Rhythm, biological

Melatonin. Melatonin (A/-acetyl-5-metlioxytryptaniine) [73-31-4] C 2H gN2O2(250) is secreted from the pineal gland and retina during dark periods of the vertebrate circadian rhythm (65). Melatonin regulates biological rhythms and neuroendocrine function and is formed from serotonin (5-HT). 

Goldbeter, A. (2007) Biological rhythms as temporal dissipative structures. Adv. Chem. Phys., 135, 253-295. 

College of Physicians and Surgeons of Columbia University, New York, USA, which is a major provider of medical education, health-care and research in New York. An internationally recognized sleep researcher, his interests focus on sleep and biological rhythms research. 

From a mathematical point of view, the onset of sustained oscillations generally corresponds to the passage through a Hopf bifurcation point [19] For a critical value of a control parameter, the steady state becomes unstable as a focus. Before the bifurcation point, the system displays damped oscillations and eventually reaches the steady state, which is a stable focus. Beyond the bifurcation point, a stable solution arises in the form of a small-amplitude limit cycle surrounding the unstable steady state [15, 17]. By reason of their stability or regularity, most biological rhythms correspond to oscillations of the limit cycle type rather than to Lotka-Volterra oscillations. Such is the case for the periodic phenomena in biochemical and cellular systems discussed in this chapter. The phase plane analysis of two-variable models indicates that the oscillatory dynamics of neurons also corresponds to the evolution toward a limit cycle [20]. A similar evolution is predicted [21] by models for predator-prey interactions in ecology. 

Figure 1. In most examples of biological rhythms, sustained oscillations correspond to the evolution toward a hmit cycle. The limit cycle shown here was obtained in a model for circadian oscillations of the PER protein and per mRNA in Drosophila [107].

As indicated above, theoretical models for biological rhythms were first used in ecology to study the oscillations resulting from interactions between populations of predators and preys [6]. Neural rhythms represent another field where such models were used at an early stage The formalism developed by Hodgkin and Huxley [7] stiU forms the core of most models for oscillations of the membrane potential in nerve and cardiac cells [33-35]. Models were subsequently proposed for oscillations that arise at the cellular level from regulation of enzyme, receptor, or gene activity (see Ref. 31 for a detailed fist of references). 

Some of the main examples of biological rhythms of nonelectrical nature are discussed below, among which are glycolytic oscillations (Section III), oscillations and waves of cytosolic Ca + (Section IV), cAMP oscillations that underlie pulsatile intercellular communication in Dictyostelium amoebae (Section V), circadian rhythms (Section VI), and the cell cycle clock (Section VII). Section VIII is devoted to some recently discovered cellular rhythms. The transition from simple periodic behavior to complex oscillations including bursting and chaos is briefly dealt with in Section IX. Concluding remarks are presented in Section X. 

The most ubiquitous biological rhythms are those that occur with a period close to 24 h in all eukaryotes and in some prokaryotes such as cyanobacteria. These circadian rhythms allow organisms to adapt to the natural periodicity of the terrestrial environment, which is characterized by the alternation of day and night due to rotation of the earth on its axis. Circadian clocks provide cells with an endogenous mechanism, allowing them to anticipate the time of day. 

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