A comparative study of the simulated‐annealing and Monte Carlo‐with‐minimization approaches to the minimum‐energy structures of polypeptides: [Met]‐enkephalin

A comparison of two methods for surmounting the multiple‐minima problem, Simulated Annealing (SA) and Monte Carlo with Minimization (MCM), is presented with applications to [Met]‐enkephalin in the absence and in the presence of water. SA explores a continuous space of internal variables, while MCM explores a discrete space consisting of the local energy minima on that space. Starting from random conformations chosen from the whole conformational space in both cases, it is found that, while SA converges to low‐energy structures significantly faster than MCM, the former does not converge to a unique minimum whereas the latter does. Furthermore, the behavior of the RMS deviations with respect to the apparent global minimum (for enkephalin in the absence of water) shows no correlation with the observed overall energy decrease in the case of SA, whereas such a correlation is quite evident with MCM; this implies that, even though the potential energy decreases in the annealing process, the Monte Carlo SA trajectory does not proceed towards the global minimum. Possible reasons for these differences between the two methods are discussed. It is concluded that, while SA presents attractive prospects for possibly improving or refining given structures, it must be considered inferior to MCM, at least in problems where little or no structural information is available for the molecule of interest.

[1]  Georges Wipff,et al.  High temperature annealed molecular dynamics simulations as a tool for conformational sampling. Application to the bicyclic “222” cryptand , 1990 .

[2]  Y. Okamoto,et al.  A prediction of tertiary structures of peptide by the Monte Carlo simulated annealing method. , 1989, Protein engineering.

[3]  Harold A. Scheraga,et al.  Calculations of Conformations of Polypeptides , 1968 .

[4]  M. L. Connolly.  Analytical molecular surface calculation , 1983 .

[5]  H. Scheraga,et al.  Prediction of the native conformation of a polypeptide by a statistical‐mechanical procedure. I. Backbone structure of enkephalin , 1985, Biopolymers.

[6]  A. Gronenborn,et al.  Determination of three-dimensional structures of proteins by simulated annealing with interproton distance restraints. Application to crambin, potato carboxypeptidase inhibitor and barley serine proteinase inhibitor 2. , 1988, Protein engineering.

[7]  H. Scheraga,et al.  Use of buildup and energy‐minimization procedures to compute low‐energy structures of the backbone of enkephalin , 1985, Biopolymers.

[8]  H A Scheraga,et al.  An approach to the multiple-minima problem in protein folding by relaxing dimensionality. Tests on enkephalin. , 1987, Journal of molecular biology.

[9]  S. Wilson,et al.  Applications of simulated annealing to peptides , 1990, Biopolymers.

[10]  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 .

[11]  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 .

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

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

[14]  C. Anfinsen.  Principles that govern the folding of protein chains. , 1973, Science.

[15]  S. Doniach,et al.  A computer model to dynamically simulate protein folding: Studies with crambin , 1989, Proteins.

[16]  H. Scheraga,et al.  Computed conformational states of the 20 naturally occurring amino acid residues and of the prototype residue α-aminobutyric acid , 1983 .

[17]  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 .

[18]  H A Scheraga,et al.  Prediction of the native conformation of a polypeptide by a statistical‐mechanical procedure. III. Probable and average conformations of enkephalin , 1987, Biopolymers.

[19]  A. D. McLachlan,et al.  Solvation energy in protein folding and binding , 1986, Nature.

[20]  Steven G. Louie,et al.  A Monte carlo simulated annealing approach to optimization over continuous variables , 1984 .

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

[22]  V. Parisi,et al.  On the investigation of the low-energy conformational space of molecules , 1989 .

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