Combining Zhegalkin Polynomials and SAT Solving for Context-Specific Boolean Modeling of Biological Systems

Abstract

Large amounts of knowledge regarding biological processes are readily available in the literature and aggregated in diverse databases. Boolean networks are powerful tools to render that knowledge into models that can mimic and simulate biological phenomena at multiple scales. Yet, when a model is required to understand or predict the behavior of a biological system in given conditions, existing information often does not completely match this context. Networks built from only prior knowledge can overlook mechanisms, lack specificity, and just partially recapitulate experimental observations. To address this limitation, context-specific data needs to be integrated. However, the brute-force identification of qualitative rules matching these data becomes infeasible as the number of candidates explodes for increasingly complex systems. Here, we used Zhegalkin polynomials to transform this identification into a binary value assignment for exponentially fewer variables, which we addressed with a state-of-the-art SAT solver. We evaluated our implemented method alongside two widely recognized tools, CellNetOptimizer and Caspo-ts, on both artificial toy models and large-scale models based on experimental data from the HPN-DREAM challenge. Our approach demonstrated benchmark-leading capabilities on networks of significant size and intricate complexity. It thus appears promising for the in silico modeling of ever more comprehensive biological systems.