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Principles and mathematical modeling of biological pattern formation

Deutsch A., Dormann S.

Matematyka Stosowana : matematyka dla społeczeństwa

2002

Nr 3

16-38

An overview of principles and mathematical models of biological pattern formation is presented. One can distinguish preformation, optimization, topological and self-organization principles. Combinations of such principles are responsible for shape and tissue formation, differentia-tion, regeneration, morphogenetic motion, celi division and even malignant patterns, e.g. in tumor growth. Mathematical modeling allows for a system-atic analysis of the pattern-formation potential of morphogenetic principles. Biological patterns are the result of complex interactions between a smaller or larger number of components, particularly molecules and cells. Depend-ing on the modeling perspective microscopic (from the individual compo-nent level) and macroscopic models (from the population perspective) are distinguished. The specific question directs the choice of the appropriate perspective. A selection of microscopic and macroscopic model types is in-troduced.