BoolForge: Controlled Generation and Analysis of Boolean Functions and Networks

Abstract

Boolean networks are a widely used modeling framework in systems biology for studying gene regulation, signal transduction, and cellular decision-making. Empirical studies indicate that biological Boolean networks exhibit a high degree of canalization, a structural property of Boolean update rules that stabilizes dynamics and constrains state transitions. Despite its central role, existing software packages provide limited support for the systematic generation of Boolean functions and networks with prescribed canalization properties. We present BoolForge, a Python toolbox for the random generation and analysis of Boolean functions and networks, with a particular focus on canalization. BoolForge enables users to (i) generate random Boolean functions with specified canalizing depth, layer structure, and related constraints; (ii) construct Boolean networks with tunable topological and functional properties; and (iii) analyze structural and dynamical features including canalization measures, robustness, modularity, and attractor structure. By enabling controlled generation alongside analysis, BoolForge facilitates ensemble-based investigations of structure-dynamics relationships, benchmarking of theoretical predictions, and construction of biologically informed null models for Boolean network studies. Availability and Implementation: BoolForge is implemented in Python ($\geq$3.10) and can be installed via \texttt{pip install boolforge}. Source code and documentation are available at https://github.com/ckadelka/BoolForge. A PDF tutorial compendium is provided as Supplementary Material.

Figures (2)

• Figure 1: Overview of the BoolForge framework. User-defined constraints on network topology and Boolean update rules guide the controlled generation of Boolean functions and networks. Integrated analysis tools quantify structural and dynamical properties and enable ensemble experiments such as parameter exploration and biologically informed null-model testing (examples in Fig. \ref{['fig:examples']}).
• Figure 2: Representative ensemble analyses enabled by BoolForge. (A) Proportion of nested canalizing functions among 5,112 Boolean functions from 122 curated biological models compared with constraint-matched random expectations kadelka2024meta. (B) Coherence gap (difference between basin and attractor coherence) as a function of standardized bias across ensembles of 10,000 randomly generated nested canalizing networks with fixed layer structure and in-degree bavisetty2025attractors. (C) First-order approximation error in 122 biological networks compared with three types of matched null models generated using BoolForge (100 realizations per network and null model type) kadelka2024canalization.