Topological thermal instability and length of proteins

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 their spectral dimension, a parameter describing the low frequency behavior of the density of modes. We found a surprisingly strong correlation between the spectral dimension and the number of amino acids in the protein. Considering that larger spectral dimension values relate to more topologically com- pact folded states, our results indicate that, for a given temperature and length of protein, the folded structure corresponds to a less compact folding, one compatible with thermodynamic stability.