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. 2002 Nov;83(5):2457–2474. doi: 10.1016/S0006-3495(02)75257-0

A coarse-grained normal mode approach for macromolecules: an efficient implementation and application to Ca(2+)-ATPase.

Guohui Li 1, Qiang Cui 1
PMCID: PMC1302332  PMID: 12414680

Abstract

A block normal mode (BNM) algorithm, originally proposed by Tama et al., (Proteins Struct. Func. Genet. 41:1-7, 2000) was implemented into the simulation program CHARMM. The BNM approach projects the hessian matrix into local translation/rotation basis vectors and, therefore, dramatically reduces the size of the matrix involved in diagonalization. In the current work, by constructing the atomic hessian elements required in the projection operation on the fly, the memory requirement for the BNM approach has been significantly reduced from that of standard normal mode analysis and previous implementation of BNM. As a result, low frequency modes, which are of interest in large-scale conformational changes of large proteins or protein-nucleic acid complexes, can be readily obtained. Comparison of the BNM results with standard normal mode analysis for a number of small proteins and nucleic acids indicates that many properties dominated by low frequency motions are well reproduced by BNM; these include atomic fluctuations, the displacement covariance matrix, vibrational entropies, and involvement coefficients for conformational transitions. Preliminary application to a fairly large system, Ca(2+)-ATPase (994 residues), is described as an example. The structural flexibility of the cytoplasmic domains (especially domain N), correlated motions among residues on domain interfaces and displacement patterns for the transmembrane helices observed in the BNM results are discussed in relation to the function of Ca(2+)-ATPase. The current implementation of the BNM approach has paved the way for developing efficient sampling algorithms with molecular dynamics or Monte Carlo for studying long-time scale dynamics of macromolecules.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Aravind L., Galperin M. Y., Koonin E. V. The catalytic domain of the P-type ATPase has the haloacid dehalogenase fold. Trends Biochem Sci. 1998 Apr;23(4):127–129. doi: 10.1016/s0968-0004(98)01189-x. [DOI] [PubMed] [Google Scholar]
  2. Bahar I., Atilgan A. R., Erman B. Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential. Fold Des. 1997;2(3):173–181. doi: 10.1016/S1359-0278(97)00024-2. [DOI] [PubMed] [Google Scholar]
  3. Baker K. J., East J. M., Lee A. G. Localization of the hinge region of the Ca(2+)-ATPase of sarcoplasmic reticulum using resonance energy transfer. Biochim Biophys Acta. 1994 Jun 1;1192(1):53–60. doi: 10.1016/0005-2736(94)90142-2. [DOI] [PubMed] [Google Scholar]
  4. Bernèche S., Roux B. Energetics of ion conduction through the K+ channel. Nature. 2001 Nov 1;414(6859):73–77. doi: 10.1038/35102067. [DOI] [PubMed] [Google Scholar]
  5. Brüschweiler R, Case DA. Collective NMR relaxation model applied to protein dynamics. Phys Rev Lett. 1994 Feb 7;72(6):940–943. doi: 10.1103/PhysRevLett.72.940. [DOI] [PubMed] [Google Scholar]
  6. Chattopadhyaya R., Meador W. E., Means A. R., Quiocho F. A. Calmodulin structure refined at 1.7 A resolution. J Mol Biol. 1992 Dec 20;228(4):1177–1192. doi: 10.1016/0022-2836(92)90324-d. [DOI] [PubMed] [Google Scholar]
