Reduction of the Search Space for the Folding of Proteins at the Level of Formation and Assembly of Secondary Structures: A New View on the Solution of Levinthal′s Paradox

The complete volume of the protein conformation space is, by many orders of magnitude, smaller at the level of secondary structure elements than that at the level of amino acid residues; the latter, according to Levinthal′s estimate, scales approximately as 10^{2 L}, with L being the number of residues in the chain, whereas the former, as demonstrated in this paper, scales no faster than ～L^N, with N being the number of the secondary structure elements, which is approximately equal to L/15. This drastic decrease in the exponent (L/15 instead of 2 L) explains why sampling of the conformation space does not contradict the ability of the protein chain to find its most stable fold.