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Mathematical Biosciences and Engineering (MBE)
 

Modeling some properties of circadian rhythms

Pages: 317 - 330, Volume 11, Issue 2, April 2014      doi:10.3934/mbe.2014.11.317

 
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Miguel Lara-Aparicio - Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México,, Mexico (email)
Carolina Barriga-Montoya - Laboratorio de Cronobiología, Departamento de Fisiología, Facultad de Medicina, Universidad Nacional Autónoma de México, Mexico (email)
Pablo Padilla-Longoria - Departamento de Matemáticas y Mecánica, Instituto de Investigaciones, en Matemáticas Aplicadas y en Sistemas. Universidad Nacional Autónoma de México, Mexico (email)
Beatriz Fuentes-Pardo - Laboratorio de Cronobiología, Departamento de Fisiología, Facultad de Medicina, Universidad Nacional Autónoma de México, Mexico (email)

Abstract: Mathematical models have been very useful in biological research. From the interaction of biology and mathematics, new problems have emerged that have generated advances in the theory, suggested further experimental work and motivated plausible conjectures. From our perspective, it is absolutely necessary to incorporate modeling tools in the study of circadian rhythms and that without a solid mathematical framework a real understanding of them will not be possible. Our interest is to study the main process underlying the synchronization in the pacemaker of a circadian system: these mechanisms should be conserved in all living beings. Indeed, from an evolutionary perspective, it seems reasonable to assume that either they have a common origin or that they emerge from similar selection circumstances. We propose a general framework to understand the emergence of synchronization as a robust characteristic of some cooperative systems of non-linear coupled oscillators. In a first approximation to the problem we vary the topology of the network and the strength of the interactions among oscillators. In order to study the emergent dynamics, we carried out some numerical computations. The results are consistent with experiments reported in the literature. Finally, we proposed a theoretical framework to study the phenomenon of synchronization in the context of circadian rhythms: the dissipative synchronization of nonautonomous dynamical systems.

Keywords:  Synchronization, circadian rhythms, ultradian rhythms, cooperative networks, network architecture.
Mathematics Subject Classification:  Primary: 92B25, 34C15; Secondary: 68U20.

Received: September 2012;      Accepted: January 2013;      Available Online: October 2013.

 References