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Andreas Deutsch
Center for Information Services & High Performance Computing
Technical University Dresden

Cellular Automaton Modeling of Biological Pattern Formation

Examples of biological pattern formation are life cycles ofbacteria and social amoebae, embryonic tissue formation, wound healing or tumourgrowth. Thereby, development of a particular spatio-temporal ''multi-cellular''pattern may be interpreted as cooperative phenomenon emerging from an intricate interplay of local (e.g. by adhesion) and non-local (e.g. via diffusing signals) cell interactions. What are cooperative phenomena in interacting cell systems and how can they be studied?

Mathematical models are required for the analysis of cooperative phenomena. Typical modeling attempts focus on a macroscopic perspective, i.e. the models (e.g. partial differential equations)

describe the spatio-temporal dynamics of cell concentrations. More recently, cell-based models have been suggested in which the fate of each individual cell can be tracked. Cellular automata are discrete dynamical systems and may be utilized as cell-based models.

Here, we analyze spatio-temporal pattern formation in cellular automaton models of interacting discrete cells. We introduce lattice-gas cellular automata and a cellular automaton based on an extended Potts model that allows to consider cell shapes. Model applications are bacterial pattern formation and tumour growth.


	Andreas Deutsch Center for Information Services & High Performance Computing Technical University Dresden Cellular Automaton Modeling of Biological Pattern Formation Examples of biological pattern formation are life cycles ofbacteria and social amoebae, embryonic tissue formation, wound healing or tumourgrowth. Thereby, development of a particular spatio-temporal ''multi-cellular''pattern may be interpreted as cooperative phenomenon emerging from an intricate interplay of local (e.g. by adhesion) and non-local (e.g. via diffusing signals) cell interactions. What are cooperative phenomena in interacting cell systems and how can they be studied? Mathematical models are required for the analysis of cooperative phenomena. Typical modeling attempts focus on a macroscopic perspective, i.e. the models (e.g. partial differential equations) describe the spatio-temporal dynamics of cell concentrations. More recently, cell-based models have been suggested in which the fate of each individual cell can be tracked. Cellular automata are discrete dynamical systems and may be utilized as cell-based models. Here, we analyze spatio-temporal pattern formation in cellular automaton models of interacting discrete cells. We introduce lattice-gas cellular automata and a cellular automaton based on an extended Potts model that allows to consider cell shapes. Model applications are bacterial pattern formation and tumour growth.

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