Escherichia coli at the edge of chaos
Derek Raine
University of Leicester
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Last modified: September 30, 2007
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. Furthermore, in the periodic regime, the periods are distributed as powerlaws. 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.
