Biochemical and cellular rhythms

At the same time as the Belousov-Zhabotinsky reaction provided a chemical prototype for oscillatory behaviour, the first experimental studies on the reaction catalysed by peroxidase (Yamazaki, Yokota Nakajima, 1965 Nakamura, Yokota Yamazaki, 1969) and on the glycolytic system in yeast (Chance, Schoener Elsaesser, 1964 Ghosh Chance, 1964 Pye, 1969 Chance etal, 1973) indicated the possibility of observing biochemical oscillations in vitro. These advances opened the way to the study of the molecular bases of oscillations in biological systems. 

Early theoretical studies interpreted circadian rhythms in terms of limit cycle behaviour (Pavlidis Kauzmann, 1969 Pavlidis, 1973 Winfree, 1970,1980). The recent advances in the mechanism of circadian rhythmicity pave the way for the construction of realistic models that will address this issue in more precise biochemical terms. One such model is proposed in chapter 11 of this book. 

Thanks to the studies of Hodgkin Huxley, which culminated in 1952 with the publication of a series of articles, of which the last was of theoretical nature, the physicochemical bases of neuronal excitability giving rise to the action potential were elucidated. Soon after, Huxley (1959) showed how a nerve cell can generate a train of action potentials in a periodic manner (see also Connor, Walter McKown, 1977 Aihara Matsumoto, 1982 Rinzel Ermentrout, 1989). Even if the properties of the ionic channels involved have not yet been fully elucidated, cardiac oscillations originate in a similar manner from the pacemaker properties of the specialized, electrically excitable tissues of the heart (Noble, 1979,1984 Noble Powell, 1987 Noble, DiFrancesco Denyer, 1989 DiFrancesco, 1993). These examples remained the only biological rhythms whose molecular mechanism was known to some extent, until the discovery of biochemical oscillations. 

The oscillations observed in vitro in the glycolytic system of muscle (Frenkel, 1968 Tomheim Lowenstein, 1974, 1975) and yeast cells (Pye Chance, 1966 Hess Boiteux, 1968a,b, 1971 Hess, Boiteux Kruger, 1969 Pye, 1969, 1971) are still the prototype for biochemical oscillations resulting from the regulation of enzyme activity. These peri- 

Glycolytic oscillations and cAMP oscillations were, respectively, discovered around 1965 and 1975. Might there be a rough periodicity of some 10 years in progress on biochemical and cellular rhythms The field of biochemical oscillations has indeed changed drastically due to the discovery in 1985 of intracellular Ca oscillations that occur in a variety of cells, either spontaneously or as a result of stimulation by an external signal such as a hormone or a neurotransmitter. Since their 

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Besides their use in accounting for experimental observations on biochemical and cellular rhythms, models were also studied here in a more abstract manner, departing somewhat from experimental constraints, in order to determine the ways by which biological systems can acquire more and more complex modes of temporal self-organization, starting from simple periodic behaviour. 

A. Goldbeter, Biochemical Oscillations and Cellular Rhythms The Molecular Bases of Periodic and Chaotic Behaviour, Cambridge University Press, Cambridge, United Kingdom (1997). 

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. 

A. Goldbeter. Biochemical Oscillations and Cellular Rhythms. Cambridge University Press, 1995. 

Goldbeter, A. (1996) Biochemical Oscillations 1032. and Cellular Rhythms The Molecular Basis of... 

Based on experimental observations, the theoretical models considered throw light on the origin of simple periodic phenomena and complex oscillations, including chaos, in biochemical systems. Besides illustrating the variety of molecular mechanisms producing oscillations at the cellular level, the models allow us to delineate in a qualitative and quantitative manner the conditions in which sustained oscillations occur. The theoretical approach thereby contributes to a better understanding of the physiological roles of such rhythms. Furthermore, in such an approach the relative frequency of occurrence of simple versus complex patterns of oscillations becomes amenable to quantitative assessment. Finally, theoretical models for biochemical and cellular... 

This book, which contains more than 1200 references, provides a wide survey of work on biochemical oscillations and cellular rhythms. The author has made numerous contributions to the subject since the early developments in the field. 

This revised and enlarged edition published in 1996 by Cambridge University Press as Biochemical Oscillations and Cellular Rhythms First paperback edition 1997... 

Biochemical oscillations and cellular rhythms the molecular bases of periodic and chaotic behaviour / Albert Goldbeter. p. cm. 

Goldbeter, A. Biochemical oscillations and cellular rhythms, Cambridge, 1997. 

Glycolytic oscillations in yeast cells provided one of the first examples of oscillatory behavior in a biochemical system. They continue to serve as a prototype for cellular rhythms. This oscillatory phenomenon, discovered some 40 years ago [36, 37] and still vigorously investigated today [38], was important in several respects First, it illustrated the occurrence of periodic behavior in a key metabolic pathway. Second, because they were soon observed in cell extracts, glycolytic oscillations provided an instance of a biochemical clock amenable to in vitro studies. Initially observed in yeast cells and extracts, glycolytic oscillations were later observed in muscle cells and evidence exists for their occurrence in pancreatic p-cells in which they could underlie the pulsatile secretion of insulin [39]. 

The study of biochemical oscillations thus extends in many directions, from simple and complex periodic behaviour to chaotic dynamics, and from cellular rhythms to chronopharmacology. It is the purpose of this book to explore the molecular bases of these oscillatory phenomena and the richness of their physiological implications. 

Clin Neuropharmacol 18 (suppl 2 S7-S14, 1995 Klemfuss H, Kripke DF Effects of lithium on circadian rhythms, in Chrono-pharmacology. Cellular and Biochemical Interactions. Edited by Lemmer B. New York, Marcel Dekker, 1989, pp 281-297... 

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