Journal of Biomolecular NMR

, Volume 29, Issue 2, pp 111–138 | Cite as

An expectation/maximization nuclear vector replacement algorithm for automated NMR resonance assignments

  • Christopher James Langmead
  • Bruce Randall Donald


We report an automated procedure for high-throughput NMR resonance assignment for a protein of known structure, or of an homologous structure. Our algorithm performs Nuclear Vector Replacement (NVR) by Expectation/Maximization (EM) to compute assignments. NVR correlates experimentally-measured NH residual dipolar couplings (RDCs) and chemical shifts to a given a priori whole-protein 3D structural model. The algorithm requires only uniform 15N-labelling of the protein, and processes unassigned HN-15N HSQC spectra, HN-15N RDCs, and sparse HN-HN NOE's (dNNs). NVR runs in minutes and efficiently assigns the (HN,15N) backbone resonances as well as the sparse dNNs from the 3D 15N-NOESY spectrum, in O(n3) time. The algorithm is demonstrated on NMR data from a 76-residue protein, human ubiquitin, matched to four structures, including one mutant (homolog), determined either by X-ray crystallography or by different NMR experiments (without RDCs). NVR achieves an average assignment accuracy of over 99%. We further demonstrate the feasibility of our algorithm for different and larger proteins, using different combinations of real and simulated NMR data for hen lysozyme (129 residues) and streptococcal protein G (56 residues), matched to a variety of 3D structural models. Abbreviations: NMR, nuclear magnetic resonance; NVR, nuclear vector replacement; RDC, residual dipolar coupling; 3D, three-dimensional; HSQC, heteronuclear single-quantum coherence; HN, amide proton; NOE, nuclear Overhauser effect; NOESY, nuclear Overhauser effect spectroscopy; dNN, nuclear Overhauser effect between two amide protons; MR, molecular replacement; SAR, structure activity relation; DOF, degrees of freedom; nt., nucleotides; SPG, Streptococcal protein G; SO(3), special orthogonal (rotation) group in 3D; EM, Expectation/Maximization; SVD, singular value decomposition.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Al-Hashimi, H., Gorin, A., Majumdar, A., Gosser, Y. and Patel, D. (2002) J. Mol. Biol., 318, 637–649.Google Scholar
  2. Al-Hashimi, H. and Patel, D. (2002) J. Biomol. NMR, 22, 1–8.Google Scholar
  3. Altschul, S., Gish, W., Miller, W., Myers, E. and Lipman, D. (1990) J. Mol. Biol., 215, 403–410.Google Scholar
  4. Andrec, M., Du, P. and Levy, R. (2001) J. Biomol. NMR, 21, 335–347.Google Scholar
  5. Annila, A., Aitio, H., Thulin, E. and T., D. (1999) J. Biomol. NMR, 14, 223–230.Google Scholar
  6. Artymiuk, P.J., Blake, C.C.F., Rice, D.W. and Wilson, K.S. (1982) Acta Crystallogr. B Biol. Crystallogr., 38, 778.Google Scholar
  7. Babu, C. R., Flynn, P.F. and Wand, A.J. (2001) J. Am. Chem. Soc., 123, 2691.Google Scholar
  8. Bailey-Kellogg, C., Widge, A., Kelley III, J.J., Berardi, M., Bushweller, J. and Donald, B. (2000) J. Comput. Biol., 7, 537–558.Google Scholar
  9. Berman, H., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T., Weissig, H., Shindyalov, I. and Bourne, P. (2000) Nucl. Acids Res., 28, 235–242.Google Scholar
  10. Blundell, T., Sibanda, B., Sternberg, M. and Thornton, J. (1987) Nature, 326, 347–352.Google Scholar
  11. Chen, Y., Reizer, J., Saier Jr., M.H., Fairbrother, W.J. and Wright, P.E. (1993) Biochemistry, 32, 32–37.Google Scholar
  12. Chou, J., Li, S. and Bax, A. (2000) J. Biomol. NMR, 18, 217–227.Google Scholar
