Exploring the similarities between potential smoothing and simulated annealing

Simulated annealing and potential function smoothing are two widely used approaches for global energy optimization of molecular systems. Potential smoothing as implemented in the diffusion equation method has been applied to study partitioning of the potential energy surface (PES) for N‐Acetyl‐Ala‐Ala‐N‐Methylamide (CDAP) and the clustering of conformations on deformed surfaces. A deformable version of the united‐atom OPLS force field is described, and used to locate all local minima and conformational transition states on the CDAP surface. It is shown that the smoothing process clusters conformations in a manner consistent with the inherent structure of the undeformed PES. Smoothing deforms the original surface in three ways: structural shifting of individual minima, merging of adjacent minima, and energy crossings between unrelated minima. A master equation approach and explicit molecular dynamics trajectories are used to uncover similar features in the equilibrium probability distribution of CDAP minima as a function of temperature. Qualitative and quantitative correlations between the simulated annealing and potential smoothing approaches to enhanced conformational sampling are established. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 531–552, 2000

[1]  Jianpeng Ma,et al.  Simulated annealing using the classical density distribution , 1994 .

[2]  D. Wales,et al.  From Topographies to Dynamics on Multidimensional Potential Energy Surfaces of Atomic Clusters , 1996, Science.

[3]  Jonathan Doye,et al.  Thermodynamics of Global Optimization , 1998 .

[4]  Stuart A. Rice,et al.  Theory of Unimolecular Reactions , 1960 .

[5]  Berry,et al.  Topography and Dynamics of Multidimensional Interatomic Potential Surfaces. , 1995, Physical review letters.

[6]  Panos M. Pardalos,et al.  Recent Advances in Global Optimization , 1991 .

[7]  P. Wolynes,et al.  The energy landscapes and motions of proteins. , 1991, Science.

[8]  Keith D. Ball,et al.  Realistic master equation modeling of relaxation on complete potential energy surfaces: Kinetic results , 1998 .

[9]  C. Brooks,et al.  Cluster structure determination using Gaussian density distribution global minimization methods , 1994 .

[10]  P. Hänggi,et al.  Reaction-rate theory: fifty years after Kramers , 1990 .

[11]  Straub,et al.  Energy minimization using the classical density distribution: Application to sodium chloride clusters. , 1996, Physical review. B, Condensed matter.

[12]  Mark A. Miller,et al.  Archetypal energy landscapes , 1998, Nature.

[13]  John E. Straub,et al.  FOLDING MODEL PROTEINS USING KINETIC AND THERMODYNAMIC ANNEALING OF THE CLASSICAL DENSITY DISTRIBUTION , 1995 .

[14]  G. Ulrich Nienhaus,et al.  Multiplexed-Replica Exchange Molecular Dynamics with the UNRES Force-Field as an Effective Method for Exploring the Conformational Energy Landscape of Proteins. , 2006 .

[15]  D. Thirumalai,et al.  Metastability of the folded states of globular proteins. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[16]  R. Elber,et al.  Reaction path study of conformational transitions in flexible systems: Applications to peptides , 1990 .

[17]  M. Mézard,et al.  A first-principle computation of the thermodynamics of glasses , 1998, cond-mat/9812180.

[18]  Emile H. L. Aarts,et al.  Simulated Annealing: Theory and Applications , 1987, Mathematics and Its Applications.

[19]  M. Karplus,et al.  Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics , 1988 .

[20]  M. Karplus,et al.  CHARMM: A program for macromolecular energy, minimization, and dynamics calculations , 1983 .

[21]  D. Wales,et al.  Theoretical study of the water pentamer , 1996 .

[22]  Lorenz T. Biegler,et al.  Large-Scale Optimization with Applications , 1997 .

[23]  J. Onuchic,et al.  Theory of protein folding: the energy landscape perspective. , 1997, Annual review of physical chemistry.

[24]  K. Dill,et al.  From Levinthal to pathways to funnels , 1997, Nature Structural Biology.

[25]  J. Barker,et al.  What is "liquid"? Understanding the states of matter , 1976 .

[26]  J. Straub,et al.  Theoretical probes of conformational fluctuations in S‐peptide and RNase A/3′–UMP enzyme product complex , 1993, Proteins.

[27]  Structural and ultrametric properties of (L-alanine)20 , 1993, cond-mat/9303022.

[28]  Jonathan P. K. Doye,et al.  On potential energy surfaces and relaxation to the global minimum , 1996 .

[29]  H. Scheraga,et al.  Conformational analysis of the 20 naturally occurring amino acid residues using ECEPP. , 1977, Macromolecules.

[30]  David Sherrington.  Landscape paradigms in physics and biology: Introduction and overview , 1996 .

[31]  M. Karplus,et al.  The topology of multidimensional potential energy surfaces: Theory and application to peptide structure and kinetics , 1997 .

[32]  H. Scheraga,et al.  Performance of the diffusion equation method in searches for optimum structures of clusters of Lennard-Jones atoms , 1991 .

[33]  M. Karplus,et al.  Crystallographic R Factor Refinement by Molecular Dynamics , 1987, Science.

[34]  Kurt Binder,et al.  Monte Carlo Simulation in Statistical Physics , 1992, Graduate Texts in Physics.

[35]  W. L. Jorgensen,et al.  The OPLS [optimized potentials for liquid simulations] potential functions for proteins, energy minimizations for crystals of cyclic peptides and crambin. , 1988, Journal of the American Chemical Society.

[36]  G. Toulouse,et al.  Ultrametricity for physicists , 1986 .

[37]  Ron Elber.  Recent Developments In Theoretical Studies Of Proteins , 1996 .

[38]  D. Thirumalai,et al.  Dynamics in Rugged Energy Landscapes with Applications to the S-Peptide and Ribonuclease A , 1994 .

[39]  R Elber,et al.  Reaction path study of conformational transitions and helix formation in a tetrapeptide. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[40]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[41]  D Thirumalai,et al.  Exploring the energy landscape in proteins. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[42]  J. Doye,et al.  Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms , 1997, cond-mat/9803344.

[43]  Jay W. Ponder,et al.  Analysis and Application of Potential Energy Smoothing and Search Methods for Global Optimization , 1998 .

[44]  I. Andricioaei,et al.  Global optimization using bad derivatives: Derivative‐free method for molecular energy minimization , 1998 .

[45]  J. Ponder,et al.  An efficient newton‐like method for molecular mechanics energy minimization of large molecules , 1987 .

[46]  Peter S. Shenkin,et al.  Cluster analysis of molecular conformations , 1994, J. Comput. Chem..

[47]  Thirumalai,et al.  Ergodic behavior in supercooled liquids and in glasses. , 1989, Physical review. A, General physics.

[48]  H. Scheraga,et al.  Monte Carlo-minimization approach to the multiple-minima problem in protein folding. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[49]  H. Scheraga,et al.  On the multiple-minima problem in the conformational analysis of molecules: deformation of the potential energy hypersurface by the diffusion equation method , 1989 .