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

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Abstract
Two methods of computing the fractal dimension of biopolymer chains are compared for 50 proteins. The chain fractal dimension d̄ c is the scaling exponent of the contour length with respect to the end‐to‐end length, while the reentrant fractal dimension d̄ r scales the total mass with respect to distance. Electron spin relaxation data, which yield the spectral dimension d̃, reveal a strong correlation between d̄ c 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.