The effective graph reveals redundancy, canalization, and control pathways in biochemical regulation and signaling

Many biological networks are modeled with multivariate discrete dynamical systems. Current theory suggests that the network of interactions captures salient features of system dynamics, but it misses a key aspect of these networks: some interactions are more important than others due to dynamical redundancy and nonlinearity. This unequivalence leads to a canalized dynamics that differs from constraints inferred from network structure alone. To capture the redundancy present in biochemical regulatory and signaling interactions, we present the effective graph, an experimentally validated mathematical framework that synthesizes both structure and dynamics in a weighted graph representation of discrete multivariate systems. Our results demonstrate the ubiquity of redundancy in biology and provide a tool to increase causal explainability and control of biochemical systems.

CANA: A python package for quantifying control and canalization in Boolean Networks

Logical models offer a simple but powerful means to understand the complex dynamics of biochemical regulation, without the need to estimate kinetic parameters. However, even simple automata components can lead to collective dynamics that are …

Control of complex networks requires both structure and dynamics

The study of network structure has uncovered signatures of the organization of complex systems. Using Boolean network ensembles, we demonstrate that structure-only methods both undershoot and overshoot the number and which sets of critical variables best control the dynamics of these models, highlighting the importance of the actual system dynamics in determining control. Our analysis further shows that the logic of automata transition functions, namely how canalizing they are, plays an important role in the extent to which structure predicts dynamics.