  13. Cormen, T.H., Leiserson, C.E., Rivest, R.L. and Stein, C. (2001) Introduction to Algorithms, 2nd edn., The MIT Press, Cambridge, MA, chapter 5, pp. 109–110.Google Scholar
  14. Cornilescu, G., Marquardt, J.L., Ottiger, M. and Bax, A. (1998) J. Am. Chem. Soc., 120, 6836–6837.Google Scholar
  15. Cross, A.D.J. and Hancock, E.R. (1998) IEEE Trans. Pattern Anal. Machine Intell., 20, 1236–1253.Google Scholar
  16. Delaglio, F., Kontaxis, G. and Bax, A. (2000) J. Am. Chem. Soc., 122, 2142–2143.Google Scholar
  17. Dempster, A., Laird, N. and Rubin, D. (1977) J. Roy. Stat. Soc., Ser. B, 39, 1–38.Google Scholar
  18. Diamond, R. (1974) J Mol. Biol., 82, 371–391.Google Scholar
  19. Fejzo, J., Lepre, C., Peng, J., Bemis, G., Ajay, Murcko, M. and Moore, J. (1999) Chem. Biol., 6, 755–769.Google Scholar
  20. Fetrow, J. and Bryant, S. (1993) Bio/Technology, 11, 479–484.Google Scholar
  21. Fiaux, J., Bertelsen, E.B., Horwich, A.L. and Wüthrich, K. (2002) Nature, 418, 207–211.Google Scholar
  22. Fowler, C., Tian, F., Al-Hashimi, H.M. and Prestegard, J.H. (2000) J. Mol. Biol., 304, 447–460.Google Scholar
  23. Gallagher, T., Alexander, P., Bryan, P. and Gilliland, G.L. (1994) Biochemistry, 33, 4721–4729.Google Scholar
  24. Gemmecker, G., Jahnke, W. and Kessler, H. (1993) J. Am. Chem. Soc., 115, 11620–11621.Google Scholar
  25. Girard, E., Chantalat, L., Vicat, J. and Kahn, R. (2001) Acta Crystallogr. D Biol. Crystallogr., 58, 1–9.Google Scholar
  26. Gnu (2002) The GNU General Public License, Scholar
  27. Greer, J. (1991) Meth. Enzymol., 202, 239–252.Google Scholar
  28. Grishaev, A. and Llinas, M. (2002) PNAS, 99, 6707–6712.Google Scholar
  29. Gronenborn, A.M., Filpula, D.R., Essig, N.Z., Achari, A., Whitlow, M., Wingfield, P.T. and Clore, G.M. (1991) Science, 253, 657.Google Scholar
  30. Grzesiek, S. and Bax, A. (1993) J. Biomol. NMR, 3, 627–638.Google Scholar
  31. Harris, R. (2002) The Ubiquitin NMR Resource Page, BBSRC Bloomsbury Center for Structural Biology Scholar
  32. Hoch, J., Burns, M. M. and Redfield, C. (1990) In Frontiers of NMR in Molecular Biology, Alan R. Liss, Inc., NY, pp. 167–175.Google Scholar
  33. Hus, J., Marion, D. and Blackledge, M. (2000) J. Mol. Biol., 298, 927–936.Google Scholar
  34. Hus, J., Prompers, J. and Bruschweiler, R. (2002) J. Magn. Reson., 157, 119–125.Google Scholar
  35. Johnson, E., Lazar, G.A., Desjarlais, J.R. and Handel, T.M. (1999) Struct. Fold Des., 7, 967–976.Google Scholar
  36. Johnson, M., Srinivasan, N., Sowdhamini, R. and Blundell, T. (1994) Mol. Biochem. 29, 1–68.Google Scholar
  37. Koradi, R., Billeter, M. and Wüthrich, K. (1996) J. Mol. Graph., 14, 51–55.Google Scholar
  38. Kuhn, H. (1955) Nav. Res. Logist. Quart., 2, 83–97.Google Scholar
  39. Kurinov, I.V. and Harrison, R.W. (1995) Acta Crystallogr. D Biol. Crystallogr., 51, 98–109.Google Scholar
  40. Kuszewski, J., Gronenborn, A.M. and Clore, G.M. (1999) J. Am. Chem. Soc., 121, 2337–2338.Google Scholar
  41. Langmead, C.J. and Donald, B.R. (2003) In Proceedings of the IEEE Computer Society Bioinformatics Conference (CSB), Stanford University, Palo Alto, CA (August 11–14), pp. 209–217.Google Scholar
  42. Langmead, C.J., Yan, A.K., Wang, L., Lilien, R.H. and Donald, B.R. (2003) In Proceedings of the 7th Ann. Intl. Conf. on Research in Comput. Biol. (RECOMB) Berlin, Germany, April 10–13, pp. 176–187.Google Scholar
  43. Lathrop, R. and Smith, T. (1996) J. Mol. Biol., 255, 641–665.Google Scholar
  44. Lim, K., Nadarajah, A., Forsythe, E.L. and Pusey, M.L. (1998) Acta Crystallogr. D Biol. Crystallogr., 54, 899–904.Google Scholar
  45. Losonczi, J., Andrec, M., Fischer, W. and J.H., P. (1999) J Magn. Reson., 138, 334–342.Google Scholar
