A Case Study on the Parametric Occurrence of Multiple Steady States

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.
Document type :
Conference papers
Liste complète des métadonnées

Cited literature [27 references]  Display  Hide  Download

https://hal.inria.fr/hal-01648694
Contributor : Thomas Sturm <>
Submitted on : Wednesday, November 29, 2017 - 7:48:25 PM
Last modification on : Wednesday, April 3, 2019 - 1:22:57 AM

Links full text

Identifiers

Citation

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⟩

Share

Metrics

Record views

264