Proteins as fractals: Role of the hydrodynamic interaction

Exploiting the fractal nature of folded proteins, we study the effect of the hydrodynamic interaction between amino acids using a Zimm-type model. We compute the time-dependent mean square displacement of an amino acid and the time-dependent autocorrelation function of the distance between two amino acids, and we show that these dynamic quantities evolve anomalously, similar to the Rouse-type behavior, yet with modified dynamic exponents. Good agreement is found with recent neutron spin-echo studies of myoglobin and hemoglobin.