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Broad edge of chaos in strongly heterogeneous Boolean networks

Deok-Sun Lee·Heiko Rieger
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Abstract

The dynamic stability of the Boolean networks representing a model for the gene transcriptional regulation (Kauffman model) is studied by calculating analytically and numerically the Hamming distance between two evolving configurations. This turns out to behave in a universal way close to the phase boundary only for in-degree distributions with a finite second moment. In-degree distributions of the form $P_d(k)\sim k^{-γ}$ with $2<γ<3$, thus having a diverging second moment, lead to a slower increase of the Hamming distance when moving towards the unstable phase and to a broadening of the phase boundary for finite $N$ with decreasing $γ$. We conclude that the heterogeneous regulatory network connectivity facilitates the balancing between robustness and evolvability in living organisms.

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Deok-Sun Lee, Heiko Rieger. 2008-09-19. Broad edge of chaos in strongly heterogeneous Boolean networks. https://doi.org/10.1088/1751-8113%2F41%2F41%2F415001

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