes provide a promising avenue to explore biological pattern formation. In particular, theoretical models connect processes on the molecular scale to biological function on the tissue level and may provide mechanistic descriptions of how patterns are generated and maintained.