Modeling some properties of circadian rhythms.

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.

A qualitative model of a motor circadian rhythm.

In Nature it is possible to observe diverse rhythms. Because of their adaptive characteristics, the circadian rhythms are of major importance and have been the subject of numerous experimental and theoretical studies. In this article, we give a presentation of the main results we have obtained about the motor circadian rhythm along some years of collaboration between biologists and mathematicians.

On the ontogeny of the motor circadian rhythm in crayfish.

In this paper we attack the problem of understanding the localization of the main structures involved in the motor circadian rhythm of crayfish by analysing its ontogeny. We present experimental results giving the properties of this rhythm in young and adult crayfish. Then we construct a mathematical model (based on a previous one for the electroretinogram circadian rhythm in the same species) simulating those properties.