Escherichia coli at the “edge of chaos”?

Y. Grondin, D.J. Raine, University of Leicester, UK

Genetic regulatory networks are often represented as Boolean networks characterised by average parameters such as internal homogeneity. Here we present a modified formalism in which the nodes interact through positive and negative links, with the state of the nodes determined by a single, general logical function. In this model, the parameter that specifies the proportion of negative links is similar to the Boolean internal homogeneity parameter in that it determines the global behaviour of the network. However, they differ in one major aspect. Both parameters are not equal: the divergence between them depending on the degree of connectivity. This has an important consequence: we show that the proportion of negative links in Escherichia coli corresponds in our model to a regime in which the network operates at the edge of chaos. Furthermore, we show the diversity of attractors of the system as the distribution of cycle lengths follows a power-law.