A Fractal Model of Protein Conformations and Spectral Exponents for the Densities of Low-Frequency Normal Modes of Vibration

Spectral exponents m defined in the power law relationship [formula omitted] between the density of vibrational states p(v) and the frequency v at very low frequencies are calculated by means of the normal mode analysis of molecular mechanics for nine globular proteins. For the sake of comparison, fractal dimensions d are also estimated from the backbone conformations of the same set of proteins. The results show that m and d range from 1.53 to 1.77 and from 1.49 to 1.85, respectively, and well agree with the fractal model of protein conformations proposed by Stapleton et al. (Phys. Rev. Lett. 45 (1980) 1456), in which it is asserted that m is equal to d and d is close to the theoretical value 5/3 associated with a self-avoiding random walk.