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 International Conference on Complex Systems (ICCS2007)

Escherichia coli at the edge of chaos

Derek Raine
University of Leicester

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     Last modified: September 30, 2007

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. Furthermore, in the periodic regime, the periods are distributed as power-laws. This approach facilitates comparison to real biological systems. For instance, 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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