A semantics for Boolean networks consistent with regulatory threshold constraints.
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| Title: | A semantics for Boolean networks consistent with regulatory threshold constraints. |
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| Authors: | Dague, Philippe1 (AUTHOR) philippe.dague@universite-paris-saclay.fr |
| Source: | Journal of Theoretical Biology. May2026, Vol. 624, pN.PAG-N.PAG. 1p. |
| Subjects: | Boolean networks, Semantics methodology, Constraint satisfaction, Biological mathematical modeling, Computational complexity, Gene regulatory networks, Dynamical systems, Satisfiability (Computer science) |
| Abstract: | Modeling biological systems with Boolean networks (BNs) is a well-established approach that enables qualitative reasoning about their dynamics, including gene and signaling networks. Several semantics for BNs, i.e., scheduling of component updates, have been proposed that can significantly affect the predicted dynamic behaviors. The synchronous and asynchronous ones are the most popular, but they fail to capture some of the behaviors observed in reality and accounted for by quantitative models. Recently, the most permissive semantics has been introduced, guaranteed not to miss any behavior achievable by a quantitative model following the same logic as the BN, and, in addition, significantly reducing the computational complexity of dynamical analysis. But this time, it appears too permissive and tolerates spurious behaviors in many real situations. After clarifying the relationships among existing semantics, we define the threshold semantics whose dynamic behaviors are all those of a single-threshold network, a subclass of multivalued networks, for any possible threshold map. The spurious behaviors are excluded by the threshold semantics, whose qualitative behaviors constitute a proper abstraction of real biological processes, grounded in activation and inhibition influences regulated by single thresholds whose values are unknown, as is generally the case. We show that threshold semantics is stricter (for reachability between Boolean configurations) than the cuttable extended semantics (called here linear semantics) and stricter than a given constrained version of the most permissive semantics. We then seek to operationalize this threshold semantics. For this, we equip the constrained version of the most permissive semantics with a system of symbolic constraints, attached to any given trajectory and verifiable by a satisfiability solver. The satisfiability of this set of constraints ensures the consistency of the formal threshold conditions associated with the transitions along the trajectory. It defines a new operational semantics at the trajectory level. Then we prove that this semantics is equivalent to the threshold semantics. Finally, we prove that the computational complexity of this semantics is the same as that of classical semantics, i.e., PSPACE, and we state several conjectures for future work. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Theoretical Biology is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: A semantics for Boolean networks consistent with regulatory threshold constraints. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Dague%2C+Philippe%22">Dague, Philippe</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> philippe.dague@universite-paris-saclay.fr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Theoretical+Biology%22">Journal of Theoretical Biology</searchLink>. May2026, Vol. 624, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Boolean+networks%22">Boolean networks</searchLink><br /><searchLink fieldCode="DE" term="%22Semantics+methodology%22">Semantics methodology</searchLink><br /><searchLink fieldCode="DE" term="%22Constraint+satisfaction%22">Constraint satisfaction</searchLink><br /><searchLink fieldCode="DE" term="%22Biological+mathematical+modeling%22">Biological mathematical modeling</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+complexity%22">Computational complexity</searchLink><br /><searchLink fieldCode="DE" term="%22Gene+regulatory+networks%22">Gene regulatory networks</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Satisfiability+%28Computer+science%29%22">Satisfiability (Computer science)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Modeling biological systems with Boolean networks (BNs) is a well-established approach that enables qualitative reasoning about their dynamics, including gene and signaling networks. Several semantics for BNs, i.e., scheduling of component updates, have been proposed that can significantly affect the predicted dynamic behaviors. The synchronous and asynchronous ones are the most popular, but they fail to capture some of the behaviors observed in reality and accounted for by quantitative models. Recently, the most permissive semantics has been introduced, guaranteed not to miss any behavior achievable by a quantitative model following the same logic as the BN, and, in addition, significantly reducing the computational complexity of dynamical analysis. But this time, it appears too permissive and tolerates spurious behaviors in many real situations. After clarifying the relationships among existing semantics, we define the threshold semantics whose dynamic behaviors are all those of a single-threshold network, a subclass of multivalued networks, for any possible threshold map. The spurious behaviors are excluded by the threshold semantics, whose qualitative behaviors constitute a proper abstraction of real biological processes, grounded in activation and inhibition influences regulated by single thresholds whose values are unknown, as is generally the case. We show that threshold semantics is stricter (for reachability between Boolean configurations) than the cuttable extended semantics (called here linear semantics) and stricter than a given constrained version of the most permissive semantics. We then seek to operationalize this threshold semantics. For this, we equip the constrained version of the most permissive semantics with a system of symbolic constraints, attached to any given trajectory and verifiable by a satisfiability solver. The satisfiability of this set of constraints ensures the consistency of the formal threshold conditions associated with the transitions along the trajectory. It defines a new operational semantics at the trajectory level. Then we prove that this semantics is equivalent to the threshold semantics. Finally, we prove that the computational complexity of this semantics is the same as that of classical semantics, i.e., PSPACE, and we state several conjectures for future work. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Theoretical Biology is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jtbi.2026.112377 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Boolean networks Type: general – SubjectFull: Semantics methodology Type: general – SubjectFull: Constraint satisfaction Type: general – SubjectFull: Biological mathematical modeling Type: general – SubjectFull: Computational complexity Type: general – SubjectFull: Gene regulatory networks Type: general – SubjectFull: Dynamical systems Type: general – SubjectFull: Satisfiability (Computer science) Type: general Titles: – TitleFull: A semantics for Boolean networks consistent with regulatory threshold constraints. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Dague, Philippe IsPartOfRelationships: – BibEntity: Dates: – D: 22 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00225193 Numbering: – Type: volume Value: 624 Titles: – TitleFull: Journal of Theoretical Biology Type: main |
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