Rate of protein folding near the point of thermodynamic equilibrium between the coil and the most stable chain fold

Background: The problem of how a protein chain can find its most stable structure without exhaustive sorting of all its possible conformations is known as the 'Levinthal paradox'. The purpose of this paper is to elucidate this problem and to estimate the rate of folding to the most stable structure near the point of thermodynamic equilibrium between this structure and the coil. Results: Folding is rapid when it occurs in the vicinity of a thermodynamic 'all-or-none' transition from the coil to the lowest-energy fold: here the misfolded and semifolded states cannot 'trap' the folding chain since, even taken together, all these states are less stable than both the initial coil and the final stable fold of the chain. A stable globular structure can be rapidly achieved via a 'nucleation-and-growth' folding pathway that provides a continuous entropy-by-energy compensation along the folding pathway and thus provides a low free energy of the transition state. Conclusions: At the point of transition of the coil to the lowest-energy fold, an N-residue chain folds normally in similar to exp(N-2/3) ns. Therefore, a 100-residue chain finds its most stable fold within minutes rather than in 10(100) ps approximate to 10(80) years, according to the famous paradoxical estimate of Levinthal.