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.

From the temperature dependence of the Orbach relaxation rate of the paramagnetic center in horseradish peroxidase (HRP), we deduce an excited-state energy of 40.9 +/- 1.1 K. Similar studies on the broad EPR signal of HRP compound I indicate a much weaker Orbach relaxation process involving an excited state at 36.8 +/- 2.5 K. The strength of the Orbach process in HRP-I is weaker than one would normally estimate by 2-4 orders of magnitude. This fact lends support to the model of HRP-I involving a spin 1/2 free radical coupled to a spin 1 Fe4+ heme iron via a weak exchange interaction. Such a system should exhibit an Orbach relaxation process involving delta E, the excited state of the Fe4+ ion, but reduced in strength by (Jyy/delta E)2, where Jyy is related to the strength of the exchange interaction between the two spin systems.

Two methods of computing the fractal dimension of biopolymer chains are compared for 50 proteins. The chain fractal dimension d̄c is the scaling exponent of the contour length with respect to the end-to-end length, while the reentrant fractal dimension d̄r scales the total mass with respect to distance. Electron spin relaxation data, which yield the spectral dimension d̃, reveal a strong correlation between d̄c and d̃. A study of the apparent value of d̃ for myoglobin azide under 11 solvent conditions is presented and explained in terms of a variation in the protein-solvent coupling. A sharp transition in the effective spectral dimension at T=6 K is interpreted as reflecting a crossover from vibrational modes of the solvent to those of the protein.

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Published relaxation data from ten samples of paramagnetic proteins are compared to illustrate the uncertainty which existed in identifying the anomalous low temperature relaxation mechanism in frozen solutions of proteins. Relaxation involving localized two level tunneling states or a phonon-limited direct process can explain the T2 temperature dependence of the relaxation rate that is observed in some proteins at temperatures above 1 K. Relaxation data on myoglobin at a microwave frequency of 16.545 GHz and in the temperature range between 0.4 and 1.2 K are presented. These data exhibit a coth2(ℏω/2kBT) dependence upon temperature and identify the relaxation process as phonon limited.