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 Kosta; 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 Kosta, Ovidiu Radulescu, Thomas Sturm, Andreas Weber

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding › peer-review

23 Citations (Scopus)

162 Downloads (Pure)

Abstract

The determination of multiple steady states for positive values is very important in the analysis of biological networks. The investigation of the potential of models of the mitogen-activated protein kinases (MAPK) network for such multistationarity has consumed considerable effort using special insights into the structure of corresponding models. We apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtual
substitution, lazy real triangularization and cylindrical algebraic decomposition. We demonstrate that the determination of multistationarity of an 11-dimensional MAPK network with can be achieved by currently available methods
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 and furthermore positivity conditions on all variables and parameters

Original language	English
Title of host publication	Proceedings of the 42nd International Symposium on Symbolic and Algebraic Computation
Subtitle of host publication	ISSAC '17
Publisher	Association for Computing Machinery
Pages	45-52
Number of pages	8
DOIs	https://doi.org/10.1145/3087604.3087622
Publication status	Published - 25 Jul 2017
Event	42nd International Symposium on Symbolic and Algebraic Computation - Kaiserslautern, Germany Duration: 25 Jul 2017 → 28 Jul 2017 http://www.issac-symposium.org/2017/

Conference

Conference	42nd International Symposium on Symbolic and Algebraic Computation
Abbreviated title	ISSAC '17
Country/Territory	Germany
City	Kaiserslautern
Period	25/07/17 → 28/07/17
Internet address	http://www.issac-symposium.org/2017/

Keywords

Applied computing
Biological networks
Computing Methodologies
Equation and inequality solving algorithms

Access to Document

10.1145/3087604.3087622

Post-PrintAccepted author manuscript, 0.99 MB

Dataset supporting the paper: "A Case Study on the Parametric Occurrence of Multiple Steady States"
Bradford, R. (Contributor), Hoyt, C. (Contributor), Radulescu, O. (Contributor), Weber, A. (Contributor), Sturm, T. (Contributor), Gerdt, V. (Contributor), Davenport, J. H. (Contributor), Grigoriev, D. (Contributor), Košta, M. (Contributor), Errami, H. (Contributor) & England, M. (Contributor), Zenodo, 25 May 2017
DOI: 10.5281/zenodo.583280, https://zenodo.org/record/583280
Dataset

Matthew England
- Research Centre for Computational Science and Mathematical Modelling - Centre Director
Person

Cite this

Bradford, R., Davenport, J. H., England, M., Errami, H., Gerdt, V., Grigoriev, D., Hoyt, C., Kosta, M., Radulescu, O., Sturm, T., & Weber, A. (2017). A Case Study on the Parametric Occurrence of Multiple Steady States. In Proceedings of the 42nd International Symposium on Symbolic and Algebraic Computation: ISSAC '17 (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.
Proceedings of the 42nd International Symposium on Symbolic and Algebraic Computation: ISSAC '17. Association for Computing Machinery, 2017. p. 45-52.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding › peer-review

Bradford, R, Davenport, JH, England, M, Errami, H, Gerdt, V, Grigoriev, D, Hoyt, C, Kosta, M, Radulescu, O, Sturm, T & Weber, A 2017, A Case Study on the Parametric Occurrence of Multiple Steady States. in Proceedings of the 42nd International Symposium on Symbolic and Algebraic Computation: ISSAC '17. Association for Computing Machinery, pp. 45-52, 42nd International Symposium on Symbolic and Algebraic Computation, Kaiserslautern, Germany, 25/07/17. https://doi.org/10.1145/3087604.3087622

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abstract = "The determination of multiple steady states for positive values is very important in the analysis of biological networks. The investigation of the potential of models of the mitogen-activated protein kinases (MAPK) network for such multistationarity has consumed considerable effort using special insights into the structure of corresponding models. We apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtualsubstitution, lazy real triangularization and cylindrical algebraic decomposition. We demonstrate that the determination of multistationarity of an 11-dimensional MAPK network with can be achieved by currently available methodswhen numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters and furthermore positivity conditions on all variables and parameters",

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AB - The determination of multiple steady states for positive values is very important in the analysis of biological networks. The investigation of the potential of models of the mitogen-activated protein kinases (MAPK) network for such multistationarity has consumed considerable effort using special insights into the structure of corresponding models. We apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtualsubstitution, lazy real triangularization and cylindrical algebraic decomposition. We demonstrate that the determination of multistationarity of an 11-dimensional MAPK network with can be achieved by currently available methodswhen numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters and furthermore positivity conditions on all variables and parameters

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A Case Study on the Parametric Occurrence of Multiple Steady States

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Dataset supporting the paper: "A Case Study on the Parametric Occurrence of Multiple Steady States"

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Matthew England

Cite this