A parallel buildup algorithm for global energy minimizations of molecular clusters using effective energy simulated annealing
 Thomas Coleman,
 David Shalloway,
 Zhijun Wu
 … show all 3 hide
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This work studies the buildup method for the global minimization problem for molecular conformation, especially protein folding. The problem is hard to solve for large molecules using general minimization approaches because of the enormous amount of required computation. We therefore propose a buildup process to systematically “construct” the optimal molecular structures. A prototype algorithm is designed using the anisotropic effective energy simulated annealing method at each buildup stage. The algorithm has been implemented on the Intel iPSC/860 parallel computer, and tested with the LennardJones microcluster conformation problem. The experiments showed that the algorithm was effective for relatively large test problems, and also very suitable for massively parallel computation. In particular, for the 72atom LennardJones microcluster, the algorithm found a structure whose energy is lower than any others found in previous studies.
 Emile Aarts, and Jan Korst,Simulated Annealing and Boltzmann Machines, John Wiley & Sons, New York, NY, 1989.
 Charles L. Brooks III, Martin Karplus and B. Montgomery Pettitt,Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics, John Wiley & Sons, New York, NY, 1988.
 Richard H. Byrd, Elizabeth Eskow, Robert B. Schnabel and Sharon L. Smith, Parallel Global Optimization: Numerical Methods, Dynamic Scheduling Methods, and Application to Molecular Configuration,Technical Report CUCS55391, Department of Computer Science, University of Colorado at Boulder, Boulder, CO, 1991.
 Thomas Coleman, David Shalloway and Zhijun Wu, Isotropic Effective Energy Simulated Annealing Searches for Low Energy Molecular Cluster States,Technical Report CTC92TR113, Advanced Computing Research Institute, Cornell University, Ithaca, NY, 1992.
 J. E. Dennis, Jr. and R. B. Schnabel,Numerical Methods for Unconstrained Optimization and Nonlinear Equations, PrenticeHall, Englewood Cliffs, NJ, 1983.
 Philip E. Gill, Walter Murray and Margaret H. Wright,Practical Optimization, Academic Press, London, 1981.
 Bruce A. Hendrickson,The Molecular Problem: Determining Conformation from Pairwise Distances, Ph.D. Thesis, Department of Computer Science, Cornell University, Ithaca, NY, 1991.
 Brian E. Hingerty, Samuel Figueroa, Thomas L. Hayden and Suse Broyde, Prediction of DNA Structure from Sequence: A BuildUp Technique,Biopolymers, Vol. 28(1989), pp. 1195–1222.
 M. R. Hoare, Structure and Dynamics of Simple Microclusters,Advanced Chemical Physics, Vol. 40(1979), pp. 49–135.
 S. Kirkpatrick, C. D. Gellat, Jr., and M. P. Vecchi, Optimization by Simulated Annealing,Science, Vol. 220(1983), pp. 671–680.
 J. Kostrowicki, L. Piela, B.J. Cherayil and H.A. Scheraga, Performance of the Diffusion Equation Method in Searches for Optimum Structures of Clusters of LennardJones Atoms,Journal of Physical Chemistry, Vol. 95(1991), pp. 4113–4119.
 Z. Li and H. Scheraga, Monte CarloMinimization Approach to the MultipleMinima Problem in Protein Folding,Proceedings of the national Academy of Sciences USA, Vol. 84(1987), pp. 6611–6615.
 Shangkeng Ma, Introduction to the Renormalization Group,Reviews of Modern Physics, Vol. 45(1973), pp. 589–614.
 N. Metropolis, A. Rosenbluth, A. Teller, E. Teller, Equation of Several State Calculations by Fast Computing Machines,Journal of Chemical Physics, Vol. 21(1953), pp. 1087–1892.
 J.A. Northby, Structure and Binding of LennardJones Clusters: 13 ≤n ≤ 147,Journal of Chemical Physics, Vol. 87(1987), pp. 6166–6178.
 L. Piela, J. Kostrowicki and H.A. Scheraga, The MultipleMinima Problem in the Conformational Analysis of Molecules. Deformation of the Potential Energy Hypersurface by the Diffusion Equation Method,Journal of Physical Chemistry, Vol. 93(1989), pp. 3339–3346.
 M. Pincus, R. Klausner and H. Scheraga, Calculation of the ThreeDimensional Structure of the MembraneBound Portion of Melittin from its Amino Acid Sequence,Proceedings of National Academy of Science, USA, Vol. 79(1982), pp. 5107–5110.
 D. Shalloway, Packet Annealing: A Deterministic Method for Global Minimization. Application to Molecular Conformation, InRecent Advances in Global Optimization, C. Floudas and P. Pardalos (eds.), Princeton University Press: Princeton, N.J., (1992) pp. 433–477.
 D. Shalloway, Application of the Renormalization Group to Deterministic Global Minimization of Molecular Conformation Energy Functions,Journal Global Optimization, Vol. 2(1992), pp. 281–311.
 Jae Kwang Shin and Mu Shik Jhon, High Directional Monte Carlo Procedure Coupled with the Temperature Heating and Annealing as a Method to Obtain the Global Energy Minimum Structure of Polypeptides and Proteins,Biopolymers, Vol. 31(1991), pp. 177–185.
 David Vanderbilt and Steven G. Louie, A Monte Carlo Simulated Annealing Approach to Optimization over Continuous Variables,Journal of Computational Physics, Vol. 59(1984), pp. 259–271.
 L.T. Wille, MinimumEnergy Configurations of Atomic Clusters: New Results Obtained by Simulated Annealing,Chemical Physics Letters, Vol. 133(1987), pp. 405–410.
 K.G. Wilson, The Renormalization Group: Critical Phenomena and the Kondo Problem.Reviews of Modern Physics, Vol. 47(1975), pp. 773–840.
 G.L. Xue, Improvement of the Northby Algorithm for Molecular Conformation: Better Results, accepted for publication inJournal of Global Optimization.
 Title
 A parallel buildup algorithm for global energy minimizations of molecular clusters using effective energy simulated annealing
 Journal

Journal of Global Optimization
Volume 4, Issue 2 , pp 171185
 Cover Date
 19940301
 DOI
 10.1007/BF01096721
 Print ISSN
 09255001
 Online ISSN
 15732916
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Global/local minimization
 effective energy simulated annealing
 parallel computation
 protein folding
 Industry Sectors
 Authors

 Thomas Coleman ^{(1)}
 David Shalloway ^{(2)}
 Zhijun Wu ^{(3)}
 Author Affiliations

 1. Department of Computer Science, Cornell University, 14853, Ithaca, NY
 2. Section of Biochemistry, Molecular and Cell Biology, Cornell University, 14853, Ithaca, NY
 3. Advanced Computing Research Institute, Cornell University, 14853, Ithaca, NY