Characterizing short-term stability for Boolean networks over any distribution of transfer functions

TL;DR

This paper develops a universal formula to determine short-term stability or chaos in random Boolean networks with any distribution of transfer functions, extending previous work limited to special cases.

Contribution

It introduces a general formula for assessing short-term stability in Boolean networks with arbitrary transfer function distributions, including unbalanced families common in biological systems.

Findings

The formula accurately predicts chaos or stability in various network configurations.

Empirical validation confirms the formula's predictive power.

Previous methods failed for unbalanced transfer function families.

Abstract

We present a characterization of short-term stability of random Boolean networks under \emph{arbitrary} distributions of transfer functions. Given any distribution of transfer functions for a random Boolean network, we present a formula that decides whether short-term chaos (damage spreading) will happen. We provide a formal proof for this formula, and empirically show that its predictions are accurate. Previous work only works for special cases of balanced families. It has been observed that these characterizations fail for unbalanced families, yet such families are widespread in real biological networks.