Efficiency of monte carlo minimization procedures and their use in analysis of NMR data obtained from flexible peptides

The Monte Carlo minimization (MCM) method of Li and Scheraga is an efficient tool for generating low energy minimized structures of peptides, in particular the global energy minimum (GEM). In a recent article we proposed an enhancement to MCM, called the free energy Monte Carlo minimization (FMCM) procedure. With FMCM the conformational search is carried out with respect to the harmonic free energy, which approximates the free energy of the potential energy wells around the energy minimized structures (these wells are called localized microstates). In this work we apply both methods to the pentapeptide Leu‐enkephalin described by the potential energy function ECEPP, and study their efficiency in identifying the GEM structure as well as the global harmonic free energy (GFM) structure. We also investigate the efficiency of these methods to generate localized microstates, which pertain to different energy and harmonic free energy intervals above the GEM and GFM, respectively. Such microstates constitute an important ingredient of our statistical mechanical methodology for analyzing nuclear magnetic resonance data of flexible peptides. Aspects of this methodology related to the stability properties of the localized microstates are examined. © 1997 by John Wiley & Sons, Inc.

[1]  M. Saunders.  Stochastic exploration of molecular mechanics energy surfaces. Hunting for the global minimum , 1987 .

[2]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

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

[4]  Saul Wolfe,et al.  A COMPREHENSIVE APPROACH TO THE CONFORMATIONAL ANALYSIS OF CYCLIC COMPOUNDS , 1994 .

[5]  E. Meirovitch,et al.  New theoretical methodology for elucidating the solution structure of peptides from NMR data. II. Free energy of dominant microstates of Leu-enkephalin and population-weighted average nuclear Overhauser effects intensities. , 1996, Biopolymers.

[6]  B. Berg,et al.  Multicanonical algorithms for first order phase transitions , 1991 .

[7]  D. Ferguson,et al.  A new approach to probing conformational space with molecular mechanics: Random incremental pulse search , 1989 .

[8]  Thomas A. Weber,et al.  Inherent structure in water , 1983 .

[9]  H. Kessler,et al.  Coupling constants as restraints in ensemble distance driven dynamics , 1994 .

[10]  R Brüschweiler,et al.  Conformational backbone dynamics of the cyclic decapeptide antamanide. Application of a new multiconformational search algorithm based on NMR data. , 1993, Biochemistry.

[11]  Wilfred F. van Gunsteren,et al.  Conformational search by potential energy annealing: Algorithm and application to cyclosporin A , 1992, J. Comput. Aided Mol. Des..

[12]  F. Stillinger,et al.  Packing Structures and Transitions in Liquids and Solids , 1984, Science.

[13]  A Caflisch,et al.  Monte carlo minimization with thermalization for global optimization of polypeptide conformations in cartesian coordinate space , 1992, Proteins.

[14]  Harold A. Scheraga,et al.  On the Use of Classical Statistical Mechanics in the Treatment of Polymer Chain Conformation , 1976 .

[15]  W. Braun,et al.  Surface area included in energy refinement of proteins. A comparative study on atomic solvation parameters. , 1993, Journal of molecular biology.

[16]  Harold A. Scheraga,et al.  The multiple-minima problem in the conformational analysis of polypeptides. III. An Electrostatically Driven Monte Carlo Method: Tests on enkephalin , 1989, Journal of protein chemistry.

[17]  H. Meirovitch,et al.  Computer simulation of the free energy of peptides with the local states method: Analogues of gonadotropin releasing hormone in the random coil and stable states , 1994, Biopolymers.

[18]  Martin Saunders,et al.  Conformations of cycloheptadecane. A comparison of methods for conformational searching , 1990 .

[19]  Hagai Meirovitch,et al.  A Simple and Effective Procedure for Conformational Search of Macromolecules: Application to Met- and Leu-Enkephalin , 1994 .

[20]  Arnold T. Hagler,et al.  Computer simulation of the conformational properties of oligopeptides. Comparison of theoretical methods and analysis of experimental results , 1979 .

[21]  D. Case.  Normal mode analysis of protein dynamics , 1994 .

[22]  R. Brüschweiler,et al.  Multi-conformational peptide dynamics derived from NMR data: A new search algorithm and its application to antamanide , 1991, Journal of biomolecular NMR.

[23]  E. Meirovitch,et al.  New theoretical methodology for elucidating the solution structure of peptides from NMR data. 1. The relative contribution of low-energy microstates to the partition function , 1995 .

[24]  H. Meirovitch.  A new method for simulation of real chains: scanning future steps , 1982 .

[25]  Clark R. Landis,et al.  Elucidation of solution structures by conformer population analysis of NOE data , 1991 .

