Identifying parameter regions for multistationarity.
Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative features, such as switching behaviour, bistability or oscillation...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Public Library of Science (PLoS)
2017-10-01
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| Series: | PLoS Computational Biology |
| Online Access: | https://doi.org/10.1371/journal.pcbi.1005751 |
| _version_ | 1818578147993452544 |
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| author | Carsten Conradi Elisenda Feliu Maya Mincheva Carsten Wiuf |
| author_facet | Carsten Conradi Elisenda Feliu Maya Mincheva Carsten Wiuf |
| author_sort | Carsten Conradi |
| collection | DOAJ |
| description | Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative features, such as switching behaviour, bistability or oscillations. Mathematically, the latter question amounts to identifying parameter values associated with a given qualitative feature. We introduce a procedure to partition the parameter space of a parameterized system of ordinary differential equations into regions for which the system has a unique or multiple equilibria. The procedure is based on the computation of the Brouwer degree, and it creates a multivariate polynomial with parameter depending coefficients. The signs of the coefficients determine parameter regions with and without multistationarity. A particular strength of the procedure is the avoidance of numerical analysis and parameter sampling. The procedure consists of a number of steps. Each of these steps might be addressed algorithmically using various computer programs and available software, or manually. We demonstrate our procedure on several models of gene transcription and cell signalling, and show that in many cases we obtain a complete partitioning of the parameter space with respect to multistationarity. |
| first_indexed | 2024-12-16T06:41:12Z |
| format | Article |
| id | doaj.art-56b6b94e1ae0473bb8f41c171c5479ee |
| institution | Directory Open Access Journal |
| issn | 1553-734X 1553-7358 |
| language | English |
| last_indexed | 2024-12-16T06:41:12Z |
| publishDate | 2017-10-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS Computational Biology |
| spelling | doaj.art-56b6b94e1ae0473bb8f41c171c5479ee2022-12-21T22:40:40ZengPublic Library of Science (PLoS)PLoS Computational Biology1553-734X1553-73582017-10-011310e100575110.1371/journal.pcbi.1005751Identifying parameter regions for multistationarity.Carsten ConradiElisenda FeliuMaya MinchevaCarsten WiufMathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative features, such as switching behaviour, bistability or oscillations. Mathematically, the latter question amounts to identifying parameter values associated with a given qualitative feature. We introduce a procedure to partition the parameter space of a parameterized system of ordinary differential equations into regions for which the system has a unique or multiple equilibria. The procedure is based on the computation of the Brouwer degree, and it creates a multivariate polynomial with parameter depending coefficients. The signs of the coefficients determine parameter regions with and without multistationarity. A particular strength of the procedure is the avoidance of numerical analysis and parameter sampling. The procedure consists of a number of steps. Each of these steps might be addressed algorithmically using various computer programs and available software, or manually. We demonstrate our procedure on several models of gene transcription and cell signalling, and show that in many cases we obtain a complete partitioning of the parameter space with respect to multistationarity.https://doi.org/10.1371/journal.pcbi.1005751 |
| spellingShingle | Carsten Conradi Elisenda Feliu Maya Mincheva Carsten Wiuf Identifying parameter regions for multistationarity. PLoS Computational Biology |
| title | Identifying parameter regions for multistationarity. |
| title_full | Identifying parameter regions for multistationarity. |
| title_fullStr | Identifying parameter regions for multistationarity. |
| title_full_unstemmed | Identifying parameter regions for multistationarity. |
| title_short | Identifying parameter regions for multistationarity. |
| title_sort | identifying parameter regions for multistationarity |
| url | https://doi.org/10.1371/journal.pcbi.1005751 |
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