  7. Cheetham G. M., Jeruzalmi D., Steitz T. A. Structural basis for initiation of transcription from an RNA polymerase-promoter complex. Nature. 1999 May 6;399(6731):80–83. doi: 10.1038/19999. [DOI] [PubMed] [Google Scholar]
  8. Cheetham G. M., Steitz T. A. Insights into transcription: structure and function of single-subunit DNA-dependent RNA polymerases. Curr Opin Struct Biol. 2000 Feb;10(1):117–123. doi: 10.1016/s0959-440x(99)00058-5. [DOI] [PubMed] [Google Scholar]
  9. Clarke D. M., Maruyama K., Loo T. W., Leberer E., Inesi G., MacLennan D. H. Functional consequences of glutamate, aspartate, glutamine, and asparagine mutations in the stalk sector of the Ca2+-ATPase of sarcoplasmic reticulum. J Biol Chem. 1989 Jul 5;264(19):11246–11251. [PubMed] [Google Scholar]
  10. Crivici A., Ikura M. Molecular and structural basis of target recognition by calmodulin. Annu Rev Biophys Biomol Struct. 1995;24:85–116. doi: 10.1146/annurev.bb.24.060195.000505. [DOI] [PubMed] [Google Scholar]
  11. Doyle D. A., Morais Cabral J., Pfuetzner R. A., Kuo A., Gulbis J. M., Cohen S. L., Chait B. T., MacKinnon R. The structure of the potassium channel: molecular basis of K+ conduction and selectivity. Science. 1998 Apr 3;280(5360):69–77. doi: 10.1126/science.280.5360.69. [DOI] [PubMed] [Google Scholar]
  12. Finn B. E., Evenäs J., Drakenberg T., Waltho J. P., Thulin E., Forsén S. Calcium-induced structural changes and domain autonomy in calmodulin. Nat Struct Biol. 1995 Sep;2(9):777–783. doi: 10.1038/nsb0995-777. [DOI] [PubMed] [Google Scholar]
  13. Fischer S., Michnick S., Karplus M. A mechanism for rotamase catalysis by the FK506 binding protein (FKBP). Biochemistry. 1993 Dec 21;32(50):13830–13837. doi: 10.1021/bi00213a011. [DOI] [PubMed] [Google Scholar]
  14. Halle Bertil. Flexibility and packing in proteins. Proc Natl Acad Sci U S A. 2002 Jan 29;99(3):1274–1279. doi: 10.1073/pnas.032522499. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Henderson I. M., Starling A. P., Wictome M., East J. M., Lee A. G. Binding of Ca2+ to the (Ca(2+)-Mg2+)-ATPase of sarcoplasmic reticulum: kinetic studies. Biochem J. 1994 Feb 1;297(Pt 3):625–636. doi: 10.1042/bj2970625. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Humphrey W., Dalke A., Schulten K. VMD: visual molecular dynamics. J Mol Graph. 1996 Feb;14(1):33-8, 27-8. doi: 10.1016/0263-7855(96)00018-5. [DOI] [PubMed] [Google Scholar]
  17. Jencks W. P. How does a calcium pump pump calcium? J Biol Chem. 1989 Nov 15;264(32):18855–18858. [PubMed] [Google Scholar]
  18. Jencks W. P. On the mechanism of ATP-driven Ca2+ transport by the calcium ATPase of sarcoplasmic reticulum. Ann N Y Acad Sci. 1992 Nov 30;671:49–57. doi: 10.1111/j.1749-6632.1992.tb43783.x. [DOI] [PubMed] [Google Scholar]
  19. Jencks W. P., Yang T., Peisach D., Myung J. Calcium ATPase of sarcoplasmic reticulum has four binding sites for calcium. Biochemistry. 1993 Jul 13;32(27):7030–7034. doi: 10.1021/bi00078a031. [DOI] [PubMed] [Google Scholar]
  20. Kidera A., Inaka K., Matsushima M., Go N. Normal mode refinement: crystallographic refinement of protein dynamic structure. II. Application to human lysozyme. J Mol Biol. 1992 May 20;225(2):477–486. doi: 10.1016/0022-2836(92)90933-b. [DOI] [PubMed] [Google Scholar]
