Application of the renormalization group to deterministic global minimization of molecular conformation energy functions

We outline a new global minimization method in which the Gibbs distribution of the objective function is deterministically annealed by tracing the evolution of a multiple-Gaussian-packet approximation. Solutions are reached by iterative approximations with decreasing coarse-graining of both objective-function and spatial scales. Results from application of a partial implementation to the atomic-microcluster conformation problem are presented.

[1]  H. C. Andersen,et al.  Molecular dynamics study of melting and freezing of small Lennard-Jones clusters , 1987 .

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

[3]  D. L. Freeman,et al.  Quantum Monte Carlo study of the thermodynamic properties of argon clusters: The homogeneous nucleation of argon in argon vapor and ‘‘magic number’’ distributions in argon vapor , 1985 .

[4]  T. Ackermann.  C. L. Brooks III, M. Karplus, B. M. Pettitt. Proteins: A Theoretical Perspective of Dynamics, Structure and Thermodynamics, Volume LXXI, in: Advances in Chemical Physics, John Wiley & Sons, New York 1988. 259 Seiten, Preis: US $ 65.25 , 1990 .

[5]  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 .

[6]  Walter Kauzmann,et al.  Kinetic theory of gases , 1966 .

[7]  L. T. Wille,et al.  Searching potential energy surfaces by simulated annealing , 1986, Nature.

[8]  Philip E. Gill,et al.  Practical optimization , 1981 .

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

[10]  J. C. Phillips.  Chemical bonding, kinetics and the approach to equilibrium structures of simple metallic, molecular, and network microclusters , 1986 .

[11]  M. Hoare,et al.  Statistical mechanics and morphology of very small atomic clusters , 1976 .

[12]  R. Pool,et al.  Clusters: Strange Morsels of Matter: When metals or semiconductors are shrunk down to clumps only 10 or 100 atoms in size, they become a "totally new class of materials" with potentially valuable applications. , 1990, Science.

[13]  M. Hoare,et al.  Physical cluster mechanics: Statics and energy surfaces for monatomic systems , 1971 .

[14]  Harold A. Scheraga.  Conformational Analysis of Polypeptides and Proteins for the Study of Protein Folding, Molecular Recognition, and Molecular Design , 1987 .

[15]  F. Richards,et al.  The protein folding problem. , 1991, Scientific American.

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

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

[18]  Robert W. Dutton,et al.  A macrocell placement algorithm using mathematical programming techniques , 1989 .

[19]  M. Levitt.  Protein folding by restrained energy minimization and molecular dynamics. , 1983, Journal of molecular biology.

[20]  L. Wille.  Minimum-energy configurations of atomic clusters: new results obtained by simulated annealing , 1987 .

[21]  C. Levinthal.  Are there pathways for protein folding , 1968 .

[22]  A. Messiah.  Quantum Mechanics , 1961 .

[23]  J. Farges,et al.  Cluster models made of double icosahedron units , 1985 .

[24]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

[25]  Sandro Ridella,et al.  Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithmCorrigenda for this article is available here , 1987, TOMS.

[26]  T. L. Blundell,et al.  Knowledge-based prediction of protein structures and the design of novel molecules , 1987, Nature.

[27]  M. E. Johnson,et al.  Generalized simulated annealing for function optimization , 1986 .

[28]  K. Wilson.  The renormalization group: Critical phenomena and the Kondo problem , 1975 .

[29]  J. King,et al.  Deciphering the Rules of Protein Folding , 1989 .

[30]  M. R. Hoare,et al.  Morphology and statistical statics of simple microclusters , 1983 .