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

Alexander J. Gates, Rion Brattig Correia, Xuan Wang, and Luis M. Rocha

PNAS March 23, 2021 118 (12) e2022598118

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.

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