Biological order, structure and instabilities

Prigogine, I.; Nicolis, Grégoire

doi:10.1017/s0033583500000615

Cited by 363 publications

(191 citation statements)

References 35 publications

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“…Stationary spatial dissipative structures do not depend so strongly on the boundary conditions. Moreover they have a definite wavelength and possess the ability to localize inside the system (11,12,(17)(18)(19).…”

Section: Patterns Of Spatiotemporal Organizationmentioning

confidence: 99%

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Patterns of Spatiotemporal Organization in an Allosteric Enzyme Model

Goldbeter

1973

Proc. Natl. Acad. Sci. U.S.A.

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The behavior of a model for an allosteric enzyme oscillator activated by the reaction product is analyzed in the presence of diffusion. When the concentrations of the chemicals are fixed at the boundaries, dynamic dissipative structures are shown to arise in the form of propagating concentration waves. The model is applied to the phosphofructokinase reaction and suggests that a spatiotemporal organization may originate at a macroscopic (supracellular) level from the glycolytic system.Glycolytic oscillations observed in yeast cells (1) and in cellfree extracts of yeast (2, 3) and muscle (4) originate from the positive feedback exerted on phosphofrucktokinase by one of the products of the enzymatic reaction (1-4). Several models based on this property have been proposed for glycolytic periodicities (5, 6). Taking explicitly into account the cooperative kinetics of phosphofrucktokinase (3,7,8), Lefever and I have recently analyzed a model for an allosteric enzyme activated by the reaction product (9). The limit cycle behavior of this model compares with glycolytic oscillations observed in yeast extracts (9,10).Additional patterns of dynamic behavior are allowed by diffusion (11). In particular, the existence of chemical waves has been reported in a theoretical analysis of a model (12,13) and in experiments on the Belousov-Zhabotinsky reaction (14, 15). The object of this communication is to determine how diffusion and boundary constraints may induce the formation of such a spatiotemporal organization in the allosteric model.With the periodic boundary conditionst considered earlier (9), the stability analysis of the homogeneous steady state shows that even when this state is unstable with respect to inhomogeneous perturbations the system undergoes a spatially uniform stable limit cycle. Thus the effect of diffusion does not lead to any space-dependent structure under these conditions. In this paper, I show that concentration waves may arise in the system when the periodic boundary conditions are replaced by the assumption that the concentrations of the chemicals are maintained constant at the boundaries.I briefly recall in section 1 the general features of the model and some results concerning the limit cycle oscillations. In section 2, I deal with the occurrence of propagating waves and other types of space-dependent regimes. Section 3 is devoted to a discussion of these results. * As a detailed presentation of the model has appeared elsewhere (9), I summarize the main assumptions and give the final kinetic equations of the system. Structural Hypotheses. We consider a monosubstrate allosteric enzyme consisting of two protomers. Each protomer may exist under two conformations: active (R) and inactive (T). The transition between these two conformations is fully concerted (16). The substrate binds to the R and T forms with different affinities but only the R complexes decompose to yield the product; the latter binds exclusively to the active form and is therefore a positive effector of the enzyme.Environmen...

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Section: Patterns Of Spatiotemporal Organizationmentioning

confidence: 99%

“…Additional patterns of dynamic behavior are allowed by diffusion (11). In particular, the existence of chemical waves has been reported in a theoretical analysis of a model (12,13) and in experiments on the Belousov-Zhabotinsky reaction (14,15).…”

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confidence: 93%

Patterns of Spatiotemporal Organization in an Allosteric Enzyme Model

Goldbeter

1973

Proc. Natl. Acad. Sci. U.S.A.

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“…However, historically, efforts along these lines have encountered serious difficulty outside of the nearequilibrium, linear-response regime [5] because the number of time, length, and energy scales that are important in determining the dynamics can multiply confoundingly once external drives become arbitrarily strong.…”

Section: Introductionmentioning

confidence: 99%

Statistical Physics of Adaptation

2016

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Whether by virtue of being prepared in a slowly relaxing, high-free energy initial condition, or because they are constantly dissipating energy absorbed from a strong external drive, many systems subject to thermal fluctuations are not expected to behave in the way they would at thermal equilibrium. Rather, the probability of finding such a system in a given microscopic arrangement may deviate strongly from the Boltzmann distribution, raising the question of whether thermodynamics still has anything to tell us about which arrangements are the most likely to be observed. In this work, we build on past results governing nonequilibrium thermodynamics and define a generalized Helmholtz free energy that exactly delineates the various factors that quantitatively contribute to the relative probabilities of different outcomes in far-fromequilibrium stochastic dynamics. By applying this expression to the analysis of two examples-namely, a particle hopping in an oscillating energy landscape and a population composed of two types of exponentially growing self-replicators-we illustrate a simple relationship between outcome-likelihood and dissipative history. In closing, we discuss the possible relevance of such a thermodynamic principle for our understanding of self-organization in complex systems, paying particular attention to a possible analogy to the way evolutionary adaptations emerge in living things.

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“…Thus, entropy does not meet the following basic requirements: first, the requirements of the second law of thermodynamics that describes the fact and measure of the irreversibility, and second, requirements to the coordinate that must change simultaneously with the change of the potential (here, T) by analogy with coordinates working processes ([4], pp. [17][18][22][23].…”

Section: Entropy: Meaning and Expressionmentioning

confidence: 99%

“…For example, one of the founders of synergetics, Haken, wrote that "Shannon information is closely related to statistical entropy as introduced by Boltzmann" ( [21], p. 12). This led to the emergence of a large scientific direction holding this view, which has generated dozens of monographs and a huge number of scientific articles including works by M. Eigen [22] and I. Prigogine [23], and filled the entire…”

Section: The Second Law Of Thermodynamics and Biologymentioning

confidence: 99%

Chaos and Case or Implementation of the Program of Evolution of Space

Shterenberg¹

2016

OALib

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The classical concept of entropy is shown not to reflect the essence of the second law of thermodynamics both phenomenologically and theoretically. A new concept of entropy S n , is given, which offers a particular physical meaning of entropy and provides an experimental determination of the entropy value. At the same time, it is suggested not to define entropy but irreversibility-ω -as the key characteristic of thermodynamics second law for real processes. In addition, this article demonstrates that it is wrong to mechanically transfer the statistical concept and mathematical formula of the entropy to the field of real systems. This approach has led to incorrect basis for a number of theoretical sciences, which study both the phenomenon of life and the different systems-automates, computers, robots etc.-which model life's separate functions. This allows one to avoid many attempts at defining the phenomenon of life via entropy characteristics and give definitions of life and an elementary structure of both life itself and devices that simulate life (automata, computers, and robots). This, in turn, allows one to assign a substantive sense to the mathematical character of corresponding sciences (information theory, cybernetics, system theory, etc.) and define operational a single basic concepts of information, knowledge, meaning, and control, as well as to formulate operational concepts of order, organization, and self-organization and implement a new approach to problems of biology, biophysics, information theory, cybernetics, and system theory. Additionally, on the basis of scientific facts the evolution of the universe is considered as an implementation of the existing program, which allows a new approach to problems of world outlook and science, on the one hand, and a more efficient approach to the problem of genome decoding and to analysis of brain structure and its functioning in the immediate scientific practice, on the other hand.

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Biological order, structure and instabilities

Cited by 363 publications

References 35 publications

Patterns of Spatiotemporal Organization in an Allosteric Enzyme Model

Patterns of Spatiotemporal Organization in an Allosteric Enzyme Model

Statistical Physics of Adaptation

Chaos and Case or Implementation of the Program of Evolution of Space

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