Mutual information in random Boolean models of regulatory networks

Abstract

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.

Identifying Critical States through the Relevance Index

“…This observation supports the idea that a similar distribution of organizations is present at many scales (represented here by different group sizes). Moreover, series involving larger RBNs identify more precisely the critical point (a fact already observed in the literature, as for example in [24]) and have narrower RI distributions. Similar observations can be made for other p-K diagram sections (data not shown).…”

On the Design of Boolean Network Robots

“…BNs can exhibit complex dynamics and some special ensembles have been deeply investigated, such as that of Random BNs. Recent advances in this research field, along with efficient mathematical and experimental methods and tools for analysing BN dynamics, can be mainly found in works addressing issues in GRNs or investigating properties of BN models [1,9,20,24]. These methods make it possible to analyse network dynamics and thus have insight into the behaviour of a BN system.…”

Maximum Power Efficiency and Criticality in Random Boolean Networks

“…Conclusion We have shown that critical RBNs maximize power efficiency; critical RBNs also maximize pairwise mutual information [23]. We conjecture a direct causal link between these three phenomena.…”