Computational core and fixed-point organisation in Boolean networks

TL;DR

This paper introduces methods to analyze the computational core and fixed points of large Boolean networks, revealing phase transitions and applying these techniques to biological gene-regulatory networks.

Contribution

Develops an algorithmic scheme to identify the computational core and applies the cavity method to analyze fixed points and phase transitions in Boolean networks.

Findings

Identifies a phase transition between easy and complex regulatory regimes.

Finds exponential fixed-point clusters in the complex phase.

Applies methods to real biological gene networks.

Abstract

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.