ArticleProceedings of the National Academy of Sciences of the United States of America2021
The effective graph reveals redundancy, canalization, and control pathways in biochemical regulation and signaling.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 40 papers, 1 of them a synthesis that pooled it.
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Who cites it
40 citing papers in PubMed, 1 synthesis or guideline pooled it, 79 citations in OpenAlex.
- A meta-analysis of Boolean network models reveals design principles of gene regulatory networks.Science advances · 2024Pooled it
- BoolForge: controlled generation and analysis of Boolean functions and networks.Bioinformatics (Oxford, England) · 2026Article
- Dynamics of attractor transitions in Boolean networks under noise.Chaos (Woodbury, N.Y.) · 2026Article
- Canalization as a stabilizing principle of gene regulatory networks: a discrete dynamical systems perspective.NPJ systems biology and applications · 2026Review
- Neurosenescence, inflammaging and neuroinflammation in neurodegenerative disorders.Frontiers in aging · 2026Review
- BioLogical: a universal analysis framework for biosystem logical dynamics.Computational and structural biotechnology journal · 2026Article
- Attractors are less stable than their basins: Canalization creates a coherence gap in gene regulatory networks.bioRxiv : the preprint server for biology · 2025Article
- CANA v1.0.0: efficient quantification of canalization in automata networks.Bioinformatics (Oxford, England) · 2025Article
- Quantifying edge relevance for epidemic spreading via the semi-metric topology of complex networks.Journal of physics. Complexity · 2025Article
- Critical assessment of the ability of Boolean threshold models to describe gene regulatory network dynamics.PNAS nexus · 2025Article
- Article
- An open problem: Why are motif-avoidant attractors so rare in asynchronous Boolean networks?Journal of mathematical biology · 2025Article
- Mapping the attractor landscape of Boolean networks with biobalm.Bioinformatics (Oxford, England) · 2025Article
- Challenges and opportunities for digital twins in precision medicine from a complex systems perspective.NPJ digital medicine · 2025Review
- Operating principles of interconnected feedback loops driving cell fate transitions.NPJ systems biology and applications · 2025Article
- Control of Cellular Differentiation Trajectories for Cancer Reversion.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2025Article
- The conserved genetic program of male germ cells uncovers ancient regulators of human spermatogenesis.eLife · 2024Article
- Canalization reduces the nonlinearity of regulation in biological networks.NPJ systems biology and applications · 2024Article
- Biologically meaningful regulatory logic enhances the convergence rate in Boolean networks and bushiness of their state transition graph.Briefings in bioinformatics · 2024Article
- Preponderance of generalized chain functions in reconstructed Boolean models of biological networks.Scientific reports · 2024Article
Corrections and comments
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Authors and funding
4 authors at 4 institutions in 3 countries.
Funding
Abstract
The ability to map causal interactions underlying genetic control and cellular signaling has led to increasingly accurate models of the complex biochemical networks that regulate cellular function. These network models provide deep insights into the organization, dynamics, and function of biochemical systems: for example, by revealing genetic control pathways involved in disease. However, the traditional representation of biochemical networks as binary interaction graphs fails to accurately represent an important dynamical feature of these multivariate systems: some pathways propagate control signals much more effectively than do others. Such heterogeneity of interactions reflects canalization-the system is robust to dynamical interventions in redundant pathways but responsive to interventions in effective pathways. Here, we introduce the effective graph, a weighted graph that captures the nonlinear logical redundancy present in biochemical network regulation, signaling, and control. Using 78 experimentally validated models derived from systems biology, we demonstrate that 1) redundant pathways are prevalent in biological models of biochemical regulation, 2) the effective graph provides a probabilistic but precise characterization of multivariate dynamics in a causal graph form, and 3) the effective graph provides an accurate explanation of how dynamical perturbation and control signals, such as those induced by cancer drug therapies, propagate in biochemical pathways. Overall, our results indicate that the effective graph provides an enriched description of the structure and dynamics of networked multivariate causal interactions. We demonstrate that it improves explainability, prediction, and control of complex dynamical systems in general and biochemical regulation in particular.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.