Abstract
The determination of multiple steady states for positive values is very important in the analysis of biological networks. The investigation of the potential of models of the mitogen-activated protein kinases (MAPK) network for such multistationarity has consumed considerable effort using special insights into the structure of corresponding models. We apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtual
substitution, lazy real triangularization and cylindrical algebraic decomposition. We demonstrate that the determination of multistationarity of an 11-dimensional MAPK network with can be achieved by currently available methods
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 and furthermore positivity conditions on all variables and parameters
substitution, lazy real triangularization and cylindrical algebraic decomposition. We demonstrate that the determination of multistationarity of an 11-dimensional MAPK network with can be achieved by currently available methods
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 and furthermore positivity conditions on all variables and parameters
Original language | English |
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Title of host publication | Proceedings of the 42nd International Symposium on Symbolic and Algebraic Computation |
Subtitle of host publication | ISSAC '17 |
Publisher | Association for Computing Machinery |
Pages | 45-52 |
Number of pages | 8 |
DOIs | |
Publication status | Published - 25 Jul 2017 |
Event | 42nd International Symposium on Symbolic and Algebraic Computation - Kaiserslautern, Germany Duration: 25 Jul 2017 → 28 Jul 2017 http://www.issac-symposium.org/2017/ |
Conference
Conference | 42nd International Symposium on Symbolic and Algebraic Computation |
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Abbreviated title | ISSAC '17 |
Country/Territory | Germany |
City | Kaiserslautern |
Period | 25/07/17 → 28/07/17 |
Internet address |
Keywords
- Applied computing
- Biological networks
- Computing Methodologies
- Equation and inequality solving algorithms
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Dataset supporting the paper: "A Case Study on the Parametric Occurrence of Multiple Steady States"
Bradford, R. (Contributor), Hoyt, C. (Contributor), Radulescu, O. (Contributor), Weber, A. (Contributor), Sturm, T. (Contributor), Gerdt, V. (Contributor), Davenport, J. H. (Contributor), Grigoriev, D. (Contributor), Košta, M. (Contributor), Errami, H. (Contributor) & England, M. (Contributor), Zenodo, 25 May 2017
DOI: 10.5281/zenodo.583280, https://zenodo.org/record/583280
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Matthew England
- Research Centre for Computational Science and Mathematical Modelling - Associate Professor Academic, Centre Director
Person: Teaching and Research, Professional Services