Oscillations and Waves

Periodic temporal and spatial patterns of Ca2+ signaling give rise to calcium oscillations and waves 384... 

R. Field and M. Burger, eds.. Oscillations and Waves in Chemical Systems, John Wiley Sons, New York, 1985. 

The 1970s saw an explosion of theoretical and experimental studies devoted to oscillating reactions. This domain continues to expand as more and more complex phenomena are observed in the experiments or predicted theoretically. The initial impetus for the smdy of oscillations owes much to the concomitance of several factors. The discovery of temporal and spatiotemporal organization in the Belousov-Zhabotinsky reaction [22], which has remained the most important example of a chemical reaction giving rise to oscillations and waves. 

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 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. 

Y. Tang and H. G. Othmer, Excitation, oscillations and wave propagation in a G-protein-based model of signal transduction in Dictyostelium discoideum. Philos. Trans. R. Soc. Land. B. Biol. Sci. 349, 179-195 (1995). 

A. G. Gurevich and G. A. Melkov, Magnetization Oscillations and Waves, CRC Press, Boca Raton, FL, 1996, p. 279 see also particularly V. S. L vov, Wave Turbulence Under Parametric Excitation Applications to Magnets, Springer-Verlag, Berlin, 1994, pp. 214-218, 226-234, 281-289. 

Sneyd J, Keizer J, Sanderson MJ. Mechanisms of calcium oscillations and waves a quantitative analysis. FASEB J. 1995 9 1463-1472. 

Zhabotinsky AM 1991 A history of chemical oscillations and waves Chaos 1 379-86... 

Zhabotinsky A M, Buchholtz F, Kiyatin A B and Epstein I R 1993 Oscillations and waves in metal-ion catalysed bromate oscillating reaction in highly oxidised states J. Phys. Chem. 97 7578-84... 

Atri, A., Amundson, J., Clapham, D., and Sneyd, J. (1993) A single-pool model for intracellular calcium oscillations and waves in the Xenopus laevis oocyte. Biophysical Journal, 65 1727-1739. 

More recently, Jafri et al. (1992) proposed an electrochemical model for Ca oscillations in Xenopus oocytes based on the exchanges of Ca between the cytosol and the endoplasmic reticulum the regulation considered is again based on CICR, as the Ca conductance in that model is activated in a nonlinear, cooperative manner by cytosolic Ca. Another single pool model for Ca oscillations and waves in Xenopus oocytes, due to Atri et al. (1993), incorporates both CICR and Ca inhibition of Ca release at higher cytosolic Ca levels. 

In conclusion, the study of models for Ca signalling indicates that the phenomena of Ca oscillations and waves are closely intertwined. The spatiotemporal patterns correspond to the propagation of a Ca front in a biochemically excitable or oscillatory medium, at a rate much higher than that associated with simple diffusion. Such a property could also underlie a possible role of Ca waves in intercellular communication (Charles et al., 1991). The results presented in figs. 9.30 and 9.31 show that a unique mechanism, based on CICR, can account for the... 

Dupont, G. A. Goldbeter. 1992b. Oscillations and waves of cytosolic calcium Insights from theoretical models. BioEssays 14 485-93. 

Physarum, mitotic oscillator, 409,410,411 Physiological significance of Ca oscillations and waves, 354,392 of chaos, 341,511... 

Plasma electrodynamics is a very important and widespread branch of plasma physics that covers in particular such topics as plasma sheaths, plasma oscillations and waves, propagation of electromagnetic waves in plasma, plasma instabilities, magneto-hydrodynamics of plasma, and collective and non-linear plasma phenomena. Only the most general aspects of plasma electrodynamics relevant to plasma chemistry will be discussed here. Details on the subject can be found in particular, in books of Kadomtsev (1976), Ginzburg (1960), Boyd and Sanderson (2003), and Fridman and Kennedy (2004). 

We have also discussed the formation of spatio-temporal patterns in non-variational systems. A typical example of such systems at nano-meter scales is reaction-diffusion systems that are ubiquitous in biology, chemical catalysis, electrochemistry, etc. These systems are characterized by the energy supply from the outside and can exhibit complex nonlinear behavior like oscillations and waves. A macroscopic example of such a system is Rayleigh-Benard convection accompanied by mean flow that leads to strong distortion of periodic patterns and the formation of labyrinth patterns and spiral waves. Similar nano-meter scale patterns are observed during phase separation of diblock copolymer Aims in the presence of hydrodynamic effects. The pattern s nonlinear dynamics in both macro- and nano-systems can be described by a Swift-Hohenberg equation coupled to the non-local mean-flow equation. 

In the equilibrium regime, the dynamic behavior of an RD column in transformed concentration variables is essentially the same like the dynamic behavior of a non-RD column. Hence it is not surprising that under these conditions we can observe all kinds of multiplicity, oscillations, and wave propagation phenomena like in non-RD. Any novel feature, such as reactive azeotropy, is introduced by the static transformation between physical and transformed concentrations. 

Rabinovich, M. I. Trubetskov, D. I. Oscillations and Waves in Linear and Nonlinear Systems, Kluwer Academic Publishers Norwell, MA, 1994. 

Yashin, V.V., et al. Mechano-chemical oscillations and waves in reactive gels. Rep. Prog. Phys. 75(6), 066601 (2012)... 

An understanding of chemical oscillations and wave patterns in the Belousov-Zhabotinskii reaction requires some familiarity with the language and methods of chemical kinetics on one hand and some facility with the mathematics of differential equations on the other. Since not every reader can be expected to know both fields to the extent which we will need later,... 

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