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Algorithmic dimensionality reduction for molecular structure analysis

J. Chem. Phys. 129, 064118 (2008); doi:10.1063/1.2968610

Published 14 August 2008

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W. Michael Brown,1 Shawn Martin,2 Sara N. Pollock,3,4 Evangelos A. Coutsias,4 and Jean-Paul Watson1
1Discrete Mathematics and Complex Systems, Sandia National Laboratories, Albuquerque, New Mexico 87185-1316, USA
2Computer Science and Informatics, Sandia National Laboratories, Albuquerque, New Mexico 87185-1316, USA
3Department of Biochemistry and Molecular Biology Division of Biocomputing, University of New Mexico, Albuquerque, New Mexico 87131, USA
4Department of Mathematics, University of New Mexico, Albuquerque, New Mexico 87131, USA
Dimensionality reduction approaches have been used to exploit the redundancy in a Cartesian coordinate representation of molecular motion by producing low-dimensional representations of molecular motion. This has been used to help visualize complex energy landscapes, to extend the time scales of simulation, and to improve the efficiency of optimization. Until recently, linear approaches for dimensionality reduction have been employed. Here, we investigate the efficacy of several automated algorithms for nonlinear dimensionality reduction for representation of trans, trans-1,2,4-trifluorocyclo-octane conformation—a molecule whose structure can be described on a 2-manifold in a Cartesian coordinate phase space. We describe an efficient approach for a deterministic enumeration of ring conformations. We demonstrate a drastic improvement in dimensionality reduction with the use of nonlinear methods. We discuss the use of dimensionality reduction algorithms for estimating intrinsic dimensionality and the relationship to the Whitney embedding theorem. Additionally, we investigate the influence of the choice of high-dimensional encoding on the reduction. We show for the case studied that, in terms of reconstruction error root mean square deviation, Cartesian coordinate representations and encodings based on interatom distances provide better performance than encodings based on a dihedral angle representation. ©2008 American Institute of Physics
History: Received 28 April 2008; accepted 16 July 2008; published 14 August 2008
Permalink: http://link.aip.org/link/?JCPSA6/129/064118/1
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KEYWORDS and PACS

Keywords
PACS
  • 31.15.V-
    Electron correlation calculations for atoms, ions and molecules
  • 33.15.Bh
    General molecular conformation and symmetry; stereochemistry
  • YEAR: 2008

