ArticleFrontiers in bioengineering and biotechnology2015
Approximating Attractors of Boolean Networks by Iterative CTL Model Checking.
Article in Frontiers in bioengineering and biotechnology, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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9 citing papers in PubMed.
- Succession-diagram-based Markov chains reveal the attractor landscape of asynchronous Boolean networks.NPJ systems biology and applications · 2026Article
- Node and edge control strategy identification via trap spaces in Boolean networks.BMC bioinformatics · 2025Article
- An open problem: Why are motif-avoidant attractors so rare in asynchronous Boolean networks?Journal of mathematical biology · 2025Article
- Identification of periodic attractors in Boolean networks using a priori information.PLoS computational biology · 2022Article
- Attractor detection and enumeration algorithms for Boolean networks.Computational and structural biotechnology journal · 2022Review
- Qualitative Modeling, Analysis and Control of Synthetic Regulatory Circuits.Methods in molecular biology (Clifton, N.J.) · 2021Review
- High-fidelity discrete modeling of the HPA axis: a study of regulatory plasticity in biology.BMC systems biology · 2018Article
- Target Control in Logical Models Using the Domain of Influence of Nodes.Frontiers in physiology · 2018Article
- Griffin: A Tool for Symbolic Inference of Synchronous Boolean Molecular Networks.Frontiers in genetics · 2018Article
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2 authors.
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Abstract
This paper introduces the notion of approximating asynchronous attractors of Boolean networks by minimal trap spaces. We define three criteria for determining the quality of an approximation: "faithfulness" which requires that the oscillating variables of all attractors in a trap space correspond to their dimensions, "univocality" which requires that there is a unique attractor in each trap space, and "completeness" which requires that there are no attractors outside of a given set of trap spaces. Each is a reachability property for which we give equivalent model checking queries. Whereas faithfulness and univocality can be decided by model checking the corresponding subnetworks, the naive query for completeness must be evaluated on the full state space. Our main result is an alternative approach which is based on the iterative refinement of an initially poor approximation. The algorithm detects so-called autonomous sets in the interaction graph, variables that contain all their regulators, and considers their intersection and extension in order to perform model checking on the smallest possible state spaces. A benchmark, in which we apply the algorithm to 18 published Boolean networks, is given. In each case, the minimal trap spaces are faithful, univocal, and complete, which suggests that they are in general good approximations for the asymptotics of Boolean networks.
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