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  Identifying the Parametric Occurrence of Multiple Steady States for some Biological Networks

Bradford, R., Davenport, J. H., England, M., Errami, H., Gerdt, V., Grigoriev, D., et al. (2019). Identifying the Parametric Occurrence of Multiple Steady States for some Biological Networks. Retrieved from http://arxiv.org/abs/1902.04882.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0002-FF3C-D Version Permalink: http://hdl.handle.net/21.11116/0000-0002-FF3D-C
Genre: Paper

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arXiv:1902.04882.pdf (Preprint), 3MB
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File downloaded from arXiv at 2019-02-14 12:13 author preprint. Accepted in the Journal of Symbolic Computation
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 Creators:
Bradford, Russell1, Author
Davenport, James H.1, Author
England, Matthew1, Author
Errami, Hassan1, Author
Gerdt, Vladimir1, Author
Grigoriev, Dima1, Author
Hoyt, Charles1, Author
Košta, Marek1, Author              
Radulescu, Ovidiu1, Author
Sturm, Thomas2, Author              
Weber, Andreas1, Author
Affiliations:
1External Organizations, ou_persistent22              
2Automation of Logic, MPI for Informatics, Max Planck Society, ou_1116545              

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Free keywords: Computer Science, Symbolic Computation, cs.SC
 Abstract: We consider a problem from biological network analysis of determining regions in a parameter space over which there are multiple steady states for positive real values of variables and parameters. We describe multiple approaches to address the problem using tools from Symbolic Computation. We describe how progress was made to achieve semi-algebraic descriptions of the multistationarity regions of parameter space, and compare symbolic results to numerical methods. The biological networks studied are models of the mitogen-activated protein kinases (MAPK) network which has already consumed considerable effort using special insights into its structure of corresponding models. Our main example is a model with 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment. The model also imposes positivity conditions on all variables and parameters. We apply combinations of symbolic computation methods designed for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition, as well as a simplification technique adapted from Gaussian elimination and graph theory. We are able to determine multistationarity of our main example over a 2-dimensional parameter space. We also study a second MAPK model and a symbolic grid sampling technique which can locate such regions in 3-dimensional parameter space.

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Language(s): eng - English
 Dates: 2019-02-132019
 Publication Status: Published online
 Pages: 60 p.
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1902.04882
URI: http://arxiv.org/abs/1902.04882
BibTex Citekey: Bradford_arXiv1902.04882
 Degree: -

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