Complexity of regulatory logic and dynamics of Boolean models of biological networks [HBNI Th284]

Abstract

Gene regulatory networks (GRNs) orchestrate cellular behavior through complex combinatorial interactions among genes. Boolean models provide a tractable framework for studying GRN dynamics and have been widely used to analyze stability, multistability, and attractor-based representations of cellular phenotypes. While extensive research has established that biological GRNs are highly constrained in both network topology and regulatory logic, the specific effects of different classes of regulatory logic on global network dynamics have not been systematically characterized. The key objective of this thesis is to develop a systematic understanding of how different classes of Boolean functions (BFs) influence the dynamics of Boolean GRN models across varying network topologies and levels of abstraction, thereby informing principled choices of regulatory logic in Boolean modeling of biological systems. Using both random Boolean networks (RBNs) and reconstructed biological GRNs, we show that regulatory logic plays a central role in determining network stability and dynamical organization. First, we analyze ensembles of RBNs to disentangle the effects of regulatory logic from those of network topology. By systematically varying network size, connectivity, and degree distribution, and by employing multiple notions of dynamical stability, we show that biologically meaningful classes of BFs consistently steer network dynamics toward ordered or near-critical regimes. In contrast, networks governed by random BFs exhibit strong sensitivity to topological parameters and frequently transition toward chaotic behavior with increasing connectivity or size. Across diverse stability measures, biologically meaningful BFs display reduced variability and enhanced robustness. Second, we analyze the effect of BF classes on the stability of reconstructed Boolean GRNs using ensembles in which network structure and biological attractors are held fixed while regulatory logic is varied. Adopting a global state-space perspective, we systematically examine how different classes of BFs shape the structure of the state transition graph (STG). To characterize global dynamical organization, we adapt concepts originally developed in the study of cellular automata (CA) and introduce CA-inspired measures of bushiness and convergence. We find that biologically meaningful BFs lead to faster convergence and more contractive STG structures than random logic. Finally, we critically evaluate threshold majority rules (TMRs), a subclass of threshold functions frequently employed in GRN modeling due to their implementation simplicity. Through a comparative analysis with nested canalyzing functions (NCFs), we show that TMRs exhibit higher complexity and sensitivity, are underrepresented in empirical datasets of regulatory logic, and often fail to recover biological attractors and associated basin sizes. These results indicate that, despite their convenience, TMRs are poorly suited as a modeling choice for biological GRNs. Altogether, this thesis establishes regulatory logic as a key determinant of Boolean GRN dynamics and provides systematic guidance for selecting biologically grounded BFs in the modeling of GRNs.