Upper bound for the stability of Boolean networks.
Arxiv
|September 22, 2025
Summary
This study proves a conjecture on Boolean network stability, showing robustness and basin entropy are negatively linearly related. This advances understanding of complex biological system dynamics.
Area of Science:
- Computational Biology
- Systems Biology
- Network Science
Background:
- Boolean networks model complex biological system dynamics, with attractors representing phenotypes.
- Understanding the stability of basins of attraction is crucial for predicting system behavior.
- Previous work established conjectures regarding upper bounds for basin stability.
Purpose of the Study:
- To provide a formal proof for a conjecture on upper bounds of basin of attraction stability in Boolean networks.
- To extend stability analysis from single basins to the entire network.
- To investigate the relationship between network robustness and basin entropy.
Main Methods:
- Mathematical proof techniques applied to Boolean network models.
- Analysis of attractor stability and basin properties.
- Derivation of asymptotic upper bounds for network characteristics.
Main Results:
- A conjecture by Williadsen, Triesch, and Wiles regarding upper bounds for basin stability is proven.
- The relationship between robustness and basin entropy for the entire network is established.
- A negative linear relationship is demonstrated between the asymptotic upper bound for robustness and basin entropy.
Conclusions:
- The findings provide a theoretical framework for understanding Boolean network stability.
- The results offer insights into the robustness and complexity of biological systems modeled by Boolean networks.
- This work contributes to the theoretical foundations of gene regulatory network modeling.
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