Journal of Biomolecular NMR

, Volume 29, Issue 3, pp 223–242 | Cite as

Exact Solutions for Internuclear Vectors and Backbone Dihedral Angles from NH Residual Dipolar Couplings in Two Media, and their Application in a Systematic Search Algorithm for Determining Protein Backbone Structure

  • Lincong Wang
  • Bruce Randall Donald
Article

Abstract

We have derived a quartic equation for computing the direction of an internuclear vector from residual dipolar couplings (RDCs) measured in two aligning media, and two simple trigonometric equations for computing the backbone (φ,ψ) angles from two backbone vectors in consecutive peptide planes. These equations make it possible to compute, exactly and in constant time, the backbone (φ,ψ) angles for a residue from RDCs in two media on any single backbone vector type. Building upon these exact solutions we have designed a novel algorithm for determining a protein backbone substructure consisting of α-helices and β-sheets. Our algorithm employs a systematic search technique to refine the conformation of both α-helices and β-sheets and to determine their orientations using exclusively the angular restraints from RDCs. The algorithm computes the backbone substructure employing very sparse distance restraints between pairs of α-helices and β-sheets refined by the systematic search. The algorithm has been demonstrated on the protein human ubiquitin using only backbone NH RDCs, plus twelve hydrogen bonds and four NOE distance restraints. Further, our results show that both the global orientations and the conformations of α-helices and β-strands can be determined with high accuracy using only two RDCs per residue. The algorithm requires, as its input, backbone resonance assignments, the identification of α-helices and β-sheets as well as sparse NOE distance and hydrogen bond restraints.

Abbreviations: NMR – nuclear magnetic resonance; RDC – residual dipolar coupling; NOE – nuclear Overhauser effect; SVD – singular value decomposition; DFS – depth-first search; RMSD – root mean square deviation; POF – principal order frame; PDB – protein data bank; SA – simulated annealing; MD – molecular dynamics.

