Analysis and Application of Potential Energy Smoothing and Search
Methods for Global Optimization
Rohit V. Pappu, Reece K. Hart, and Jay W. Ponder
Department of Biochemistry and Molecular Biophysics
Washington University School of Medicine
St. Louis, Missouri 63110
Submitted 1998/02/18
Abstract
Global energy optimization of a molecular system is difficult due to the
well-known "multiple minimum" problem. The rugged potential energy surface
(PES) characteristic of multidimensional systems can be transformed
reversibly using potential smoothing to generate a new surface that is
easier to search for favorable configurations. The Diffusion Equation
Method (DEM) is one example of a potential smoothing algorithm. Potential
smoothing as implemented in DEM is intuitively appealing and has certain
appropriate statistical mechanical properties, but often fails to identify
the global minimum even for relatively small problems. In the present
paper, extensions to DEM capable of correcting its empirical behavior are
systematically investigated. Two types of local search (LS) procedures are
applied during the reversing schedule from the smooth deformed PES to the
undeformed surface. Changes needed to generate smoothable versions of
standard molecular mechanics force fields such as AMBER/OPLS and MM2 are
also described. The resulting methods are applied in an attempt to
determine the global energy minimum for a variety of systems in different
coordinate representations. The problems studied include argon clusters,
cycloheptadecane, capped polyalanine, and the docking of
a-helices. Depending on the specific problem, Potential Smoothing and
Search (PSS) is performed in Cartesian, torsional or rigid body space. For
example, PSS finds a very low energy structure for cycloheptadecane with
much greater efficiency than a search restricted to the undeformed
potential surface. It is shown that potential smoothing is characterized
by three salient features. As the level of smoothing is increased unique
minima merge into a common basin, crossings can occur in the relative
energies of a pair of minima, and the spatial locations of minima are
shifted due to the averaging effects of smoothing. Local search procedures
improve the ability of smoothing methods to locate global minima because
they facilitate the post facto correction of errors due to energy
crossings that may have occurred at higher levels of smoothing. PSS
methods should serve as useful tools for global energy optimization on a
variety of difficult problems of practical interest.