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Life at the “edge of chaos” in a genetic model

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Unifying Themes in Complex Systems VII

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Abstract

Genetic regulatory networks are often represented as Boolean networks and characterised by average parameters such as internal homogeneity (the probability that a node outputs a 1). Here we present a different formalism in which the nodes interact through positive and negative links with the state of the nodes determined by a single, general logical function. The main parameter of the system is in this case the proportion of negative links. At a critical value of the proportion of negative links the networks display a phase transition from a periodic to a chaotic regime The proportion of negative links in the bacterium Escherichia coli corresponds in our model to a range where the network behaves at the edge of chaos.

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Author information

Authors and Affiliations

  1. Centre for Interdisciplinary Science, Department of Physics and Astronomy, University of Leicester, Leicester, LEI 7RH, UK

    Y. Grondin & D. J. Raine

  2. Assemblages Moléculaires: Modélisation et Imagerie SIMS, FRE CNRS 2829, Faculté des Sciences et Techniques de Rouen, F76821, Mont Saint Aignan, France

    V. Norris

  3. Epigenomics Project, genopole®, 93 rue Henri-Rochefort, 91000, Evry, France

    V. Norris

Authors
  1. Y. Grondin
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  2. D. J. Raine
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  3. V. Norris
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, and Computer Science, University of Cincinnati, P.O. Box 210030, Rhodes Hall 814, Cincinnati, OH, 45221-0030, USA

    Ali A. Minai

  2. New England Complex Systems Institute, 238 Main Street Suite 319, Cambridge, MA, 02142, USA

    Dan Braha  & Yaneer Bar-Yam  & 

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© 2012 NECSI Cambridge, Massachusetts

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Grondin, Y., Raine, D.J., Norris, V. (2012). Life at the “edge of chaos” in a genetic model. In: Minai, A.A., Braha, D., Bar-Yam, Y. (eds) Unifying Themes in Complex Systems VII. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18003-3_12

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