algorithms for protein structure determination conformational search exact solutions for backbone dihedral angles exact solutions for internuclear vectors global fold determination high-throughput NMR methods protein kinematics residual dipolar couplings structural genomics systematic search 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Al-Hashimi, H.M., Valafar, H., Terrell, M., Zartler, E.R., Eidsness, M.K. and Prestegard, J.H. (2000) J. Magn. Reson., 143, 402-406.PubMedGoogle Scholar
  2. Andrec, M., Du, P. and Levy, R.M. (2001) J. Biomol. NMR, 21, 335-347.PubMedGoogle Scholar
  3. Bailey-Kellogg, C., Widge, A., Kelley, J.J., Berardi, M.J., Bushweller, J.H. and Donald, B.R. (2000) J. Comput. Biol., 7, 537-558.PubMedGoogle Scholar
  4. Barbieri, R., Bertini, I., Cavallaro, G., Lee, Y., Luchinat, C. and Rosato, A. (2002) J. Am. Chem. Soc., 124, 5581-5587.PubMedGoogle Scholar
  5. Berman, H.M., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T.N., Weissig, H., Shindyalov, I.N. and Bourne, P.E. (2000) Nucl. Acids Res., 28, 235-242.PubMedGoogle Scholar
  6. Bertram, R., Quine, J.R., Chapman, M.S. and Cross, T.A. (2000) J. Magn. Reson., 147, 9-16.PubMedGoogle Scholar
  7. Brünger, A.T. (1993) XPLOR: A System for X-Ray Crystallography and NMR, Yale University Press, New Haven.Google Scholar
  8. Chou, J.J., Gaemers, S., Howder, B., Louis, J.M. and Bax, A. (2001) J. Biomol. NMR, 21, 377-382.PubMedGoogle Scholar
  9. Clore, G.M., Gronenborn, A.M. and Bax, A. (1998) J. Magn. Reson., 133, 216-221.PubMedGoogle Scholar
  10. Clore, G.M., Starich, M.R., Bewley, C.A., Cai, M.L. and Kuszewski, J. (1999) J. Am. Chem. Soc., 121, 6513-6514.Google Scholar
  11. Cormen, T.H., Leiserson, C.E., Rivest, R.L. and Stein, C. (2001) Introduction to Algorithms, The MIT Press.Google Scholar
  12. Cornilescu, G., Marquardt, J.L., Ottiger, M. and Bax, A. (1998) J. Am. Chem. Soc., 120, 6836-6837.Google Scholar
  13. Delaglio, F., Kontaxis, G. and Bax, A. (2000) J. Am. Chem. Soc., 122, 2142-2143.Google Scholar
  14. Dominguez, C., Boelens, R. and Bonvin, A.M.J.J. (2003) J. Am. Chem. Soc., 125, 1731-1737.PubMedGoogle Scholar
  15. Engh, R.A. and Huber, R. (1991) Acta Cryst., A47, 392-400.Google Scholar
  16. Fowler, A.C., Tian, F., Al-Hashimi, H.M. and Prestegard, J.H. (2000) J. Mol. Biol., 304, 447-460.PubMedGoogle Scholar
  17. Gardner, K.H. and Kay, L.E. (1997) J. Am. Chem. Soc., 119, 7599-7600.Google Scholar
  18. Giesen, A.W., Homans, S.W. and Brown, J.M. (2003) J. Biomol. NMR 25, 63-71.PubMedGoogle Scholar
  19. Gnu (2002) The gnu general public license, http://www.gnu.org/licenses/licenses.html Google Scholar
  20. Güntert, P., Mumenthaler, C. and Wüthrich, K. (1997) J. Mol. Biol., 273, 283-298.PubMedGoogle Scholar
  21. Hansen, M.R., Hanson, P. and Pardi, A. (2000) Meth. Enzymol., 317, 220-240.PubMedGoogle Scholar
  22. Hus, J.C., Marion, D. and Blackledge, M. (2001) J. Am. Chem. Soc., 123, 1541-1542.PubMedGoogle Scholar
  23. Kac, M. (1948) Proc. London Math. Soc., 50, 390-408.Google Scholar
  24. Kemple, M.D., D., R.B., Lipkowitz, K.B., Prendergast, F.G. and Rao, B.D. (1988) J. Am. Chem. Soc., 110, 8275-8287.Google Scholar
  25. Kolinski, A. and Skolnick, J. (1998) Proteins, 32, 475-494.PubMedGoogle Scholar
  26. Losonczi, J.A., Andrec, M., Fischer, M.W. and Prestegard, J.H. (1999) J. Magn. Reson., 138, 334-342.PubMedGoogle Scholar
  27. Meiler, J., Blomberg, N., Nilges, M. and Griesinger, C. (2000) J. Biomol. NMR, 16, 245-252.PubMedGoogle Scholar
  28. Nomura, K. and Kainosho, M. (2002) J. Magn. Reson., 154, 146-153.PubMedGoogle Scholar
  29. Ottiger, M. and Bax, A. (1998) J. Am. Chem. Soc., 120, 12334-12341.Google Scholar
  30. Quine, J.R., Brenneman, M. and Cross, T. (1997) Biophys. J., 72, 2342-2348.PubMedGoogle Scholar
  31. Ramirez, B.E. and Bax, A. (1998) J. Am. Chem. Soc., 120, 9106-9107.Google Scholar
  32. Rienstra, C.M., Tucker-Kellogg, L., Jaroniec, C.P., Hohwy, M., Reif, B., McMahon, M.T., Tidor, B., Lozano-Pèrez, T. and Griffin, R.G. (2002) Proc. Natl. Acad. Sci. USA, 99, 10260-10265.PubMedGoogle Scholar
  33. Rohl, C.A. and Baker, D. (2002) J. Am. Chem. Soc., 124, 2723-2729.PubMedGoogle Scholar
  34. Saupe, A. (1968) Angew. Chem., 7, 97-112.Google Scholar
  35. Stryer, L. (1994) Biochemistry, W.H. Freeman and Company.Google Scholar
  36. Tian, F., Valafar, H. and Prestegard, J.H. (2001) J. Am. Chem. Soc., 123, 11791-11796.PubMedGoogle Scholar
  37. Tjandra, N. and Bax, A. (1997) Science, 278, 1111-1114.PubMedGoogle Scholar
  38. Tolman, J.R., Flanagan, J.M., Kennedy, M.A. and Prestegard, J.H. (1995) Proc. Natl. Acad. Sci. USA, 92, 9279-9283.PubMedGoogle Scholar
  39. Vijay-Kumar, S., Bugg, C.E. and Cook, W.J. (1987) J. Mol. Biol., 194, 531-544.PubMedGoogle Scholar
  40. Wang, L., Pang, Y., Holder, T., Brender, J., Kurochkin, A.V. and Zuiderweg, E.R.P. (2001) Proc. Natl. Acad. Sci. USA, 98, 7684-7689.PubMedGoogle Scholar
  41. Wang, Y.X., Marquardt, J.L., Wingfield, P., Stahl, S.J., Lee-Huang, S., Torchia, D. and Bax, A. (1998) J. Am. Chem. Soc., 120, 7385-7386.Google Scholar
  42. Wedemeyer, W.J., Rohl, C.A. and Scheraga, H.A. (2002) J. Biomol. NMR, 22, 137-151.PubMedGoogle Scholar
  43. Yue, K. and Dill, K.A. (2000) Protein Sci., 9, 1935-1946.PubMedGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Lincong Wang
    • 1
  • Bruce Randall Donald
    • 2
    • 3
  1. 1.Dartmouth Computer Science DepartmentHanoverU.S.A
  2. 2.Dartmouth Computer Science Department, Dartmouth Chemistry Department, and Dartmouth Department of Biological SciencesHanoverU.S.A
  3. 3.Dartmouth Computer Science DepartmentSudikoff LaboratoryHanoverU.S.A.

Personalised recommendations