A theoretic control approach in signal-controlled metabolic pathways
Cells use a signal transduction mechanism to regulate certainmetabolic pathways. In this paper, the regulatory mechanism isanalyzed mathematically. For this analysis, a mathematical modelfor the pathways is first established using a system of differentialequations. Then the linear stability, contro...
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| Format: | Article |
| Language: | English |
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AIMS Press
2007-04-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.471 |
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| author | Ramesh Garimella Uma Garimella Weijiu Liu |
| author_facet | Ramesh Garimella Uma Garimella Weijiu Liu |
| author_sort | Ramesh Garimella |
| collection | DOAJ |
| description | Cells use a signal transduction mechanism to regulate certainmetabolic pathways. In this paper, the regulatory mechanism isanalyzed mathematically. For this analysis, a mathematical modelfor the pathways is first established using a system of differentialequations. Then the linear stability, controllability, andobservability of the system are investigated. We show that thelinearized system is controllable and observable, and that the realparts of all eigenvalues of the linearized system are nonpositiveusing Routh's stability criterion. Controllability and observabilityare structural properties of a dynamical system. Thus our resultsmay explain why the metabolic pathways can be controlled andregulated. Finally observer-based and proportional output feedbackcontrollers are designed to regulate the end product to its desired level. Applications to the regulation of blood glucose levels are discussed. |
| format | Article |
| id | doaj-art-08df6c541491479090627ed4b44abb90 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2007-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-08df6c541491479090627ed4b44abb902025-01-24T01:53:48ZengAIMS PressMathematical Biosciences and Engineering1551-00182007-04-014347148810.3934/mbe.2007.4.471A theoretic control approach in signal-controlled metabolic pathwaysRamesh Garimella0Uma Garimella1Weijiu Liu2Department of Mathematics, University of Central Arkansas, 201 Donaghey Avenue, Conway, AR 72035Department of Mathematics, University of Central Arkansas, 201 Donaghey Avenue, Conway, AR 72035Department of Mathematics, University of Central Arkansas, 201 Donaghey Avenue, Conway, AR 72035Cells use a signal transduction mechanism to regulate certainmetabolic pathways. In this paper, the regulatory mechanism isanalyzed mathematically. For this analysis, a mathematical modelfor the pathways is first established using a system of differentialequations. Then the linear stability, controllability, andobservability of the system are investigated. We show that thelinearized system is controllable and observable, and that the realparts of all eigenvalues of the linearized system are nonpositiveusing Routh's stability criterion. Controllability and observabilityare structural properties of a dynamical system. Thus our resultsmay explain why the metabolic pathways can be controlled andregulated. Finally observer-based and proportional output feedbackcontrollers are designed to regulate the end product to its desired level. Applications to the regulation of blood glucose levels are discussed.https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.471regulation.cell signalingoutputfeedback controlmetabolic pathway |
| spellingShingle | Ramesh Garimella Uma Garimella Weijiu Liu A theoretic control approach in signal-controlled metabolic pathways Mathematical Biosciences and Engineering regulation. cell signaling outputfeedback control metabolic pathway |
| title | A theoretic control approach in signal-controlled metabolic pathways |
| title_full | A theoretic control approach in signal-controlled metabolic pathways |
| title_fullStr | A theoretic control approach in signal-controlled metabolic pathways |
| title_full_unstemmed | A theoretic control approach in signal-controlled metabolic pathways |
| title_short | A theoretic control approach in signal-controlled metabolic pathways |
| title_sort | theoretic control approach in signal controlled metabolic pathways |
| topic | regulation. cell signaling outputfeedback control metabolic pathway |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.471 |
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