Computational core and fixed-point organisation in Boolean networks

Details Computational core and fixed-point organisation in Boolean networks Computational core and fixed-point organisation in Boolean networks

2005-12-05

arxiv.org/abs/cond-mat/0512089v2

J. Stat. Mech. (2006) P03002

Physics

Condensed Matter

Statistical Mechanics

29 pages, 18 figures, version accepted for publication in JSTAT

Scientific paper

10.1088/1742-5468/2006/03/P03002

In this paper, we analyse large random Boolean networks in terms of a constraint satisfaction problem. We first develop an algorithmic scheme which allows to prune simple logical cascades and under-determined variables, returning thereby the computational core of the network. Second we apply the cavity method to analyse number and organisation of fixed points. We find in particular a phase transition between an easy and a complex regulatory phase, the latter one being characterised by the existence of an exponential number of macroscopically separated fixed-point clusters. The different techniques developed are reinterpreted as algorithms for the analysis of single Boolean networks, and they are applied to analysis and in silico experiments on the gene-regulatory networks of baker's yeast (saccaromices cerevisiae) and the segment-polarity genes of the fruit-fly drosophila melanogaster.

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