Simple threshold-based Boolean rules fall short in capturing biological regulatory network dynamics

Abstract

Among the various frameworks for modeling gene regulatory network (GRN) dynamics, Boolean modeling remains both powerful and accessible. Nevertheless, selecting update rules so that they capture the combinatorial control of various targets remains challenging due to limited quantitative data. Threshold majority rules (TMRs), a subtype of threshold functions (ThFs), update a genes state based on the signed sum of its regulators and its own activity, offering an elegant simplification. However, does the use of TMRs come at the cost of biological realism? Here, we rigorously evaluate the two standard TMR variants regarding their suitability in GRN modeling. We find that they provide limited canalyzation, exhibit discordant bias patterns, and often eliminate self-inhibitions. They are also underrepresented in empirical datasets, the opposite of what is expected for biologically relevant rules. Compared to nested canalyzing functions (NCFs), another class of ThFs but known to be preponderant in empirical datasets, TMRs exhibit heightened complexity and sensitivity to perturbations. At the network level, TMRs frequently fail to recover biological attractors and the associated basin size distributions. Using ensembles of random Boolean networks, we also show that one TMR type drives the network dynamics toward the chaotic regime. These findings invite a thoughtful reevaluation of TMRs as an appropriate logic for modeling GRNs despite their theoretical appeal.