Symmetry Breaking Instabilities in Dissipative Systems. II

Prigogine, I.; Lefever, René

doi:10.1063/1.1668896

Cited by 1,238 publications

(533 citation statements)

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“…These observations suggest the existence of a kind of early ooplasmic and embryonic predisposition. It is, thus, by unidirectional changing of the established equilibrium (principle of unidirectional chaos: Prigogine and Lefever, 1968) in the germ disc region that inductive signals appear, leading to the epigenetic phenomena. So during the ensuing gastrulation, the upper layer material of the sickle-shaped predisposed anlage fields will converge and ingress by means of the PS, localized over the permantly functional radius below which a maximum of ooplasm is concentrated (Figs.…”

Section: From Radial Symmetry By Means Of Sickle-shaped Bilateral Symmentioning

confidence: 99%

Origin, fate, and function of the components of the avian germ disc region and early blastoderm: Role of ooplasmic determinants

Callebaut

2005

Developmental Dynamics

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In the avian oocytal germ disc region, at the end of oogenesis, we discerned four ooplasms (␣, ␤, ␥, ␦) presenting an onion-peel distribution (from peripheral and superficial to central and deep. Their fate was followed during early embryonic development. The most superficial and peripheral ␣ ooplasm plays a fundamental role during cleavage. The ␤ ooplasm, originally localized in the peripheral region of the blastodisc, becomes mainly concentrated in the primitive streak. At the moment of bilateral symmetrization, a spatially oblique, sickle-shaped uptake of ␥ and ␦ ooplasms occurs so that ␥ and ␦ ooplasms become incorporated into the deeper part of the avian blastoderm. These ooplasms seem to contain ooplasmic determinants that initiate either early neurulation or gastrulation events. The early neural plate-inducing structure that forms a deep part of the blastoderm is the ␦ ooplasm-containing endophyll (primary hypoblast). Together with the primordial germ cells, it is derived from the superficial centrocaudal part of the nucleus of Pander, which also contains ␦ ooplasm. The other structure (␥ ooplasm) that is incorporated into the caudolateral deep part of the blastoderm forms Rauber's sickle. It induces gastrulation in the concavity of Rauber's sickle and blood island formation exterior to Rauber's sickle. Rauber's sickle develops by ingrowth of blastodermal cells into the ␥ ooplasm, which surrounds the nucleus of Pander. Rauber's sickle constitutes the primary major organizer of the avian blastoderm and generates only extraembryonic tissues (junctional and sickle endoblast). By imparting positional information, it organizes and dominates the whole blastoderm (controlling gastrulation, neurulation, and coelom and cardiovascular system formation). Fragments of the horns of Rauber's sickle extend far cranially into the lateral quadrants of the unincubated blastoderm, so that often Rauber's sickle material forms three quarters of a circle. This finding explains the regulative capacities of isolated blastoderm parts, with the exception of the anti-sickle region and central blastoderm region, where no Rauber's sickle material is present. In avian blastoderms, there exists a competitive inhibition by Rauber's sickle on the primitive streak and neural plate-inducing effects of sickle endoblast. Avian primordial germ cells contain ␦ ooplasm derived from the superficial part of the nucleus of Pander. Their original deep and central ooplasmic localization has been confirmed by the use of a chicken vasa homologue. We conclude that the unincubated blastoderm consists of three elementary tissues: upper layer mainly containing ␤ ooplasm, endophyll containing ␦ ooplasm, and Rauber's sickle containing ␥ ooplasm). These elementary tissues form before the three classic germ layers have developed.

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Section: From Radial Symmetry By Means Of Sickle-shaped Bilateral Symmentioning

confidence: 99%

Origin, fate, and function of the components of the avian germ disc region and early blastoderm: Role of ooplasmic determinants

Callebaut

2005

Developmental Dynamics

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“…where x and y are the dimensionless concentrations of two chemical species [3,1] while the (positive) parameters A and B are the rate constants for the production of x and y. This system has one steady state, x * = A, y * = B/A which is unstable if A 2 < (B − 1).…”

Section: Mismatched Oscillatorsmentioning

confidence: 99%

“…An important emergent phenomenon in this context is the suppression of oscillations, formally termed amplitude death (AD): as a consequence of the interaction oscillations of the entire system cease, leading to stationarity [1,2,3]. Such behaviour is emergent in the sense that the isolated or uncoupled systems do not exhibit stationary dynamics.…”

Section: Introductionmentioning

confidence: 99%

Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

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When nonlinear dynamical systems are coupled, depending on the intrinsic dynamics and the manner in which the coupling is organized, a host of novel phenomena can arise. In this context, an important emergent phenomenon is the complete suppression of oscillations, formally termed amplitude death (AD). Oscillations of the entire system cease as a consequence of the interaction, leading to stationary behavior. The fixed points that the coupling stabilizes can be the otherwise unstable fixed points of the uncoupled system or can correspond to novel stationary points. Such behaviour is of relevance in areas ranging from laser physics to the dynamics of biological systems. In this review we discuss the characteristics of the different coupling strategies and scenarios that lead to AD in a variety of different situations, and draw attention to several open issues and challenging problems for further study.

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“…The early theoretical work of Goodwin, Higgins, Prigogine and Lefever, Sel'kov and Schlögl (Goodwin 1965;Higgins 1967;Prigogine & Lefever 1968;Sel'kov 1968;Schlögl 1972) convinced biophysical chemists that oscillations and bistability were definitely to be expected in biochemical reaction systems with positive and negative feedbacks to destabilize steady-state solutions. Although a ternary autocatalytic reaction such as YC2X/3X is unlikely in physical chemistry, high-order nonlinearities in substrate concentration can be achieved by multi-subunit enzymes of the type being discovered at that time to regulate biochemical pathways (Monod et al 1965;Goldbeter & Lefever 1972).…”

Section: Historical Contextmentioning

confidence: 99%

“…A particularly simple example of a chemical reaction network exhibiting exotic dynamics (oscillations, bistability, pattern formation, travelling waves) was the 'Brusselator' of Prigogine & Lefever (1968), whose temporal dynamics are governed by dx dt Z aKbx C cx 2 yKdx; dy dt Z bx Kcx 2 yKey: Cca 2 !0. When the steady state is unstable, it is surrounded by a unique, stable limit cycle oscillation (figure 1).…”

Section: Historical Contextmentioning

confidence: 99%

Biological switches and clocks

Tyson

Albert

Goldbeter³

et al. 2008

J. R. Soc. Interface.

108

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To introduce this special issue on biological switches and clocks, we review the historical development of mathematical models of bistability and oscillations in chemical reaction networks. In the 1960s and 1970s, these models were limited to well-studied biochemical examples, such as glycolytic oscillations and cyclic AMP signalling. After the molecular genetics revolution of the 1980s, the field of molecular cell biology was thrown wide open to mathematical modellers. We review recent advances in modelling the gene-protein interaction networks that control circadian rhythms, cell cycle progression, signal processing and the design of synthetic gene networks.

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Symmetry Breaking Instabilities in Dissipative Systems. II

Cited by 1,238 publications

References 10 publications

Origin, fate, and function of the components of the avian germ disc region and early blastoderm: Role of ooplasmic determinants

Origin, fate, and function of the components of the avian germ disc region and early blastoderm: Role of ooplasmic determinants

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Biological switches and clocks

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