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 proceedingConference proceeding

17 Citations (Scopus)
54 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 languageEnglish
Title of host publicationProceedings of the 42nd International Symposium on Symbolic and Algebraic Computation
Subtitle of host publicationISSAC '17
PublisherAssociation for Computing Machinery
Pages45-52
Number of pages8
DOIs
Publication statusPublished - 25 Jul 2017
Event42nd International Symposium on Symbolic and Algebraic Computation - Kaiserslautern, Germany
Duration: 25 Jul 201728 Jul 2017
http://www.issac-symposium.org/2017/

Conference

Conference42nd International Symposium on Symbolic and Algebraic Computation
Abbreviated titleISSAC '17
CountryGermany
CityKaiserslautern
Period25/07/1728/07/17
Internet address

Keywords

  • Applied computing
  • Biological networks
  • Computing Methodologies
  • Equation and inequality solving algorithms

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  • 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 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