Fractal Models of Protein Structure, Dynamics, and Magnetic Relaxation

Gerald C. Wagner, Harvey J. Stapleton, J. Trevor Colvin, James P. Allen

Research output: Contribution to journalArticlepeer-review

67 Scopus citations


A geometric model is presented to interpret the anomalous T3+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) ∝ νm-1, where 0 ≤ v ≤ νmax. 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 ofm 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 d. Estimates of d for 70 proteins are computed by a method that identifies geometric and statistical self-similarities of a-carbon coordinates; values range within the limits (1 ≤d ≤2) of well-defined test structures and correlate principally with dominant elements of secondary structures. In six iron proteins, the highest values ofm derived from relaxation data are approximated by the estimated values ofd calculated from the covalent structure. The interrelationship between the fractal models of protein structure and molecular dynamics, i.e.,m = d, is also evident in the good agreement between the predicted p(v) ∝vd-1and the reported distribution of low-frequency normal modes (v ≤ 75 cm-1) calculated for bovine pancreas trypsin inhibitor. The present findings indicated defines a fundamental parameter that is inherent to both the structural and dynamic properties of a protein.

Original languageEnglish (US)
Pages (from-to)5589-5594
Number of pages6
JournalJournal of the American Chemical Society
Issue number20
StatePublished - Oct 1985
Externally publishedYes

ASJC Scopus subject areas

  • Catalysis
  • General Chemistry
  • Biochemistry
  • Colloid and Surface Chemistry


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