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Dynamics in genetic networks. (English) Zbl 1327.92032

Summary: Living organisms contain thousands of genes. These genes contain the genetic code for protein molecules required for the functioning of the organism. During the development of the organism, genes are activated and deactivated at different times and in different places. Molecular biologists have developed remarkable techniques for determining the expression patterns of genes and the mechanisms regulating their expression. Mathematical modeling of these networks proves a formidable task. We show how logical circuits and piecewise linear equations are being used to meet this challenge. The mathematics not only can successfully model gene control in complex organisms but is also posing new questions for mathematical analysis.

MSC:

92D10 Genetics and epigenetics
92C42 Systems biology, networks
34A36 Discontinuous ordinary differential equations
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