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

A method based on the effective-medium approximation is developed for calculation of the low-frequency density of vibrational states, g(ω), in proteins. The calculated values of fractal exponent γ [g(ω)∼${\mathrm{\omega }}^{\gamma }$] are anomalously low (0<γ<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 γ value is the limited cross-chain connectivity in proteins, rather than the geometric arrangement of the polypeptide chain.