  In this paper we analyze the vibrational spectra of a large ensemble of
non-homologous protein structures by means of a novel tool, that we coin the
Hierarchical Network Model (HNM). Our coarse-grained scheme accounts for the
intrinsic heterogeneity of force constants displayed by protein arrangements
and also incorporates side-chain degrees of freedom.
  Our analysis shows that vibrational entropy per unit residue correlates with
the content of secondary structure. Furthermore, we assess the individual
contribution to vibrational entropy of the novel features of our scheme as
compared with the predictions of state-of-the-art network models. This analysis
highlights the importance of properly accounting for the intrinsic hierarchy in
force strengths typical of the different atomic bonds that build up and
stabilize protein scaffolds.
  Finally, we discuss possible implications of our findings in the context of
protein aggregation phenomena.
