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 proceedingpeer-review

    23 Citations (Scopus)
    118 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
    Publisher Association 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
    Country/TerritoryGermany
    CityKaiserslautern
    Period25/07/1728/07/17
    Internet address

    Keywords

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

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