  46. Meiler, J., Peti, W. and Griesinger, C. (2000) J. Biomol. NMR, 17, 283–294.Google Scholar
  47. Mueller, G., Choy, W., Yang, D., Forman-Kay, J., Venters, R. and Kay, L. (2000) J. Mol. Biol., 300, 197–212.Google Scholar
  48. Neal, S., Nip, A.M., Zhang, H. and Wishart, D.S. (2003) J. Biomol. NMR, 26, 215–240.Google Scholar
  49. Oki, H., Matsuura, Y., Komatsu, H. and Chernov, A. A. (1999) Acta Crystallogr. D Biol. Crystallogr., 55, 114.Google Scholar
  50. Ottiger, M. and Bax, A. (1998) J. Am. Chem. Soc., 120, 12334–12341.Google Scholar
  51. Palmer, A.G. (1997) Curr. Opin. Struct. Biol., 7, 732–737.Google Scholar
  52. Ramage, R., Green, J., Muir, T.W., Ogunjobi, O.M., Love, S. and Shaw, K. (1994) J. Biochem., 299, 151–158.Google Scholar
  53. Redfield, C., Hoch, J. and Dobson, C. (1983) FEBS Lett., 159, 132–136.Google Scholar
  54. Rohl, C. and Baker, D. (2002) J. Am. Chem. Soc., 124, 2723–2729.Google Scholar
  55. Rossman, M. and Blow, D. (1962) Acta Crystallogr., 15, 24–31.Google Scholar
  56. Sali, A., Overington, J., Johnson, M. and Blundell, T. (1990) Trends Biochem. Sci., 15, 235–240.Google Scholar
  57. Saupe, A. (1968) Angew. Chem., 7, 97–112.Google Scholar
  58. Schneider, D., Dellwo, M. and Wand, A.J. (1992) Biochemistry, 31, 3645–3652.Google Scholar
  59. Schwalbe, H., Grimshaw, S.B., Spencer, A., Buck, M., Boyd, J., Dobson, C.M., Redfield, C. and Smith, L.J. (2001) Protein Sci., 10, 677–688.Google Scholar
  60. Seavey, B., Farr, E., Westler, W. and Markley, J. (1991) J. Biomol. NMR, 1, 217–236.Google Scholar
  61. Shuker, S.B., Hajduk, P.J., Meadows, R.P. and Fesik, S.W. (1996) Science, 274, 1531–1534.Google Scholar
  62. Tian, F., Valafar, H. and Prestegard, J. H. (2001) J. Am. Chem. Soc., 123, 11791–11796.Google Scholar
  63. Tjandra, N. and Bax, A. (1997) Science, 278, 1111–1114.Google Scholar
  64. Tolman, J.R., Flanagan, J.M., Kennedy, M.A. and Prestegard, J.H. (1995) Proc. Natl. Acad. Sci. USA, 92, 9279–9283.Google Scholar
  65. Vaney, M.C., Maignan, S., Ries-Kautt, M. and Ducruix, A. (1996) Acta Crystallogr. D Biol. Crystallogr., 52, 505–517.Google Scholar
  66. Vijay-Kumar, S., Bugg, C.E. and Cook, W.J. (1987) J. Mol. Biol., 194, 531–544.Google Scholar
  67. Wang, L. and Donald, B.R. (2004) J. Biomol. NMR, in press.Google Scholar
  68. Weber, P.L., Brown, S.C. and Mueller, L. (1987) Biochemistry, 26, 7282–7290.Google Scholar
  69. Wedemeyer, W.J., Rohl, C.A. and Scheraga, H.A. (2002) J. Biomol. NMR, 22, 137–151.Google Scholar
  70. Xu, X. and Case, D. (2001) J. Biomol. NMR, 21, 321–333.Google Scholar
  71. Xu, Y., Xu, D., Crawford, O.H., Einstein, J.R. and Serpersu, E. (2000) Proc. RECOMB, pp. 299–307.Google Scholar
  72. Yan, A., Langwead, C. and Donald, B.R. (2003) A Probability-Based Similarity Measure for Saupe Alignment Tensors with Applications to Residual Dipolar Couplings in NMR Structural Biology. Technical Report No. TR2003-474, Dartmouth Computer Science Department, Scholar
  73. Zweckstetter, M. (2003) J. Biomol. NMR, 27, 41–56.Google Scholar
  74. Zweckstetter, M. and Bax, A. (2000) J. Am. Chem. Soc., 122, 3791–3792.Google Scholar
  75. Zweckstetter, M. and Bax, A. (2001) J. Am. Chem. Soc., 123, 9490–9491.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Christopher James Langmead
    • 1
  • Bruce Randall Donald
    • 4
  1. 1.Dartmouth Computer Science DepartmentHanoverUSA
  2. 2.Dartmouth Chemistry DepartmentUSA
  3. 3.Dartmouth Biological Sciences DepartmentUSA
  4. 4.Dartmouth Center for Structural Biology and Computational ChemistryHanoverUSA

Personalised recommendations