### Abstract

A geometric model is presented to interpret the anomalous T^{3+2m} temperature dependence of the Raman spin-lattice relaxation rates in heme and iron-sulfur proteins. Analysis of relaxation data is based on a modified Debye relationship between the spectral exponent m and the density of vibrational states ρ(v) ∝ v^{m-1}, where 0 ≤ v ≤ v_{max}. Magnetic relaxation measurements on cytochrome c-551 and putidaredoxin yield noninteger values of m that are influenced by changes in the ionic medium. The apparent physical significance of m is revealed, in part, by correlation to a protein's fractal geometry, which characterizes a repeating structural motif by a single parameter called the fractal dimension d̄. Estimates of d̄ for 70 proteins are computed by a method that identifies geometric and statistical self-similarities of α-carbon coordinates; values range within the limits (1 ≤ d̄ ≤ 2) of well-defined test structures and correlate principally with dominant elements of secondary structures. In six iron proteins, the highest values of m derived from relaxation data are approximated by the estimated values of d̄ calculated from the covalent structure. The interrelationship between the fractal models of protein structure and molecular dynamics, i.e., m = d̄, is also evident in the good agreement between the predicted ρ(v) ∝ v^{d̄-1} and the reported distribution of low-frequency normal modes (v ≤ 75 cm^{-1}) calculated for bovine pancreas trypsin inhibitor. The present findings indicate d̄ defines a fundamental parameter that is inherent to both the structural and dynamic properties of a protein.

Original language | English |
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Pages (from-to) | 5589-5594 |

Number of pages | 6 |

Journal | Journal of the American Chemical Society |

Volume | 107 |

Issue number | 20 |

Publication status | Published - 1985 |

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### ASJC Scopus subject areas

- Chemistry(all)

### Cite this

*Journal of the American Chemical Society*,

*107*(20), 5589-5594.