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A Case Study on the Parametric Occurrence of Multiple Steady States

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Sturm,  Thomas
Automation of Logic, MPI for Informatics, Max Planck Society;

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arXiv:1704.08997.pdf
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Citation

Bradford, R., Davenport, J. H., England, M., Errami, H., Gerdt, V., Grigoriev, D., et al. (2017). A Case Study on the Parametric Occurrence of Multiple Steady States. Retrieved from http://arxiv.org/abs/1704.08997.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-91D0-E
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.