Upper bound for the stability of Boolean networks

TL;DR

This paper proves an upper bound on the stability of Boolean networks, linking robustness and basin entropy, which enhances understanding of biological system models and their stability limits.

Contribution

It provides a formal proof of a conjecture regarding stability bounds and extends the result to entire networks, connecting robustness and basin entropy.

Findings

Asymptotic upper bound for robustness and basin entropy are negatively linearly related.

Proof of a conjecture by Williadsen, Triesch, and Wiles.

Extended stability bounds from single basins to whole networks.

Abstract

Boolean networks, inspired by gene regulatory networks, were developed to understand the complex behaviors observed in biological systems, with network attractors corresponding to biological phenotypes or cell types. In this article, we present a proof for a conjecture by Williadsen, Triesch and Wiles about upper bounds for the stability of basins of attraction in Boolean networks. We further extend this result from a single basin of attraction to the entire network. Specifically, we demonstrate that the asymptotic upper bound for the robustness and the basin entropy of a Boolean network are negatively linearly related.