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Before discussing rhythms and pacemakers, we would like to begin this chapter by quoting Albert Einstein (Einstein, 1934): “Our experience hitherto justifies us in trusting that nature is the realization of the simplest that is mathematically conceivable. I am convinced that purely mathematical construction enables us to find those concepts and those lawlike connections between them that provide the key to the understanding of natural phenomena”. Indeed, it seems that nature can be described and understood in mathematical terms. In the context of physical phenomena nobody can deny the usefulness, applicability and relevance of mathematical models. However, as strange and paradoxical as it might appear, the importance of mathematics in biology is still questioned. In the case of biological systems it is particularly important to discuss whether this confidence is based on facts. Among life scientists it is a widespread opinion that mathematical models just put in very complicated terms what they already knew. On the other hand this is in sharp contrast with what Darwin expresses in a letter, regretting not having deepened in some basic mathematical principles (Nowak, 2006). Mathematical models incorporate experimental information, both, quantitative and qualitative. Models have to mimic the observed behavior, but this is not enough. They have to allow for the understanding of the mechanisms underlying the studied phenomenon and also have to be able to make predictions (again, both qualitative and quantitative). The construction of a mathematical model is not an unidirectional process. The feedback at the different stages of the process is one of the most important and useful characteristics (see Figure 1). A mathematical model provides the necessary elements to compare and even discard different hypotheses, and, in many cases, to propose new experiments (FuentesPardo et al., 2005). Just to provide a few examples in which the construction of a mathematical model has been essential in the understanding of a biological process we mention the work by Hodgkin and Huxley in the early fifties, on the existence of selective ion channels on the membrane of a neuron. Their model not only enabled them to test this hypothesis, namely, but also to deduce qualitative properties of the transmission of electrical impulses, leading to the notion of action potential (Hodkgin et al., 1952a; Hodgkin & Huxley, 1952b, 1952c, 1952d, 1952e). In

Ultradian Rhythms Underlying the Dynamics of the Circadian Pacemaker