An Integer Programming Framework for Identifying Stable Components in Asynchronous Boolean Networks

Executable models of biological circuits offer the ability to simulate their behavior under different settings with important biomedical applications. In particular, Boolean network models have been a prime research focus and dozens of manually curated Boolean models are available in public databases. A key challenge in studying the dynamics of these models is determining their asymptotic behavior, that is the state-sets or attractors they converge to. This is particularly challenging for large networks, as the state space size grows exponentially. Here we introduce a novel method for identifying stable components within attractors under an asynchronous update scheme. Our method leverages the observation that the majority of cellular functions in current models can be described as linear threshold functions, facilitating an efficient integer programming formulation for the problem. We conduct simulations on both synthetic and real biological networks, demonstrating that our proposed method is highly efficient and outperforms previous methods.