We present an analysis of the effects of global topology on the structural
stability of folded proteins in thermal equilibrium with a heat bath. For a
large class of single domain proteins, we computed the harmonic spectrum within
the Gaussian Network Model (GNM) and determined the spectral dimension, a
parameter describing the low frequency behaviour of the density of modes. We
find a surprisingly strong correlation between the spectral dimension and the
number of amino acids of the protein. Considering that larger spectral
dimension value relate to more topologically compact folded state, our results
indicate that for a given temperature and length of the protein, the folded
structure corresponds to the less compact folding compatible with thermodynamic
stability.Comment: 15 pages, 6 eps figures, 2 table
