Fractal and spectral dimensions of biopolymer chains: Solvent studies of electron spin relaxation rates in myoglobin azide

Colvin, J. T.; Stapleton, H. J.

doi:10.1063/1.448679

Cited by 61 publications

(27 citation statements)

References 10 publications

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“…This historical perspective helps us to understand why two of the most fundamental forms of protein information, namely, the primary structure and three-dimensional structure of proteins, respectively [16][17][18], were chosen for study in preliminary investigations. The school of primary structure studies owes its origin to polymer research and focuses primarily upon examining fractal properties within backbone connectivity.…”

Section: Schools Of Protein Interior Fractal Studiesmentioning

confidence: 99%

Fractal symmetry of protein interior: what have we learned?

Banerji

Ghosh

2011

Cell. Mol. Life Sci.

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The application of fractal dimension-based constructs to probe the protein interior dates back to the development of the concept of fractal dimension itself. Numerous approaches have been tried and tested over a course of (almost) 30 years with the aim of elucidating the various facets of symmetry of self-similarity prevalent in the protein interior. In the last 5 years especially, there has been a startling upsurge of research that innovatively stretches the limits of fractal-based studies to present an array of unexpected results on the biophysical properties of protein interior. In this article, we introduce readers to the fundamentals of fractals, reviewing the commonality (and the lack of it) between these approaches before exploring the patterns in the results that they produced. Clustering the approaches in major schools of protein self-similarity studies, we describe the evolution of fractal dimension-based methodologies. The genealogy of approaches (and results) presented here portrays a clear picture of the contemporary state of fractal-based studies in the context of the protein interior. To underline the utility of fractal dimension-based measures further, we have performed a correlation dimension analysis on all of the available non-redundant protein structures, both at the level of an individual protein and at the level of structural domains. In this investigation, we were able to separately quantify the self-similar symmetries in spatial correlation patterns amongst peptide-dipole units, charged amino acids, residues with the π-electron cloud and hydrophobic amino acids. The results revealed that electrostatic environments in the interiors of proteins belonging to 'α/α toroid' (all-α class) and 'PLP-dependent transferase-like' domains (α/β class) are highly conducive. In contrast, the interiors of 'zinc finger design' ('designed proteins') and 'knottins' ('small proteins') were identified as folds with the least conducive electrostatic environments. The fold 'conotoxins' (peptides) could be unambiguously identified as one type with the least stability. The same analyses revealed that peptide-dipoles in the α/β class of proteins, in general, are more correlated to each other than are the peptide-dipoles in proteins belonging to the all-α class. Highly favorable electrostatic milieu in the interiors of TIM-barrel, α/β-hydrolase structures could explain their remarkably conserved (evolutionary) stability from a new light. Finally, we point out certain inherent limitations of fractal constructs before attempting to identify the areas and problems where the implementation of fractal dimension-based constructs can be of paramount help to unearth latent information on protein structural properties.

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Section: Schools Of Protein Interior Fractal Studiesmentioning

confidence: 99%

Fractal symmetry of protein interior: what have we learned?

Banerji

Ghosh

2011

Cell. Mol. Life Sci.

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“…In mathematics, the support of a quantity is the set S where that quantity is nonzero. Many soft-condensed matter systems as proteins [6], polymers in general [7], and diffusion limited aggregates [8] have in physical space fractal structures with dimension D < 3. They are formed from large number of units glued together by short-range covalent chemical forces and/or van der Waals forces.…”

Section: Introductionmentioning

confidence: 99%

Condensation of elastic energy in two-dimensional packing of wires

Donato

Gomes

2007

Phys. Rev. E

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Forced packing of a long metallic wire injected into a two-dimensional cavity leads to crushed structures involving a hierarchical cascade of loops with varying curvature radii. We study the distribution of elastic energy stored in such systems from experiments, and high-resolution digital techniques. It is found that the set where the elastic energy of curvature is concentrated has dimension DS = 1.0 ± 0.1, while the set where the mass is distributed, has dimension D = 1.9 ± 0.1.

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“…The solid and dashed lines correspond to the best fits of Eqs. [1] and [2], respectively. It is seen that, except for hematin-NO, both fits to the experimental data are equivalent The EPR spectra were obtained as a function of temperature and microwave power.…”

Section: Resultsmentioning

confidence: 98%

“…[1] fits almost all samples analyzed in Table 1, we estimate the values of T 1 using this equation. Equation [2] would not yield significantly different results.…”

Section: Resultsmentioning

confidence: 99%

“…These results The observed temperature dependence of the spin-lattice relaxation (SLR) time, T 1 , of metalloproteins is of the T n , stimulated the investigation of the SLR mechanism of denatured hemeproteins, in search of information on excitations Raman type with n, however, related to the fractal dimension of the polymers (1). Relaxation of denatured azide methe-and dynamics of their disrupted structure which has no physiological function.…”

Section: Introductionmentioning

confidence: 92%

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