Origin of the lognormal shape in the boson-peak of globular proteins

We propose an explanation for the origin of the lognormal shape in the boson-peak anomaly of globular proteins. The origin is ascribed to a distribution of quasi-localization lengths for acoustic waves within the protein. The local densities of states for different sites display logarithmic singularities in this range. The distribution of these singularities, however, follows a lognormal distribution. This seems to be a universal characteristic for quasi-two dimensional random networks, which are used to model the protein dynamics. This interpretation makes explicit contact with well established models for the boson-peak anomaly in glasses and/or amorphous solids.