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0021-9606 (print)   1089-7690 (online)
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REFERENCES (79)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. K. A. Dill, Biochemistry 29, 7133 (1990).
  2. R. Hegger, A. Altis, P. H. Nguyen, and G. Stock, Phys. Rev. Lett. 98, 028102 (2007).
  3. O. F. Lange and H. Grubmuller, J. Phys. Chem. B 110, 22842 (2006).
  4. K. W. Plaxco and M. Gross, Nat. Struct. Biol. 8, 659 (2001).
  5. A. R. Dinner, A. Sali, L. J. Smith, C. M. Dobson, and M. Karplus, Trends Biochem. Sci. 25, 331 (2000).
  6. J. N. Onuchic and P. G. Wolynes, Curr. Opin. Struct. Biol. 14, 70 (2004).
  7. R. V. Pappu, R. Srinivasan, and G. D. Rose, Proc. Natl. Acad. Sci. U.S.A. 97, 12565 (2000).
  8. B. L. de Groot, X. Daura, A. E. Mark, and H. Grubmuller, J. Mol. Biol. 309, 299 (2001).
  9. R. Abseher and M. Nilges, Proteins: Struct., Funct., Genet. 39, 82 (2000).
  10. A. Amadei, B. L. de Groot, M. A. Ceruso, M. Paci, A. Di Nola, and H. J. C. Berendsen, Proteins: Struct., Funct., Genet. 35, 283 (1999).
  11. A. Amadei, A. B. M. Linssen, and H. J. C. Berendsen, Proteins: Struct., Funct., Genet. 17, 412 (1993).
  12. A. Amadei, A. B. M. Linssen, B. L. deGroot, D. M. F. vanAalten, and H. J. C. Berendsen, J. Biomol. Struct. Dyn. 13, 615 (1996).
  13. B. L. deGroot, A. Amadei, R. M. Scheek, N. A. J. vanNuland, and H. J. C. Berendsen, Proteins: Struct., Funct., Genet. 26, 314 (1996).
  14. T. Noguti and N. Go, Biopolymers 24, 527 (1985).
  15. B. R. Brooks, D. Janezic, and M. Karplus, J. Comput. Chem. 16, 1522 (1995).
  16. D. Janezic and B. R. Brooks, J. Comput. Chem. 16, 1543 (1995).
  17. D. Janezic, R. M. Venable, and B. R. Brooks, J. Comput. Chem. 16, 1554 (1995).
  18. S. Hayward and N. Go, Annu. Rev. Phys. Chem. 46, 223 (1995).
  19. M. L. Teodoro, G. N. Phillips, and L. E. Kavraki, J. Comput. Biol. 10, 617 (2003).
  20. R. Bruschweiler and D. A. Case, Phys. Rev. Lett. 72, 940 (1994).
  21. D. A. Case, Acc. Chem. Res. 35, 325 (2002).
  22. B. L. de Groot, S. Hayward, D. M. F. van Aalten, A. Amadei, and H. J. C. Berendsen, Proteins: Struct., Funct., Genet. 31, 116 (1998).
  23. L. Meinhold and J. C. Smith, Biophys. J. 88, 2554 (2005).
  24. T. D. Romo, J. B. Clarage, D. C. Sorensen, and G. N. Phillips, Proteins: Struct., Funct., Genet. 22, 311 (1995).
  25. M. Stepanova, Phys. Rev. E 76, 051918 (2007).
  26. D. M. F. van Aalten, D. A. Conn, B. L. de Groot, H. J. C. Berendsen, J. B. C. Findlay, and A. Amadei, Biophys. J. 73, 2891 (1997).
  27. O. F. Lange and H. Grubmuller, J. Chem. Phys. 124, 214903 (2006).
  28. V. Spiwok, P. Lipovova, and B. Kralova, J. Phys. Chem. B 111, 3073 (2007).
  29. D. Mustard and D. W. Ritchie, Proteins: Struct., Funct., Genet. 60, 269 (2005).
  30. M. Zacharias, Proteins: Struct., Funct., Bioinf. 54, 759 (2004).
  31. B. Qian, A. R. Ortiz, and D. Baker, Proc. Natl. Acad. Sci. U.S.A. 101, 15346 (2004).
  32. M. Kirby, Geometric Data Analysis (Wiley, New York, 2001).
  33. L. S. D. Caves, J. D. Evanseck, and M. Karplus, Protein Sci. 7, 649 (1998).
  34. A. Kitao and N. Go, Curr. Opin. Struct. Biol. 9, 164 (1999).
  35. J. B. Clarage, T. Romo, B. K. Andrews, B. M. Pettitt, and G. N. Phillips, Proc. Natl. Acad. Sci. U.S.A. 92, 3288 (1995).
  36. A. Altis, P. H. Nguyen, R. Hegger, and G. Stock, J. Chem. Phys. 126, 244111 (2007).
  37. O. F. Lange and H. Grubmuller, Proteins: Struct., Funct., Bioinf. 62, 1053 (2006).
  38. D. K. Agrafiotis and H. F. Xu, Proc. Natl. Acad. Sci. U.S.A. 99, 15869 (2002).
  39. P. H. Nguyen, Proteins: Struct., Funct., Bioinf. 65, 898 (2006).
