Sign-sensitivities for reaction networks: an algebraic approach
This paper presents an algebraic framework to study sign-sensitivities for reaction networks modeled by means of systems of ordinary differential equations. Specifically, we study the sign of the derivative of the concentrations of the species in the network at steady state with respect to a small p...
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| Format: | Article |
| Language: | English |
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AIMS Press
2019-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/10.3934/mbe.2019414?viewType=HTML |
| _version_ | 1811220167298908160 |
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| author | Elisenda Feliu |
| author_facet | Elisenda Feliu |
| author_sort | Elisenda Feliu |
| collection | DOAJ |
| description | This paper presents an algebraic framework to study sign-sensitivities for reaction networks modeled by means of systems of ordinary differential equations. Specifically, we study the sign of the derivative of the concentrations of the species in the network at steady state with respect to a small perturbation on the parameter vector. We provide a closed formula for the derivatives that accommodates common perturbations, and illustrate its form with numerous examples. We argue that, mathematically, the study of the response to the system with respect to changes in total amounts is not well posed, and that one should rather consider perturbations with respect to the initial conditions. We find a sign-based criterion to determine, without computing the sensitivities, whether the sign depends on the steady state and parameters of the system. This is based on earlier results of so-called injective networks. Finally, we address systems with multiple steady states and the restriction to stable steady states. |
| first_indexed | 2024-04-12T07:36:54Z |
| format | Article |
| id | doaj.art-9c1e20206b924678b13576f2874052dd |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-12T07:36:54Z |
| publishDate | 2019-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-9c1e20206b924678b13576f2874052dd2022-12-22T03:41:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182019-09-011668195821310.3934/mbe.2019414Sign-sensitivities for reaction networks: an algebraic approachElisenda Feliu0Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, DenmarkThis paper presents an algebraic framework to study sign-sensitivities for reaction networks modeled by means of systems of ordinary differential equations. Specifically, we study the sign of the derivative of the concentrations of the species in the network at steady state with respect to a small perturbation on the parameter vector. We provide a closed formula for the derivatives that accommodates common perturbations, and illustrate its form with numerous examples. We argue that, mathematically, the study of the response to the system with respect to changes in total amounts is not well posed, and that one should rather consider perturbations with respect to the initial conditions. We find a sign-based criterion to determine, without computing the sensitivities, whether the sign depends on the steady state and parameters of the system. This is based on earlier results of so-called injective networks. Finally, we address systems with multiple steady states and the restriction to stable steady states.https://www.aimspress.com/article/10.3934/mbe.2019414?viewType=HTMLperturbationreaction networksteady statemass-actionsystems biologysensitivity |
| spellingShingle | Elisenda Feliu Sign-sensitivities for reaction networks: an algebraic approach Mathematical Biosciences and Engineering perturbation reaction network steady state mass-action systems biology sensitivity |
| title | Sign-sensitivities for reaction networks: an algebraic approach |
| title_full | Sign-sensitivities for reaction networks: an algebraic approach |
| title_fullStr | Sign-sensitivities for reaction networks: an algebraic approach |
| title_full_unstemmed | Sign-sensitivities for reaction networks: an algebraic approach |
| title_short | Sign-sensitivities for reaction networks: an algebraic approach |
| title_sort | sign sensitivities for reaction networks an algebraic approach |
| topic | perturbation reaction network steady state mass-action systems biology sensitivity |
| url | https://www.aimspress.com/article/10.3934/mbe.2019414?viewType=HTML |
| work_keys_str_mv | AT elisendafeliu signsensitivitiesforreactionnetworksanalgebraicapproach |