Good and bad children in metabolic networks
Equilibrium bifurcations arise from sign changes of Jacobian determinants, as parameters are varied. Therefore we address the Jacobian determinant for metabolic networks with general reaction kinetics. Our approach is based on the concept of Child Selections: each (mother) metabolite is mapped, inje...
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2020388?viewType=HTML |
| _version_ | 1819129047346577408 |
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| author | Nicola Vassena |
| author_facet | Nicola Vassena |
| author_sort | Nicola Vassena |
| collection | DOAJ |
| description | Equilibrium bifurcations arise from sign changes of Jacobian determinants, as parameters are varied. Therefore we address the Jacobian determinant for metabolic networks with general reaction kinetics. Our approach is based on the concept of Child Selections: each (mother) metabolite is mapped, injectively, to one of those (child) reactions that it drives as an input. Our analysis distinguishes reaction network Jacobians with constant sign from the bifurcation case, where that sign depends on specific reaction rates. In particular, we distinguish "good" Child Selections, which do not affect the sign, from more interesting and mischievous "bad" children, which gang up towards sign changes, instability, and bifurcation. |
| first_indexed | 2024-12-22T08:37:30Z |
| format | Article |
| id | doaj.art-42741cda6aa842738bdf719ad36321e5 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-22T08:37:30Z |
| publishDate | 2020-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-42741cda6aa842738bdf719ad36321e52022-12-21T18:32:19ZengAIMS PressMathematical Biosciences and Engineering1551-00182020-11-011767621764410.3934/mbe.2020388Good and bad children in metabolic networksNicola Vassena0Department of Mathematics, Free University of Berlin, GermanEquilibrium bifurcations arise from sign changes of Jacobian determinants, as parameters are varied. Therefore we address the Jacobian determinant for metabolic networks with general reaction kinetics. Our approach is based on the concept of Child Selections: each (mother) metabolite is mapped, injectively, to one of those (child) reactions that it drives as an input. Our analysis distinguishes reaction network Jacobians with constant sign from the bifurcation case, where that sign depends on specific reaction rates. In particular, we distinguish "good" Child Selections, which do not affect the sign, from more interesting and mischievous "bad" children, which gang up towards sign changes, instability, and bifurcation.https://www.aimspress.com/article/doi/10.3934/mbe.2020388?viewType=HTMLmetabolic networksstructural analysisjacobian determinantmultistationaritystability changesaddle-node bifurcation |
| spellingShingle | Nicola Vassena Good and bad children in metabolic networks Mathematical Biosciences and Engineering metabolic networks structural analysis jacobian determinant multistationarity stability change saddle-node bifurcation |
| title | Good and bad children in metabolic networks |
| title_full | Good and bad children in metabolic networks |
| title_fullStr | Good and bad children in metabolic networks |
| title_full_unstemmed | Good and bad children in metabolic networks |
| title_short | Good and bad children in metabolic networks |
| title_sort | good and bad children in metabolic networks |
| topic | metabolic networks structural analysis jacobian determinant multistationarity stability change saddle-node bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2020388?viewType=HTML |
| work_keys_str_mv | AT nicolavassena goodandbadchildreninmetabolicnetworks |