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SYBN: Biological and Social Networks

SYBN 3: Biologische und Soziale Netzwerke, Postersitzung

SYBN 3.6: Poster

Monday, March 7, 2005, 14:00–15:30, Poster TU E

Robust Pattern Formation by Coupled Regulatory Networks — •Thimo Rohlf¹ and Stefan Bornholdt² — ¹Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig, Germany — ²Institut für Theoretische Physik, Universität Bremen, Otto-Hahn-Allee, D-28334 Bremen, Germany

Based on a very general non-equilibrium mechanism for spatial pattern formation [1] we study how morphogenesis can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing multicellular organism [2]. As an example we study the developmental problem of spatial domain formation and proportion regulation in the presence of noise and cell flow. We find that networks that solve this task exhibit a hierarchical structure of information processing and are of similar complexity as developmental circuits of living cells. A further focus of this study is a detailed analysis of noise-induced dynamics, which is a major ingredient of the control dynamics in the developmental network model. A master equation for domain boundary readjustments is formulated and solved for the continuum limit. Evidence for a discontinuity (similar to a first order phase transition) in equilibrium domain size at vanishing noise is given by finite size scaling. A second order phase transition at increased cell flow is studied in a mean field approximation. Finally, we discuss potential applications.

[1] Rohlf, T. and Bornholdt, S. (2003). cond-mat/0312366, submitted.

[2] Rohlf, T. and Bornholdt, S. (2004). qbio.MN/0401024, submitted.