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Abstract --- Mircea Andrecut, Institute for Biocomplexity and Informatics, University of Calgary, Alberta, CanadaMean Field Model of Genetic Regulatory Networks We discuss the dynamics of a mean field model of the genetic regulatory network. We show that depending on the set of regulatory parameters, the model exhibits complex behavior corresponding to regular and chaotic dynamics, including an order-chaos transition. A more detailed analysis shows that the complex solutions are actually confined in a finite interval corresponding to a relatively small number of interactions per gene. This interval consists in a region of relative stability between two maxima of complex behavior. Therefore, we may say that this region corresponds to a critical phase where the most complex coordinated behaviors can occur. The model also provides a possible explanation of how diversity, stability and robustness are created in a biological system, giving rise to a great variety of stable living organisms. |