Boolean modeling of collective effects in complex networks

TL;DR

This paper investigates how Boolean network models approximate complex systems, revealing limitations in chaotic regimes and proposing a modified theory to better predict system behavior, especially in biological gene regulation networks.

Contribution

It demonstrates the failure of standard Boolean models in chaotic regimes and introduces a modified Boolean theory that accounts for non-faithful information propagation in complex networks.

Findings

Large random networks often do not exhibit chaotic dynamics predicted by Boolean models.

Modified Boolean theory accurately explains behavior when information propagation is imperfect.

Application to gene regulation networks shows the theory's relevance to biological systems.

Abstract

Complex systems are often modeled as Boolean networks in attempts to capture their logical structure and reveal its dynamical consequences. Approximating the dynamics of continuous variables by discrete values and Boolean logic gates may, however, introduce dynamical possibilities that are not accessible to the original system. We show that large random networks of variables coupled through continuous transfer functions often fail to exhibit the complex dynamics of corresponding Boolean models in the disordered (chaotic) regime, even when each individual function appears to be a good candidate for Boolean idealization. A suitably modified Boolean theory explains the behavior of systems in which information does not propagate faithfully down certain chains of nodes. Model networks incorporating calculated or directly measured transfer functions reported in the literature on transcriptional regulation of genes are described by the modified theory.