Low-frequency modes in proteins: Use of the effective-medium approximation to interpret the fractal dimension observed in electron-spin relaxation measurements

Abstract

A method based on the effective-medium approximation is developed for calculation of the low-frequency density of vibrational states, g(\ensuremath{\omega}), in proteins. The calculated values of fractal exponent \ensuremath{\gamma} [g(\ensuremath{\omega})\ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}^{\ensuremath{\gamma}}$] are anomalously low (0<\ensuremath{\gamma}<1) in accord with estimates from measurements of the electron-spin relaxation time in low-spin ferric proteins. The essential element leading to the low \ensuremath{\gamma} value is the limited cross-chain connectivity in proteins, rather than the geometric arrangement of the polypeptide chain.