Entropic formulation for the protein folding process: hydrophobic stability correlates with folding rates

We assume that the protein folding process follows two autonomous steps: the conformational search for the native, mainly ruled by the hydrophobic effect; and, the final adjustment stage, which eventually gives stability to the native. Our main tool of investigation is a 3D lattice model provided with a ten-letter alphabet, the stereochemical model. This model was conceived for Monte Carlo (MC) simulations when one keeps in mind the kinetic behavior of protein-like chains in solution. In order to characterize the folding characteristic time ({\tau}) by two distinct sampling methods, first we present two sets of 10^{3} MC simulations for a fast protein-like sequence. For these sets of folding times, {\tau} and {\tau}_{q} were obtained with the application of the standard Metropolis algorithm (MA), and a modified algorithm (M_{q}A). The results for {\tau}_{q}reveal two things: i) the hydrophobic chain-solvent interactions plus a set of inter-residues steric constraints are enough to emulate the first stage of the process: for each one of the 10^{3} MC performed simulations, the native is always found without exception, ii) the ratio {\tau}_{q}/{\tau}~1/3 suggests that the effect of local thermal fluctuations, encompassed by the Tsallis weight, provides an innate efficiency to the chain escapes from energetic and steric traps. ...