Biochemical oscillation

How relevant are these phenomena First, many oscillating reactions exist and play an important role in living matter. Biochemical oscillations and also the inorganic oscillatory Belousov-Zhabotinsky system are very complex reaction networks. Oscillating surface reactions though are much simpler and so offer convenient model systems to investigate the realm of non-equilibrium reactions on a fundamental level. Secondly, as mentioned above, the conditions under which nonlinear effects such as those caused by autocatalytic steps lead to uncontrollable situations, which should be avoided in practice. Hence, some knowledge about the subject is desired. Finally, the application of forced oscillations in some reactions may lead to better performance in favorable situations for example, when a catalytic system alternates between conditions where the catalyst deactivates due to carbon deposition and conditions where this deposit is reacted away. 

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

At the same time as the Belousov-Zhabotinsky reaction provided a chemical prototype for oscillatory behavior, the first experimental studies on the reaction catalyzed by peroxidase [24] and on the glycolytic system in yeast (to be discussed in Section 111) demonstrated the occurrence of biochemical oscillations in vitro. These advances opened the way to the study of the molecular bases of oscillations in biological systems. 

The three best-known examples of biochemical oscillations were found during the decade 1965-1975 [40,41]. These include the peroxidase reaction, glycolytic oscillations in yeast and muscle, and the pulsatile release of cAMP signals in Dictyostelium amoebae (see Section V). Another decade passed before the development of Ca " " fluorescent probes led to the discovery of oscillations in intracellular Ca +. Oscillations in cytosolic Ca " " have since been found in a variety of cells where they can arise spontaneously, or after stimulation by hormones or neurotransmitters. Their period can range from seconds to minutes, depending on the cell type [56]. The oscillations are often accompanied by propagation of intracellular or intercellular Ca " " waves. The importance of Ca + oscillations and waves stems from the major role played by this ion in the control of many key cellular processes—for example, gene expression or neurotransmitter secretion. 

It should be stressed that oscillatory phenomena are well-known in biology. They span a wide range of periods, reaching from fractions of seconds (neuronal and EEG activities) and minutes (biochemical oscillators) to hours and days (circadian rhythm...). Besides these cooperative oscillations on an intra-, inter- and supercellular level, the usual oscillations on a microscopic basis (e.g. electronic transitions, intra- and intermolecular vibrations, rotational relaxation,...) must be taken into account. 

In this paper I shall discuss, in a general way, some basic dynamical properties of biochemical reaction schemes that are subjected to an external perturbation that oscillates in time. The first part of this paper will deal with the ways in which a weak external oscillating stimulus is able to alter the concentrations of metabolites in a biochemical system. This part will, in particular, consider what happens when the reaction system already oscillates in a limit cycle mode due to non-linearities in its reaction kinetics. It will be shown that such an autonomous biochemical oscillator may exhibit an enhanced sensitivity to a narrow range of externally applied frequencies. 

Although these arguments have been presented for reaction systems whose rates are forced by an external oscillator, they remain true for autonomous biochemical oscillations where ot and are nonlinear functions of metabolite concentrations. That is, the rate of removal of a labeled compound through a reaction step whose rate is oscillating due to nonlinear kinetics will be enhanced over an equivalent system that maintains the same mean chemical flux and mean concentrations of metabolites but does not oscillate. This has been demonstrated numerically ( 6) on the reaction system (1) from the previous section using the full kinetic equations... 

Figure 5.9 Biochemical oscillation of an engineered signaling system, repressi-lator. i and toc/mRNA and protein concentrations. The behavior of the other two genes, tetR and cl, is essentially the same, with a time delay. See [50] for more details.

J. J. Tyson. Biochemical oscillations. In C. P. Fall, E. Marlang, J. Wagner, and J. J. Tyson, editors, Computational Cell Biology, chapter 3, pages 230-260. Springer, New York, NY, 2002. 

Kholodenko, B.N., Demin, O.V and Westerhoff, H.V. (1996) The metabolic control theory of biochemical oscillating systems. 1. Definitions of the quantitative characteristics and their simplest properties. Biochemistry Mosc. 61, 423 34. 

Systems-level approaches were defined more than 60 years ago with the application of general systems theory to various scientific fields including chemistry and life sciences with emphasis on morphogenesis (von Bertalanffy 1968 Friboulet and Thomas 2005). In the sixties, concepts derived from Ilya Prigogine s dissipative structures theory were also applied to biochemical oscillation and morphogenesis (Friboulet and Thomas 2005). In the seventies, numerical analyses of biochemical systems were developed which could represent a first step into modem systems biology (Hammer et al. 2004 Aderem 2005). 

Although the earlier models by Sel kov exhibit only one limit cycle, later models have multiple solutions, both oscillatory and nonoscillatory. These models are quite interesting for the reason that these are the earliest models in biochemical oscillations giving clear evidence for more complex solutions than a simple limit cycle as has been the case with almost all other chemical systems except those in CSTR models. 

IIIF) 1973 Sel kov, E. E., Betz, A. On the Mechanism of Single- Frequency Glycolytic Oscillations, In Biological and Biochemical Oscillations, (Chance, et al. eds.) Academic Press, 197-220... 

IIIC) 1973 Vavilin, V. A., Zhabotinskii, A. M., Zaikin, A. N. A Study of a Self-Oscillatory Chemical Reaction, I. The Autonomous System, In Biological and Biochemical Oscillations (Ed. B. Chance), 71-79... 

Bl) 1973 Chance, B., Ghosh, A. K., Pye, E. K., Hess, B. (Eds.) Biological and Biochemical Oscillators, Academic Press, New York Academic Press, New York... 

IIIN) Taranenko, A. M. Sequences of Limit Cycles in a Model of a Biochemical Oscillator... 

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

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

The classical example of a biochemical oscillator is glycolysis. Damped oscillations were observed in the NADH fluorescence of yeast cell suspensions. Sustained oscillations were notable in yeast glycolysis (Figure 8.25) within a clearly defined range of substrate infusion rates, outside of which steady-state behavior was obtained. 

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... 

As indicated in section 1.3, cytosolic Ca oscillations, which occur in a variety of cell types as a result of stimulation by hormones or neurotransmitters, are among the most widespread of cellular rhythms, besides oscillations driven by periodic variations of the membrane potential in electrically excitable cells. These oscOlations, whose period varies from seconds to minutes depending on the cell type, sometimes occur spontaneously. Part V is devoted to this phenomenon, which clearly represents the most significant addition to the field of biochemical oscillations over the last decade, in addition to the evidence that has acciunulated to show that a continuous biochemical oscillator controls the eukaryotic cell cycle (see below). Experimental work on Ca oscillations has increased so much over the last years that it is by now the most studied biochemical rhythm. 

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