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

doi:10.1145/3087604.3087622

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 or section in a book/report/conference proceeding › Chapter in a published conference proceeding

23 Citations (SciVal)

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 language	English
Title of host publication	ISSAC 2017 - Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation
Subtitle of host publication	Part F129312
Publisher	Association for Computing Machinery
Pages	45-52
Number of pages	8
ISBN (Electronic)	9781450350648
DOIs	https://doi.org/10.1145/3087604.3087622
Publication status	Published - 23 Jul 2017
Event	42nd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2017 - Kaiserslautern, Germany Duration: 25 Jul 2017 → 28 Jul 2017

Conference

Conference	42nd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2017
Country/Territory	Germany
City	Kaiserslautern
Period	25/07/17 → 28/07/17

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1145/3087604.3087622

Cite this

Bradford, R., Davenport, J. H., 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 (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 et al.
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 or section in a book/report/conference proceeding › Chapter in a published conference proceeding

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

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A case study on the parametric occurrence of multiple steady states

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SC-square - Satisfiability Checking and Symbolic Computation: uniting two communities to solve real problems

A Strategic Alliance on Catalysis

Metaphors of Identity

James Davenport

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A case study on the parametric occurrence of multiple steady states

Abstract

Conference

ASJC Scopus subject areas

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SC-square - Satisfiability Checking and Symbolic Computation: uniting two communities to solve real problems

A Strategic Alliance on Catalysis

Metaphors of Identity

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James Davenport

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