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A Case Study on the Parametric Occurrence of Multiple Steady States

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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.

Dates and versions

hal-01648694 , version 1 (29-11-2017)

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Cite

Russell Bradford, James H. 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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