2007/07/31 by André S. Ribeiro, Andre S. Ribeiro, Stuart Kauffman +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #Bioinformatics and Genomic Networks #Boolean function #Boolean model #Boolean network #Combinatorics #Complex network #Computer science #Data mining #Discontinuity (linguistics) #Discrete mathematics #Evolution and Genetic Dynamics #Function (biology) #Gene Regulatory Network Analysis #Mathematical analysis #Mathematics #Measure (data warehouse) #Mutual information #Pairwise comparison #Physics #Series (stratigraphy) #Statistical physics #Statistics #Theoretical computer science #Topology (electrical circuits) #q-bio.OT #q-bio.QM
paper · pdf · doi:10.1103/physreve.77.011901
11 pages, 6 figures; Minor revisions for clarity and figure format, one reference added
arxiv created 2007/11/15 · openalex publication_date 2008/01/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The amount of mutual information contained in the time series of two elements gives a measure of how well their activities are coordinated. In a large, complex network of interacting elements, such as a genetic regulatory network within a cell, the average of the mutual information over all pairs, <I>, is a global measure of how well the system can coordinate its internal dynamics. We study this average pairwise mutual information in random Boolean networks (RBNs) as a function of the distribution of Boolean rules implemented at each element, assuming that the links in the network are randomly placed. Efficient numerical methods for calculating <I> show that as the number of network nodes, N, approaches infinity, the quantity N<I> exhibits a discontinuity at parameter values corresponding to critical RBNs. For finite systems it peaks near the critical value, but slightly in the disordered regime for typical parameter variations. The source of high values of N<I> is the indirect correlations between pairs of elements from different long chains with a common starting point. The contribution from pairs that are directly linked approaches zero for critical networks and peaks deep in the disordered regime.