A qualitative mathematical model of the ontogeny of a circadian rhythm in crayfish |
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Authors: | Miguel Lara-Aparicio Santiago López de Medrano Beatriz Fuentes-Pardo Enrique Moreno-Sáenz |
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Affiliation: | (1) Instituto de Matemáticas, UNAM, Apdo. Postal 70-637, 04511 México, D.F., México;(2) Departamento de Fisiología, División de Posgrado e Investigación, Facultad de Medicina, UNAM, 04510 México, D.F., México |
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Abstract: | Based on experimental work on the ontogeny of the electroretinogram circadian rhythm in crayfish, we present a mathematical model simulating changes in both frequency and amplitude of the electroretinogram oscillation during several developmental stages until shortly before the adult age. Simultaneously, we propose a hypothetical oscillation in the hormonal release whose frequency is imposed on the electroretinogram oscillation. The model consists of two coupled nonlinear oscillators in which a dynamical response is obtained mainly through an Andronov-Hopf bifurcation. Through the construction of the model, a biological hypothesis about the essential elements underlying the ERG circadian rhythm and their interrelations is formulated and discussed. |
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