Long Range Coherence and the Action of Enzymes

Fröhlich, H.

doi:10.1038/2281093a0

Cited by 290 publications

(142 citation statements)

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“…Such global stability property has not been addressed for the model proposed in Ref. [11][12][13], and seldom investigated in birhythmic systems (see Ref. [21] for an exception).…”

Section: Introductionmentioning

confidence: 99%

“…(1) to model coherent oscillations in biological systems, such as an enzymatic substrate reaction with ferroelectric behavior in brain waves models (see Ref. [11][12][13] for more details). In this case, one should include the electrical field applied to the excited enzymes, which depends for example on the external chemical influences (i.e., the flow of enzyme molecules through the transport phenomena).…”

Section: B the Model With Random Excitation And Algorithm For Numerimentioning

confidence: 99%

“…Perhaps the simplest model that exhibits birhythmicity is a variation of the well known van der Pol oscillator proposed by Kaiser [11] to model enzyme reactions. In such a model it has been shown that two attractors can coexist for some values of the parameters [11][12][13], and birhythmicity is robust enough to enable two [14] or more [15] oscillators to synchronize. The aim of this work is to adopt the Kaiser modification of the van der Pol oscillator [11,16,17] as a paradigm for birhythmicity to analyze the global stability properties of the attractors under the influence of random excitations, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Global stability analysis of birhythmicity in a self-sustained oscillator

Yamapi

Филатрелла

Aziz-Alaoui

2010

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We analyze global stability properties of birhythmicity in a self-sustained system with random excitations. The model is a multi-limit cycles variation of the van der Pol oscillator introduced to analyze enzymatic substrate reactions in brain waves. We show that the two frequencies are strongly influenced by the nonlinear coefficients α and β. With a random excitation, such as a Gaussian white noise, the attractor's global stability is measured by the mean escape time τ from one limit-cycle. An effective activation energy barrier is obtained by the slope of the linear part of the variation of the escape time τ versus the inverse noise-intensity 1/D. We find that the trapping barriers of the two frequencies can be very different, thus leaving the system on the same attractor for an overwhelming time. However, we also find that the system is nearly symmetric in a narrow range of the parameters. Some models employed to describe natural systems, such as for instance glycolysis reactions and circadian proteins rhythmics, exhibit spontaneous oscillations at two distinct frequencies. The phenomenon is known as birhythmicity, and the underlying dynamical structure is characterized by the coexistence of two stable attractors, each displaying a different frequency. Being the attractors locally stable, the system would however stay at a single frequency, the one selected by the choice of the initial conditions, unless an external source disturbs the evolution and causes a switch to the other attractor. To investigate such process, we have focused on a particular system of biological interest, a modified van der Pol oscillator (that displays birhythmicity), to determine the global stability properties of the attractors under the influence of noise. More specifically, we have characterized the stability of the attractors with the escape times, or the average time that the system requires to switch from an attractor to the other under the influence of random fluctuations. Such analysis reveals that the two attractors can possess very different properties, with very different relative residence times. Even excluding the most asymmetric cases, the system can spend something like 10 years on one attractor for each second spent on the other. We conclude that although a system can be structurally biorhythmic for the contemporary presence of two locally stable attractors at two different frequencies, actual switch from one frequency to the other could be very difficult to observe. A global stability analysis can therefore help to determine the region of the parameter space in which birhythmic behavior will be genuinely observed.

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“…Such global stability property has not been addressed for the model proposed in Ref. [11][12][13], and seldom investigated in birhythmic systems (see Ref. [21] for an exception).…”

Section: Introductionmentioning

confidence: 99%

Section: B the Model With Random Excitation And Algorithm For Numerimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Global stability analysis of birhythmicity in a self-sustained oscillator

Yamapi

Филатрелла

Aziz-Alaoui

2010

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…The obtained EIIP series represents the side-group-influenced changes of local environments along the backbone of the macromolecule, through which a hypothetical electrical impulse propagates [15,22]. The putative high-temperature superconductivity in proteins and DNA (proposed by Little [23]) could influence the long-distance intermolecular recognitions (proposed by Frolich [24]) and preselections, based on the information carried in their primary structures (proposed by Veljkovic [15,22]). …”