  40. J. B. Tenenbaum, V. de Silva, and J. C. Langford, Science 290, 2319 (2000).
  41. P. Das, M. Moll, H. Stamati, L. E. Kavraki, and C. Clementi, Proc. Natl. Acad. Sci. U.S.A. 103, 9885 (2006).
  42. M. A. Balsera, W. Wriggers, Y. Oono, and K. Schulten, J. Phys. Chem. 100, 2567 (1996).
  43. W. R. Rocha, J. R. Pliego, S. M. Resende, H. F. dos Santos, M. A. de Oliveira, and W. B. de Almeida, J. Comput. Chem. 19, 524 (1998).
  44. R. K. Bharadwaj, Mol. Phys. 98, 211 (2000).
  45. Z. Chen and F. A. Escobedo, J. Chem. Phys. 113, 11382 (2000).
  46. J. Hendrickson, J. Am. Chem. Soc. 89, 7036 (1967).
  47. D. Cremer and J. A. Pople, J. Am. Chem. Soc. 97, 1354 (1975).
  48. N. Go and H. Scheraga, Macromolecules 3, 178 (1970).
  49. K. N. Kudin and A. Y. Dymarsky, J. Chem. Phys. 122, 124103 (2005).
  50. M. Teodoro, G. Phillips, Jr., and L. Kavraki, Annual Conference on Research in Computational Molecular Biology, Washington, DC, 2002 (unpublished).
  51. G. M. Crippen and T. F. Havel, Distance Geometry and Molecular Conformation (Wiley, New York, 1988).
  52. N. Elmaci and R. S. Berry, J. Chem. Phys. 110, 10606 (1999).
  53. P. W. Pan, R. J. Dickson, H. L. Gordon, S. M. Rothstein, and S. Tanaka, J. Chem. Phys. 122, 034904 (2005).
  54. C. Jutten and J. Herault, Signal Process. 24, 1 (1991).
  55. A. Hyvarinen, Neural Computing Surveys 2, 94 (1999).
  56. B. Scholkopf, A. Smola, and K. -R. Muller, Advances in Kernel Methods SV Learning (MIT, Cambridge, MA, 1999).
  57. T. Kohonen, Self-Organizing Maps (Springer-Verlag, Berlin, 1995).
  58. G. Hinton and R. Salakhutdinov, Science 313, 504 (2006).
  59. S. Roweis and L. Saul, Science 290, 2323 (2000).
  60. J. A. Lee and M. Verleysen, Nonlinear Dimensionality Reduction (Springer-Verlag, Berlin, 2007).
  61. L. Trefethen and D. Bau, Numerical Linear Algebra (SIAM, Philadelphia, 1997).
  62. L. Saul and S. Roweis, J. Mach. Learn. Res. 4, 119 (2004).
  63. T. Havel, I. D. Kuntz, and G. M. Crippen, Bull. Math. Biol. 45, 665 (1983).
  64. S. Martin and A. Backer, Proceedings of the ACM Symposium on Applied Computing (SAC), 2005 (unpublished), pp. 22–26.
  65. J. A. Lee and M. Verleysen, Nonlinear Dimensionality Reduction (Springer, New York, 2007).
  66. The code is available for academic use by contacting one of the Sandia authors.
  67. I. S. Dhillon and B. N. Parlett, Linear Algebr. Appl. 387, 1 (2004).
  68. E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, Lapack Users' Guide 3rd ed. (Society for Industrial and Applied Mathematics, Philadelphia, 1999).
  69. E. Coutsias, C. Seok, M. Jacobson, and K. Dill, J. Comput. Chem. 25, 510 (2004).
  70. J. Porta, L. Ros, F. Thomas, F. Corcho, J. Cant, and J. Perez, J. Comput. Chem. 28, 2170 (2007).
  71. D. Manocha and Y. Zhu, in ISMB, edited by R. B. Altman, D. L. Brutlag, P. D. Karp, R. H. Lathrop, and D. B. Searls (AAAI, Menlo Park, CA, 1994), pp. 285–293.
  72. H. Lee and C. Liang, Mech. Mach. Theory 23, 219 (1988).
  73. E. Coutsias, C. Seok, M. Wester, and K. Dill, Int. J. Quantum Chem. 106, 176 (2006).
  74. D. G. Evans and J. C. A. Boeyens, Acta Crystallogr., Sect. B: Struct. Sci. 44, 663 (1988).
  75. S. Pollock and E. Coutsias (unpublished).
  76. N. L. Allinger, Y. H. Yuh, and J. H. Lii, J. Am. Chem. Soc. 111, 8551 (1989).
  77. M. Shah and D. C. Sorensen, Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference, Seville, Spain, 12–15 December 2005 (unpublished), Vols. 1–8, pp. 2260–2264.
  78. M. Praprotnik, L. Delle Site, and K. Kremer, Annu. Rev. Phys. Chem. 59, 545 (2008).
  79. R. Everaers and M. R. Ejtehadi, Phys. Rev. E 67, 041710 (2003).

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