A Case Study on the Parametric Occurrence of Multiple Steady States

Russell Bradford 1 James Davenport 1 Matthew England 2 Hassan Errami 3 Vladimir Gerdt 4 Dima Grigoriev 5 Charles Hoyt 6 Marek Košta 7 Ovidiu Radulescu 8 Thomas Sturm 9, 7 Andreas Weber 3
1 Department of Computer Science [Bath]
2 Coventry University (UK)
3 Institut für Informatik II [Bonn]
4 JINR - Joint Institute for Nuclear Research
5 LPP - Laboratoire Paul Painlevé - UMR 8524
6 B-IT - Bonn-Aachen International Center for Information Technology
7 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
LORIA - FM - Department of Formal Methods , Inria Nancy - Grand Est, MPII - Max-Planck-Institut für Informatik
8 DIMNP - Dynamique des interactions membranaires normales et pathologiques
9 MPII - Max-Planck-Institut für Informatik
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.
Keywords : • Applied computing → Biological networks • Computing CCS CONCEPTS algorithms methodologies → Equation and inequality solving
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Conference papers
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Submitted on : Wednesday, November 29, 2017 - 7:48:25 PM
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Russell Bradford, James Davenport, Matthew England, Hassan Errami, Vladimir Gerdt, et al.. A Case Study on the Parametric Occurrence of Multiple Steady States. ISSAC 2017 - International Symposium on Symbolic and Algebraic Computation, Jul 2017, Kaiserslautern, Germany. pp.45-52, ⟨10.1145/3087604.3087622⟩. ⟨hal-01648694⟩

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