Section: The Informational Spectrum Methodsmentioning

confidence: 99%

Thymopoietins and long postsynaptic neurotoxins share common information in their primary structures

Skerl¹,

Pavlović²

1988

FEBS Letters

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The informational content of the primary structure of thymopoietin (TP) is investigated using the informational spectrum method (ISM). We show that the sequence of TP shares common information with the sequences of long postsynaptic snake neurotoxins, although no apparent similarity was found among their primary structures. The most sensitive point in the sequence of TP, concerning this information, is D-34, previously determined as being the residue responsible for TP's effect on neuromuscular transmission. Our results suggest that TP and long toxins recognize the neuromuscular nicotinic acetylcholine receptor (AChR) and/or bind to the AChR in a different mode than the short toxins do.

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“…The first step is determined by selective long-range forces that are efficient at a distance longer than one linear dimension of the interacting macromolecules (10 2 -10 3 Ǻ) [18][19][20]. These forces directly influence the number of productive collisions between interacting molecules.…”

Section: Electron-ion Interaction Potential (Eiip) and Average Quasivmentioning

confidence: 99%

Pomegranate (Punica granatum): a natural source for the development of therapeutic compositions of food supplements with anticancer activities based on electron acceptor molecular characteristics

Nicolson¹,

Veljković²,

Glišić³

et al. 2016

FFHD

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Citation: Veljkovic V.V., Glisic S., Perovic V., Veljkovic N., Nicolson G.L.. Pomegranate (Punica granatum): a natural source for the development of therapeutic compositions of food supplements with anticancer activities based on electron acceptor molecular characteristics. Health and Disease 2016; 6(12):769-787 ABSTRACT Background: Numerous in vitro and in vivo studies, in addition to clinical data, demonstrate that pomegranate juice can prevent or slow-down the progression of some types of cancers. Despite the well-documented effect of pomegranate ingredients on neoplastic changes, the molecular mechanism(s) underlying this phenomenon remains elusive. Functional Foods in Methods:For the study of pomegranate ingredients the electron-ion interaction potential (EIIP) and the average quasi valence number (AQVN) were used. These molecular descriptors can be used to describe the long-range intermolecular interactions in biological systems and can identify substances with strong electron-acceptor properties. In this study, candidate human proteins interacting with pomegranate flavonoids have been analyzed by the informational spectrum method (ISM). This represents a virtual spectroscopy method for studying protein molecular interactions.Results: Our analysis indicates that the anti-cancer properties of pomegranate juice can be ascribed to the strong electron-acceptor properties of its chemical ingredients. This analysis also suggests that pomegranate flavonoids inhibit the "NF-kappaB" (NF-κB) pathway, which plays a critical role in the pathogenesis of cancer. Conclusion:The results offer a possible explanation for an important molecular mechanism underlying the anticancer activity of pomegranate ingredients, which could also serve as a basis for the development of new therapeutic compositions of food supplements with pomegranatelike anticancer properties.Key words: cancer, pomegranate, flavonoids, food supplement, informational spectrum method BACKGROUND With more than 10 million new cases world-wide reported each year, cancer is one of the most devastating human diseases [1]. Despite progress in the understanding and treatment of these diseases including significant improvements in diagnostics and therapy based on applications of modern technology, the incidence and cure rates of various cancers, even in highly developed countries, have not improved significantly [2]. For this reason, increased attention has turned to complementary therapies, including natural dietary supplements. Among these natural agents, pomegranate (Punica granatum) juice has drawn a great deal of attention from both the scientific community and the general public due to its demonstrated ability to suppress cancers [3][4][5][6][7][8][9][10][11][12][13]. For example, pomegranate has been found to possess well-documented cancer chemopreventive and chemotherapeutic effects against prostate cancer [10][11][12][13]. The results of a Phase II clinical study of patients with rising prostate-specific antigen (PSA) levels following surgery or radiation ...

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Long Range Coherence and the Action of Enzymes

Cited by 290 publications

References 2 publications

Global stability analysis of birhythmicity in a self-sustained oscillator

Global stability analysis of birhythmicity in a self-sustained oscillator

Thymopoietins and long postsynaptic neurotoxins share common information in their primary structures

Pomegranate (Punica granatum): a natural source for the development of therapeutic compositions of food supplements with anticancer activities based on electron acceptor molecular characteristics

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