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

Abstract

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.