Fractal analysis of protein potential energy landscapes

Lidar, Daniel A.; Thirumalai, D.; Elber, Ron; Gerber, R. B.

doi:10.1103/physreve.59.2231

Cited by 28 publications

(29 citation statements)

References 15 publications

(24 reference statements)

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“…Our results corroborate some of those obtained by Hegger et al [19] and Lidar and collaborators [21], such as the influence of time and the presence of the α-helix in the rugosity of the time series. However, they also indicate that the other findings have not been confirmed, since the time simulation they used is much shorter than that used in this study and so insufficient to observe the formation of secondary structures.…”

Section: Discussionsupporting

confidence: 95%

Multifractal analysis of polyalanines time series

Figueirêdo¹,

Nogueira²,

Moret³

et al. 2010

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tMultifractal properties of the energy time series of short α-helix structures, specifically from a polyalanine family, are investigated through the MF-DFA technique (multifractal detrended fluctuation analysis). Estimates for the generalized Hurst exponent h(q) and its associated multifractal exponents τ (q) are obtained for several series generated by numerical simulations of molecular dynamics in different systems from distinct initial conformations. All simulations were performed using the GROMOS force field, implemented in the program THOR. The main results have shown that all series exhibit multifractal behavior depending on the number of residues and temperature. Moreover, the multifractal spectra reveal important aspects of the time evolution of the system and suggest that the nucleation process of the secondary structures during the visits on the energy hyper-surface is an essential feature of the folding process.

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Section: Discussionsupporting

confidence: 95%

Multifractal analysis of polyalanines time series

Figueirêdo¹,

Nogueira²,

Moret³

et al. 2010

Physica A: Statistical Mechanics and its Applications

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“…͑3͒ and how the dynamics varies on different length scales, embodied in the specific elastic and friction dispersion relations q and q . Similarly, there exist complementary methods that attempt to analyze the complexity of the multidimensional energy landscape, for example, by looking at fluctuations in the total potential energy in time; 27,28 however, these studies show that the emergent fractal behavior is insensitive to global dynamics and only represent intermode coupling from anharmonicity of the local potentials.…”

Section: Discussionmentioning

confidence: 99%

Fluctuation power spectra reveal dynamical heterogeneity of peptides

Khatri

Yew

Krivov

et al. 2010

The Journal of Chemical Physics

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Emanuele (2010) 'Fluctuation power spectra reveal dynamical heterogeneity of peptides.', Journal of chemical physics., 133 (1). 015101.Further information on publisher's website: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

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“…Equations containing fractal operators are used to analyze the behavior of systems characterized by: (1) power-law nonlinearity (2) power-law long-range spatial correlations or long-term memory (3) fractal or multi-fractal properties [22]. During the last years, the number of applications of fractional dynamics in science and particularly in physics has been steadily growing and include models of fractional relaxation and oscillation phenomena, anomalous transport in fluids and plasma, wave propagation in complex media, viscoelastic materials, non-Markovian evolution of quantum fields, networks of fractional oscillators and so on [23][24][25][26][27][28][29].…”

Section: Fractality and Fractionalitymentioning

confidence: 99%

“…In recent years fractal geometry analysis has attracted attention of biologist as a useful and desirable tool to characterize the configuration and structure of biological structures. The considered issues include: fractal geometry analysis of configuration, structure and diffusion of proteins [24][25][26][27][28][29], fractal analysis of the DNA sequence, walks and aggregation [30][31][32][33][34] and fractal model of light scattering in biological tissue and cells [35]. (…”

Section: -1 Fractalitymentioning

confidence: 99%

Fractional Dynamics in Bioscience and Biomedicine and the Physics of Cancer

Nasrolahpour

2017

Preprint

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Almost all phenomena and structures in nature exhibit some degrees of fractionality or fractality. Fractional calculus and fractal theory are two interrelated concepts. In this article we study the memory effects in nature and particularly in biological structures. Based on this fact that natural way to incorporate memory effects in the modeling of various phenomena and dealing with complexities is using of fractional calculus, in this article we present different examples in various branch of science from cosmology to biology and we investigate this idea that are we able to describe all of such these phenomena using the well-know and powerful tool of fractional calculus. In particular we focus on fractional calculus approach as an effective tool for better understanding of physics of living systems and organism and especially physics of cancer.Keywords: Fractional Dynamics; Memory Effect; Biological Structures; Physics of Cancer IntroductionThe concept of memory effect plays an important role in a large number of phenomena in different contexts and systems from biological structures to cosmological phenomena. For instance: memory effects in nanoscale systems [1,2], optical memory effect [3], gravitational and cosmological memory effect (which means: the induction of a permanent change in the relative separation of the test particles when gravitational radiation passes through a configuration of test particles that make up a gravitational wave detector) [4], memory effects in gene regulatory networks [5], memory effects in economics [6] have been investigated. In addition other kinds of memory effect including: shape memory effect [7][8][9][10], magnetic shape memory effect [11] and temperature memory effect [12] have been also considered in recent years. In all above mentioned references authors have used the standard calculus, however nowadays it is well-known that a natural way to incorporate memory effects in the modeling of various phenomena is using of fractional calculus. On the other hand almost all phenomena and structures in nature exhibit some degrees and levels of fractionality or fractality (low or high level or something between them), also nowadays it is well-known that there is a close relation between fractality and fractionality. In this work we investigate this idea that are we able to describe all of such these phenomena using the well-know and powerful tool of fractional calculus. Therefore for this purpose in the following, concepts of fractality and fractional dynamics are briefly reviewed respectively in Sec. 2.Then in Sec. 3 we introduce fractional calculus as a powerful tool for modeling of memory effects in different context and we present some important applications. At last, in Sec. 4, we will present some conclusions.

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Fractal analysis of protein potential energy landscapes

Cited by 28 publications

References 15 publications

Multifractal analysis of polyalanines time series

Multifractal analysis of polyalanines time series

Fluctuation power spectra reveal dynamical heterogeneity of peptides

Fractional Dynamics in Bioscience and Biomedicine and the Physics of Cancer

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