Modeling some properties of circadian rhythms
Mathematical models have been very useful in biological research. From theinteraction of biology and mathematics, new problems have emerged that havegenerated advances in the theory, suggested further experimental work andmotivated plausible conjectures. From our perspective, it is absolutelynecessa...
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| Format: | Article |
| Language: | English |
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AIMS Press
2013-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.317 |
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| author | Miguel Lara-Aparicio Carolina Barriga-Montoya Pablo Padilla-Longoria Beatriz Fuentes-Pardo |
| author_facet | Miguel Lara-Aparicio Carolina Barriga-Montoya Pablo Padilla-Longoria Beatriz Fuentes-Pardo |
| author_sort | Miguel Lara-Aparicio |
| collection | DOAJ |
| description | Mathematical models have been very useful in biological research. From theinteraction of biology and mathematics, new problems have emerged that havegenerated advances in the theory, suggested further experimental work andmotivated plausible conjectures. From our perspective, it is absolutelynecessary to incorporate modeling tools in the study of circadian rhythmsand that without a solid mathematical framework a real understanding of themwill not be possible. Our interest is to study the main process underlyingthe synchronization in the pacemaker of a circadian system: thesemechanisms should be conserved in all living beings. Indeed, from anevolutionary perspective, it seems reasonable to assume that either theyhave a common origin or that they emerge from similar selectioncircumstances. We propose a general framework to understand the emergence ofsynchronization as a robust characteristic of some cooperative systems ofnon-linear coupled oscillators. In a first approximation to the problem wevary the topology of the network and the strength of the interactions amongoscillators. In order to study the emergent dynamics, we carried out somenumerical computations. The results are consistent with experiments reportedin the literature. Finally, we proposed a theoretical framework to study thephenomenon of synchronization in the context of circadian rhythms: thedissipative synchronization of nonautonomous dynamical systems. |
| format | Article |
| id | doaj-art-a6d96023d65f42dea474e2e21e304a90 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-a6d96023d65f42dea474e2e21e304a902025-01-24T02:28:02ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-09-0111231733010.3934/mbe.2014.11.317Modeling some properties of circadian rhythmsMiguel Lara-Aparicio0Carolina Barriga-Montoya1Pablo Padilla-Longoria2Beatriz Fuentes-Pardo3Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México,Laboratorio de Cronobiología, Departamento de Fisiología, Facultad de Medicina, Universidad Nacional Autónoma de MéxicoDepartamento de Matemáticas y Mecánica, Instituto de Investigaciones, en Matemáticas Aplicadas y en Sistemas. Universidad Nacional Autónoma de MéxicoLaboratorio de Cronobiología, Departamento de Fisiología, Facultad de Medicina, Universidad Nacional Autónoma de MéxicoMathematical models have been very useful in biological research. From theinteraction of biology and mathematics, new problems have emerged that havegenerated advances in the theory, suggested further experimental work andmotivated plausible conjectures. From our perspective, it is absolutelynecessary to incorporate modeling tools in the study of circadian rhythmsand that without a solid mathematical framework a real understanding of themwill not be possible. Our interest is to study the main process underlyingthe synchronization in the pacemaker of a circadian system: thesemechanisms should be conserved in all living beings. Indeed, from anevolutionary perspective, it seems reasonable to assume that either theyhave a common origin or that they emerge from similar selectioncircumstances. We propose a general framework to understand the emergence ofsynchronization as a robust characteristic of some cooperative systems ofnon-linear coupled oscillators. In a first approximation to the problem wevary the topology of the network and the strength of the interactions amongoscillators. In order to study the emergent dynamics, we carried out somenumerical computations. The results are consistent with experiments reportedin the literature. Finally, we proposed a theoretical framework to study thephenomenon of synchronization in the context of circadian rhythms: thedissipative synchronization of nonautonomous dynamical systems.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.317circadian rhythmsnetwork architecture.cooperative networkssynchronizationultradian rhythms |
| spellingShingle | Miguel Lara-Aparicio Carolina Barriga-Montoya Pablo Padilla-Longoria Beatriz Fuentes-Pardo Modeling some properties of circadian rhythms Mathematical Biosciences and Engineering circadian rhythms network architecture. cooperative networks synchronization ultradian rhythms |
| title | Modeling some properties of circadian rhythms |
| title_full | Modeling some properties of circadian rhythms |
| title_fullStr | Modeling some properties of circadian rhythms |
| title_full_unstemmed | Modeling some properties of circadian rhythms |
| title_short | Modeling some properties of circadian rhythms |
| title_sort | modeling some properties of circadian rhythms |
| topic | circadian rhythms network architecture. cooperative networks synchronization ultradian rhythms |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.317 |
| work_keys_str_mv | AT miguellaraaparicio modelingsomepropertiesofcircadianrhythms AT carolinabarrigamontoya modelingsomepropertiesofcircadianrhythms AT pablopadillalongoria modelingsomepropertiesofcircadianrhythms AT beatrizfuentespardo modelingsomepropertiesofcircadianrhythms |