A case study on the parametric occurrence of multiple steady states

Russell Bradford, James H. Davenport, Matthew England, Hassan Errami, Vladimir Gerdt, Dima Grigoriev, Charles Hoyt, Marek Košta, Ovidiu Radulescu, Thomas Sturm, Andreas Weber

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Citations (Scopus)

Abstract

We consider the problem of determining multiple steady states for positive real values in models of biological networks. Investigating the potential for these in models of the mitogen-activated protein kinases (MAPK) network has consumed considerable effort using special insights into the structure of corresponding models. Here we apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition. We determine multistationarity of an 11-dimensional MAPK network when numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment, and furthermore positivity conditions on all variables and parameters.

Original languageEnglish
Title of host publicationISSAC 2017 - Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation
Subtitle of host publicationPart F129312
PublisherAssociation for Computing Machinery
Pages45-52
Number of pages8
ISBN (Electronic)9781450350648
DOIs
Publication statusPublished - 23 Jul 2017
Event42nd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2017 - Kaiserslautern, Germany
Duration: 25 Jul 201728 Jul 2017

Conference

Conference42nd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2017
CountryGermany
CityKaiserslautern
Period25/07/1728/07/17

Fingerprint

Protein Kinase
Biological Networks
Symbolic Computation
Numerics
Positivity
Model
Substitution
Equality
Decompose

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Bradford, R., Davenport, J. H., England, M., Errami, H., Gerdt, V., Grigoriev, D., ... Weber, A. (2017). A case study on the parametric occurrence of multiple steady states. In ISSAC 2017 - Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation: Part F129312 (pp. 45-52). Association for Computing Machinery. https://doi.org/10.1145/3087604.3087622

A case study on the parametric occurrence of multiple steady states. / Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas.

ISSAC 2017 - Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation: Part F129312. Association for Computing Machinery, 2017. p. 45-52.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Bradford, R, Davenport, JH, England, M, Errami, H, Gerdt, V, Grigoriev, D, Hoyt, C, Košta, M, Radulescu, O, Sturm, T & Weber, A 2017, A case study on the parametric occurrence of multiple steady states. in ISSAC 2017 - Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation: Part F129312. Association for Computing Machinery, pp. 45-52, 42nd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2017, Kaiserslautern, Germany, 25/07/17. https://doi.org/10.1145/3087604.3087622
Bradford R, Davenport JH, England M, Errami H, Gerdt V, Grigoriev D et al. A case study on the parametric occurrence of multiple steady states. In ISSAC 2017 - Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation: Part F129312. Association for Computing Machinery. 2017. p. 45-52 https://doi.org/10.1145/3087604.3087622
Bradford, Russell ; Davenport, James H. ; England, Matthew ; Errami, Hassan ; Gerdt, Vladimir ; Grigoriev, Dima ; Hoyt, Charles ; Košta, Marek ; Radulescu, Ovidiu ; Sturm, Thomas ; Weber, Andreas. / A case study on the parametric occurrence of multiple steady states. ISSAC 2017 - Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation: Part F129312. Association for Computing Machinery, 2017. pp. 45-52
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