J

J. Phys. Chem. B, 103 ( 34 ), 7353 - 7366 , 1999 . 10.1021/jp991014y S1089-5647(99)01014-7
Web Release Date: August 10, 1999

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

Jaroslaw Pillardy, Adam Liwo, Malgorzata Groth,and Harold A. Scheraga*

Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, and Department of Chemistry, University of Gdask, ul. Sobieskiego 18, 80-952 Gdask, Poland

Received: March 24, 1999

In Final Form: June 9, 1999

Abstract:

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 containing low-energy minima (hereafter referred to as superbasins) in the original energy surface. This is achieved by coupling the superbasins in the original surface to basins in a highly deformed energy surface (which contains a significantly reduced number of minima, compared to the original rugged energy surface). The distance scaling method (DSM) and the diffusion equation method (DEM) have been implemented to carry out the deformation. The procedure consists of macroiterations in which the parameter a, that controls 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 deformed surface, whose energies are then minimized, usually leading to less than 10 minima; the next macroiterations are fed with the results of the previous ones. Each macroiteration consists of the following steps: (i) reversal of 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) collection of the new low-energy minima in the a_min-deformed energy surface; (iii) back-tracking these minima up to a_max 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 macroiteration, a_min is greater than 0, and a_max is chosen so that the deformed energy surface has only a few minima. In each next macroiteration, the new a_max is set at a_min of the previous macroiteration, and a_min is 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 the B-domain of staphylococcal protein A.