A fractal model of protein conformations and spectral exponents for the densities of low-frequency normal modes of vibration

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Abstract

Spectral exponents m defined in the power law relationship p(v)∝ vm-1 between the density of vibrational states p(v) and the frequency v at very low frequencies are calculated by means of the normal mode analysis of molecular mechanics for nine globular proteins. For the sake of comparison, fractal dimensions d̄ are also estimated from the backbone conformations of the same set of proteins. The results show that m and d̄ range from 1.53 to 1.77 and from 1.49 to 1.85, respectively, and well agree with the fractal model of protein conformations proposed by Stapleton et al. (Phys. Rev. Lett. 45 (1980) 1456), in which it is asserted that m is equal to d̄ and d̄ is close to the theoretical value 5/3 associated with a self-avoiding random walk.

Original languageEnglish
Pages (from-to)1926-1929
Number of pages4
JournalJournal of the Physical Society of Japan
Volume58
Issue number6
Publication statusPublished - 1989 Jun

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vibration mode
fractals
exponents
low frequencies
proteins
very low frequencies
random walk
vibrational states

Keywords

  • Fractal dimension
  • Molecular mechanics
  • Normal mode analysis
  • Protein conformation
  • Protein dynamics
  • Spectral exponent

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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title = "A fractal model of protein conformations and spectral exponents for the densities of low-frequency normal modes of vibration",
abstract = "Spectral exponents m defined in the power law relationship p(v)∝ vm-1 between the density of vibrational states p(v) and the frequency v at very low frequencies are calculated by means of the normal mode analysis of molecular mechanics for nine globular proteins. For the sake of comparison, fractal dimensions d̄ are also estimated from the backbone conformations of the same set of proteins. The results show that m and d̄ range from 1.53 to 1.77 and from 1.49 to 1.85, respectively, and well agree with the fractal model of protein conformations proposed by Stapleton et al. (Phys. Rev. Lett. 45 (1980) 1456), in which it is asserted that m is equal to d̄ and d̄ is close to the theoretical value 5/3 associated with a self-avoiding random walk.",
keywords = "Fractal dimension, Molecular mechanics, Normal mode analysis, Protein conformation, Protein dynamics, Spectral exponent",
author = "Hiroshi Wako",
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AU - Wako, Hiroshi

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AB - Spectral exponents m defined in the power law relationship p(v)∝ vm-1 between the density of vibrational states p(v) and the frequency v at very low frequencies are calculated by means of the normal mode analysis of molecular mechanics for nine globular proteins. For the sake of comparison, fractal dimensions d̄ are also estimated from the backbone conformations of the same set of proteins. The results show that m and d̄ range from 1.53 to 1.77 and from 1.49 to 1.85, respectively, and well agree with the fractal model of protein conformations proposed by Stapleton et al. (Phys. Rev. Lett. 45 (1980) 1456), in which it is asserted that m is equal to d̄ and d̄ is close to the theoretical value 5/3 associated with a self-avoiding random walk.

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