Influence and Dynamic Behavior in Random Boolean Networks

TL;DR

This paper develops a rigorous mathematical framework to analyze the dynamics of Boolean networks, proving critical transition results and highlighting the importance of transfer function influence and imbalance in network behavior.

Contribution

It provides the first formal proofs of critical transitions in Boolean networks and introduces new characterizations for random Boolean network classes.

Findings

Short-run dynamics are linked to transfer function influence.

Imbalance in transfer functions significantly affects network quiescence.

Traditional mean-field assumptions may not always hold.

Abstract

We present a rigorous mathematical framework for analyzing dynamics of a broad class of Boolean network models. We use this framework to provide the first formal proof of many of the standard critical transition results in Boolean network analysis, and offer analogous characterizations for novel classes of random Boolean networks. We precisely connect the short-run dynamic behavior of a Boolean network to the average influence of the transfer functions. We show that some of the assumptions traditionally made in the more common mean-field analysis of Boolean networks do not hold in general. For example, we offer some evidence that imbalance, or expected internal inhomogeneity, of transfer functions is a crucial feature that tends to drive quiescent behavior far more strongly than previously observed.