Fractal and spectral dimensions of biopolymer chains: Solvent studies of electron spin relaxation rates in myoglobin azide

Two methods of computing the fractal dimension of biopolymer chains are compared for 50 proteins. The chain fractal dimension dc is the scaling exponent of the contour length with respect to the end‐to‐end length, while the reentrant fractal dimension dr scales the total mass with respect to distance. Electron spin relaxation data, which yield the spectral dimension d, reveal a strong correlation between dc and d. A study of the apparent value of d 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.