Skip to main content
Log in

A parallel build-up algorithm for global energy minimizations of molecular clusters using effective energy simulated annealing

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

This work studies the build-up 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 build-up process to systematically “construct” the optimal molecular structures. A prototype algorithm is designed using the anisotropic effective energy simulated annealing method at each build-up stage. The algorithm has been implemented on the Intel iPSC/860 parallel computer, and tested with the Lennard-Jones 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 72-atom Lennard-Jones microcluster, the algorithm found a structure whose energy is lower than any others found in previous studies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Emile Aarts, and Jan Korst,Simulated Annealing and Boltzmann Machines, John Wiley & Sons, New York, NY, 1989.

    Google Scholar 

  2. 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.

    Google Scholar 

  3. 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 CU-CS-553-91, Department of Computer Science, University of Colorado at Boulder, Boulder, CO, 1991.

    Google Scholar 

  4. 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.

    Google Scholar 

  5. J. E. Dennis, Jr. and R. B. Schnabel,Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ, 1983.

    Google Scholar 

  6. Philip E. Gill, Walter Murray and Margaret H. Wright,Practical Optimization, Academic Press, London, 1981.

    Google Scholar 

  7. Bruce A. Hendrickson,The Molecular Problem: Determining Conformation from Pairwise Distances, Ph.D. Thesis, Department of Computer Science, Cornell University, Ithaca, NY, 1991.

    Google Scholar 

  8. Brian E. Hingerty, Samuel Figueroa, Thomas L. Hayden and Suse Broyde, Prediction of DNA Structure from Sequence: A Build-Up Technique,Biopolymers, Vol. 28(1989), pp. 1195–1222.

    Google Scholar 

  9. M. R. Hoare, Structure and Dynamics of Simple Microclusters,Advanced Chemical Physics, Vol. 40(1979), pp. 49–135.

    Google Scholar 

  10. S. Kirkpatrick, C. D. Gellat, Jr., and M. P. Vecchi, Optimization by Simulated Annealing,Science, Vol. 220(1983), pp. 671–680.

    Google Scholar 

  11. 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 Lennard-Jones Atoms,Journal of Physical Chemistry, Vol. 95(1991), pp. 4113–4119.

    Google Scholar 

  12. Z. Li and H. Scheraga, Monte Carlo-Minimization Approach to the Multiple-Minima Problem in Protein Folding,Proceedings of the national Academy of Sciences USA, Vol. 84(1987), pp. 6611–6615.

    Google Scholar 

  13. Shang-keng Ma, Introduction to the Renormalization Group,Reviews of Modern Physics, Vol. 45(1973), pp. 589–614.

    Google Scholar 

  14. 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.

    Google Scholar 

  15. J.A. Northby, Structure and Binding of Lennard-Jones Clusters: 13 ≤n ≤ 147,Journal of Chemical Physics, Vol. 87(1987), pp. 6166–6178.

    Google Scholar 

  16. L. Piela, J. Kostrowicki and H.A. Scheraga, The Multiple-Minima 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.

    Google Scholar 

  17. M. Pincus, R. Klausner and H. Scheraga, Calculation of the Three-Dimensional Structure of the Membrane-Bound Portion of Melittin from its Amino Acid Sequence,Proceedings of National Academy of Science, USA, Vol. 79(1982), pp. 5107–5110.

    Google Scholar 

  18. 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.

    Google Scholar 

  19. 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.

    Google Scholar 

  20. 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.

    Google Scholar 

  21. 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.

    Google Scholar 

  22. L.T. Wille, Minimum-Energy Configurations of Atomic Clusters: New Results Obtained by Simulated Annealing,Chemical Physics Letters, Vol. 133(1987), pp. 405–410.

    Google Scholar 

  23. K.G. Wilson, The Renormalization Group: Critical Phenomena and the Kondo Problem.Reviews of Modern Physics, Vol. 47(1975), pp. 773–840.

    Google Scholar 

  24. G.L. Xue, Improvement of the Northby Algorithm for Molecular Conformation: Better Results, accepted for publication inJournal of Global Optimization.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Coleman, T., Shalloway, D. & Wu, Z. A parallel build-up algorithm for global energy minimizations of molecular clusters using effective energy simulated annealing. J Glob Optim 4, 171–185 (1994). https://doi.org/10.1007/BF01096721

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01096721

Keywords

Navigation