Temporal self-organization

O. Delcroly and A. Goldbeter, Birhythmicity, chaos, and other patterns of temporal self organization in a multiply regulated biochemical system. Proc. Natl. Acad. Sci. USA 79, 6917 6921 (1982). 

The following discussions will present a detailed account of the experimental evidence for the briefly sketched effects as well as of their consequences with respect to temporal self-organization. 

The development of a theoretical basis for the analysis of strongly non equilibrium systems was initiated mainly by I. Prigogine and P. Glansdorf (1954). Particular interest in this area of thermodynamics developed after the discovery of the phenomenon of spatial or temporal self organization— that is, the spontaneous arrangement of ordered structures, in strongly nonequifibrium open systems at a strong nonlinearity in relations between thermodynamic parameters. 

From the molecular properties of regulation to the temporal self-organization of biological systems... 

The use of models based on experimental observations has shown how the regulatory properties at the level of enzymes and receptors can give rise to nonequilibrium, temporal self-organization in the form of sustained oscillations of the limit cycle type. In this, sustained oscillations represent examples of the dissipative structures described by Prigogine (1969). Like spatial or spatiotemporal dissipative structures, limit cycle oscillations occur beyond a critical point of instability and... 

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. 

Goldbeter, A. O. Decroly. 1983. Temporal self-organization in biochemical systems periodic behavior versus chaos. Am. J. Physiol. 245 R478-R483. 

Romond, P.C., J.-M. Guilmot A. Goldbeter. 1994. The mitotic oscillator Temporal self-organization in a phosphorylation-dephosphorylation enzymatic cascade. Ber. Bunsenges. Phys. Chem. 98 1152-9. 

The rich variety of this type of temporal self-organization was mainly explored in detail with the famous Belousov-Zhabotinsky reaction [6,7], but with heterogeneously catalyzed reactions the oscillatory kinetics were first reported only aroimd 1970 for the oxidation of CO on Pt catalysts [8,9]. Since then oscillatory kinetics have been found with more than a dozen catalytic reactions, and this field has also been extensively reviewed [10,17]. 

Goldbeter, A., Decroly, O. (1983). Temporal self-organization in biological systems Periodic behavior vs. chaos. American Journal of Physiology, 245, R478-R483. 

Spatial or temporal self organization effects have been observed on heterogeneous transition metals as well as oxide catalysts. We will illustrate here in detail these concepts using the CO oxidation reaction as an example. We briefly referred to self organizing catalytic systems earlier in Chapters 2 and 4. 

Decroly, O. Goldbeter, A. 1982. Birhythmicity, Chaos, and Other Patterns of Temporal Self-Organization in a Multiply Regulated Biochemical System, Proc. Natl. Acad. Sci. U.S.A. 79, 6917-6921. 

Oscillatory kinetics and spatio-temporal self-organization in reactions at solid surfaces. Science 254, 1750. 

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