Scaling laws for folding native protein structures

We propose a nucleation hypothesis for protein folding. Based on this hypothesis, we have designed a new nearest-neighbor method for the prediction of protein secondary structures, in which the reliability of each prediction is estimated based on sequence conservation and clustering in the databases of known structures. We have found that predictions with higher reliability scores were indeed correlated with a higher predictive accuracy. We also found that by selecting the top 20% of residues based on reliability scores as nucleation residues, a clear pattern emerged where hydrophobic amino acids were largely buried and hydrophilic amino acids were more exposed. This was consistent with the widely accepted HP-model for protein folding. These results were true for several databases, such as PDBSELECT (<25% sequence homology), SCOP-ASTRAL (<25% sequence homology), and SCOP-ASTRAL unique fold classes, with 1300, 3956, and 762 proteins, respectively. Therefore, it is conceivable that the nucleation residues function not only as initiation sites for folding, but also as the core residues playing a primary role in determining the protein (thermodynamic) stability. The occurrence of these two functions on one set of amino acid residues in a protein is perhaps from the result of biological evolution. Finally, we have found power law behaviors in our results, whose scaling properties were modeled using polymer physics and critical phenomena. It is concluded that proteins behave like a real chain. A new physical picture for protein folding derived from our nucleation hypothesis has been described, in which there are two continuous phase transitions corresponding to the two stages of protein folding: one is nucleation and the other collapse. By determining the critical exponents of these two-phase transitions, it has been found that the nucleation process has a spatial dimension of d=3 while the collapse process of d=2.