An efficient deformation-based global optimization method for off-lattice polymer chains: Self-consistent basin-to-deformed-basin mapping (SCBDBM). Application to united-residue polypeptide chains

A new method to surmount the multiple-minima problem in protein folding is proposed. Its underlying principle is to locate a group of large basins con taining low-energy minima (hereafter referred to as superbasins) in the ori ginal energy surface. This is achieved by coupling the superbasins in the o riginal surface to basins in a highly deformed energy surface (which contai ns a significantly reduced number of minima, compared to the original rugge d energy surface). The distance scaling method (DSM) and the diffusion equa tion method (DEM) have been implemented to carry out the deformation. The p rocedure consists of macroiterations in which the parameter a, that control s the deformation, changes between two extreme values, a(max) and a(min) (a =0 corresponds to the original energy surface). The first macroiteration is initialized by imposing a maximum deformation on the original surface and then selecting 10 randomly generated conformations in the maximally deforme d surface, whose energies are then minimized, usually leading to less than 10 minima; the next macroiterations are fed with the results of the previou s ones. Each macroiteration consists of the following steps: (i) reversal o f the deformation from a(max) to a(min); a limited search is carried out in the neighborhood of the minima at each stage of the reversal; (ii) collect ion of the new low-energy minima in the a(min)-deformed energy surface; (ii i) back-tracking these minima up to a,,, while increasing the deformation. Steps i - iii are iterated until no new minima are found in the undeformed surface, or a predefined number of iterations is exceeded. In the initial m acroiteration, a(min), is greater than 0, and a,, is chosen so that the def ormed energy surface has only a few minima. In each next macroiteration, th e new a(max) is set at a(min) of the previous macroiteration, and a(min), i s decreased, to reach 0 in the last macroiteration. The method was applied to united-residue polyalanine chains with a length of up to 100 amino acid residues, and to locate low-energy conformations of the 10-55 fragment of t he B-domain of staphylococcal protein A.