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}){~}ω^γ] 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.
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Elber et al. (1986) studied this question.
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