[26]  P Argos,et al.  Optimal protocol and trajectory visualization for conformational searches of peptides and proteins. , 1992, Journal of molecular biology.

[27]  M. Symons.  Decarboxylation of acetate ions , 1983 .

[28]  Harold A. Scheraga,et al.  Structure and free energy of complex thermodynamic systems , 1988 .

[29]  Hagai Meirovitch,et al.  New Theoretical Methodology for Elucidating the Solution Structure of Peptides from NMR Data. 3. Solvation Effects , 1996 .

[30]  G. Chang,et al.  An internal-coordinate Monte Carlo method for searching conformational space , 1989 .

[31]  Akbar Nayeem,et al.  A comparative study of the simulated‐annealing and Monte Carlo‐with‐minimization approaches to the minimum‐energy structures of polypeptides: [Met]‐enkephalin , 1991 .

[32]  Harold A. Scheraga,et al.  Analysis of the Contribution of Internal Vibrations to the Statistical Weights of Equilibrium Conformations of Macromolecules , 1969 .

[33]  H. Meirovitch.  Calculation of entropy with computer simulation methods , 1977 .

[34]  Werner Braun,et al.  Minimization of empirical energy functions in proteins including hydrophobic surface area effects , 1993, J. Comput. Chem..

[35]  M. Karplus,et al.  Molecular dynamics simulations in biology , 1990, Nature.

[36]  Hagai Meirovitch,et al.  A free energy based Monte Carlo minimization procedure for biomolecules , 1994 .

[37]  Computer simulation of the entropy of polypeptides using the local states method: application to cyclo-(Ala-Pro-D-Phe)2 in vacuum and in the crystal , 1992 .

[38]  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.

[39]  H. Scheraga,et al.  Intermolecular potentials from crystal data. 6. Determination of empirical potentials for O-H...O = C hydrogen bonds from packing configurations , 1984 .

[40]  R. Bazzo,et al.  NMR Analysis of Molecular Flexibility in Solution: A New Method for the Study of Complex Distributions of Rapidly Exchanging Conformations. Application to a 13-Residue Peptide with an 8-Residue Loop , 1995 .

[41]  W. Vangunsteren,et al.  CONFORMATIONAL DYNAMICS DETECTED BY NUCLEAR MAGNETIC-RESONANCE NOE VALUES AND J-COUPLING CONSTANTS , 1988 .

[42]  H. Scheraga,et al.  Energy parameters in polypeptides. 9. Updating of geometrical parameters, nonbonded interactions, and hydrogen bond interactions for the naturally occurring amino acids , 1983 .

[43]  SESAME: A least-squares approach to the evaluation of protein structures computed from NMR data , 1993, Journal of biomolecular NMR.

[44]  H. Scheraga,et al.  An approach to the multiple-minimum problem in protein folding, involving a long-range geometrical restriction and short-, medium-, and long-range interactions , 1981 .

[45]  V. Hruby,et al.  Conformations of the dermenkephalin backbone in DMSO solution by a new approach to the solution conformations of flexible peptides , 1993 .

[46]  Yuko Okamoto,et al.  Prediction of peptide conformation by multicanonical algorithm: New approach to the multiple‐minima problem , 1993, J. Comput. Chem..

[47]  K. Wüthrich,et al.  The program FANTOM for energy refinement of polypeptides and proteins using a Newton – Raphson minimizer in torsion angle space , 1990 .

[48]  B. Alder,et al.  Studies in Molecular Dynamics. I. General Method , 1959 .

[49]  M. Karplus,et al.  Dynamics of folded proteins , 1977, Nature.

[50]  H A Scheraga,et al.  Stability of polypeptide conformational states as determined by computer simulation of the free energy , 1987, Biopolymers.

[51]  Stephen R. Wilson,et al.  Conformational Analysis of Flexible Molecules: Location of the Global Minimum Energy Conformation by the Simulated Annealing Method , 1988 .

[52]  H. Scheraga,et al.  Free energy and stability of macromolecules studied by the double scanning simulation procedure , 1990 .

[53]  H. Scheraga,et al.  Energy parameters in polypeptides. VII. Geometric parameters, partial atomic charges, nonbonded interactions, hydrogen bond interactions, and intrinsic torsional potentials for the naturally occurring amino acids , 1975 .

[54]  Werner Braun,et al.  Efficient search for all low energy conformations of polypeptides by Monte Carlo methods , 1991 .

[55]  M. Karplus,et al.  Method for estimating the configurational entropy of macromolecules , 1981 .

[56]  M. Karplus,et al.  Multiple conformational states of proteins: a molecular dynamics analysis of myoglobin. , 1987, Science.