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Approximating Attractors of Boolean Networks by Iterative CTL Model Checking.

Klarner H, Siebert H - Front Bioeng Biotechnol (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Fachbereich Mathematik und Informatik, Freie Universit├Ąt Berlin , Berlin , Germany.

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.

No MeSH data available.


Related in: MedlinePlus

The asynchronous STGs of three different Boolean networks. The minimal trap spaces are indicated by boxes. (A) Two attractors in the same box. (B) An attractor outside of the boxes. (C) An attractor that does not oscillate in all dimensions of the box. Equations for the networks are given in the Supplementary Material.
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Figure 1: The asynchronous STGs of three different Boolean networks. The minimal trap spaces are indicated by boxes. (A) Two attractors in the same box. (B) An attractor outside of the boxes. (C) An attractor that does not oscillate in all dimensions of the box. Equations for the networks are given in the Supplementary Material.

Mentions: In Klarner et al. (2014), we observed that is a good candidate for a perfect approximation. We showed that steady states are minimal trap spaces () and that every contains only cyclic attractors. Given that can be computed efficiently using ASP, we would like to have an efficient method for determining its quality as an approximation. Figure 1 demonstrates that is, in general, neither univocal, complete nor faithful.


Approximating Attractors of Boolean Networks by Iterative CTL Model Checking.

Klarner H, Siebert H - Front Bioeng Biotechnol (2015)

The asynchronous STGs of three different Boolean networks. The minimal trap spaces are indicated by boxes. (A) Two attractors in the same box. (B) An attractor outside of the boxes. (C) An attractor that does not oscillate in all dimensions of the box. Equations for the networks are given in the Supplementary Material.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4562258&req=5

Figure 1: The asynchronous STGs of three different Boolean networks. The minimal trap spaces are indicated by boxes. (A) Two attractors in the same box. (B) An attractor outside of the boxes. (C) An attractor that does not oscillate in all dimensions of the box. Equations for the networks are given in the Supplementary Material.
Mentions: In Klarner et al. (2014), we observed that is a good candidate for a perfect approximation. We showed that steady states are minimal trap spaces () and that every contains only cyclic attractors. Given that can be computed efficiently using ASP, we would like to have an efficient method for determining its quality as an approximation. Figure 1 demonstrates that is, in general, neither univocal, complete nor faithful.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Fachbereich Mathematik und Informatik, Freie Universit├Ąt Berlin , Berlin , Germany.

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.

No MeSH data available.


Related in: MedlinePlus