Electron spin relaxation data from five ferric proteins are analyzed in terms of the fractal model of protein structures. Details of this model are presented. The results lead to a characterization of protein structures by a single parameter, the fractal dimension, d. This structural parameter is shown to determine the temperature dependence of the Raman electron spin relaxation rate, which varies as T3 + 2d. Computations of d are made using x-ray data for 17 proteins. The results range from d = 1.76 for lysozyme to d = 1.34 for ferredoxin. These values are compared with values of d obtained from the present electron spin relaxation data on five ferric proteins. Typical results are d = 1.34 +/- 0.06 from relaxation data and 1.34 +/- 0.05 from x-ray data for ferredoxin; d = 1.67 +/- 0.03 from relaxation data and 1.66 +/- 0.05 from x-ray data for ferricytochrome c. The data thus support the theoretical model. Applications of this spin resonance technique to the study of changes in protein conformation are discussed.
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