  21. Kuboniwa H., Tjandra N., Grzesiek S., Ren H., Klee C. B., Bax A. Solution structure of calcium-free calmodulin. Nat Struct Biol. 1995 Sep;2(9):768–776. doi: 10.1038/nsb0995-768. [DOI] [PubMed] [Google Scholar]
  22. Lazaridis T., Karplus M. Effective energy functions for protein structure prediction. Curr Opin Struct Biol. 2000 Apr;10(2):139–145. doi: 10.1016/s0959-440x(00)00063-4. [DOI] [PubMed] [Google Scholar]
  23. Lee A. G., East J. M. What the structure of a calcium pump tells us about its mechanism. Biochem J. 2001 Jun 15;356(Pt 3):665–683. doi: 10.1042/0264-6021:3560665. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Ma J., Karplus M. The allosteric mechanism of the chaperonin GroEL: a dynamic analysis. Proc Natl Acad Sci U S A. 1998 Jul 21;95(15):8502–8507. doi: 10.1073/pnas.95.15.8502. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. MacLennan D. H., Brandl C. J., Korczak B., Green N. M. Amino-acid sequence of a Ca2+ + Mg2+-dependent ATPase from rabbit muscle sarcoplasmic reticulum, deduced from its complementary DNA sequence. Nature. 1985 Aug 22;316(6030):696–700. doi: 10.1038/316696a0. [DOI] [PubMed] [Google Scholar]
  26. MacLennan D. H., Rice W. J., Green N. M. The mechanism of Ca2+ transport by sarco(endo)plasmic reticulum Ca2+-ATPases. J Biol Chem. 1997 Nov 14;272(46):28815–28818. doi: 10.1074/jbc.272.46.28815. [DOI] [PubMed] [Google Scholar]
  27. Makri N. Time-dependent quantum methods for large systems. Annu Rev Phys Chem. 1999;50:167–191. doi: 10.1146/annurev.physchem.50.1.167. [DOI] [PubMed] [Google Scholar]
  28. Marques O., Sanejouand Y. H. Hinge-bending motion in citrate synthase arising from normal mode calculations. Proteins. 1995 Dec;23(4):557–560. doi: 10.1002/prot.340230410. [DOI] [PubMed] [Google Scholar]
  29. Morais-Cabral J. H., Zhou Y., MacKinnon R. Energetic optimization of ion conduction rate by the K+ selectivity filter. Nature. 2001 Nov 1;414(6859):37–42. doi: 10.1038/35102000. [DOI] [PubMed] [Google Scholar]
  30. Møller J. V., Juul B., le Maire M. Structural organization, ion transport, and energy transduction of P-type ATPases. Biochim Biophys Acta. 1996 May 6;1286(1):1–51. doi: 10.1016/0304-4157(95)00017-8. [DOI] [PubMed] [Google Scholar]
  31. Northrup S. H., Pear M. R., McCammon J. A., Karplus M. Molecular dynamics of ferrocytochrome c. Nature. 1980 Jul 17;286(5770):304–305. doi: 10.1038/286304a0. [DOI] [PubMed] [Google Scholar]
  32. Roux B., Simonson T. Implicit solvent models. Biophys Chem. 1999 Apr 5;78(1-2):1–20. doi: 10.1016/s0301-4622(98)00226-9. [DOI] [PubMed] [Google Scholar]
  33. Sagnella D. E., Straub J. E. A study of vibrational relaxation of B-state carbon monoxide in the heme pocket of photolyzed carboxymyoglobin. Biophys J. 1999 Jul;77(1):70–84. doi: 10.1016/S0006-3495(99)76873-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  34. Shen Yufeng, Kong Yifei, Ma Jianpeng. Intrinsic flexibility and gating mechanism of the potassium channel KcsA. Proc Natl Acad Sci U S A. 2002 Feb 12;99(4):1949–1953. doi: 10.1073/pnas.042650399. [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. Simonson T., Perahia D. Normal modes of symmetric protein assemblies. Application to the tobacco mosaic virus protein disk. Biophys J. 1992 Feb;61(2):410–427. doi: 10.1016/S0006-3495(92)81847-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  36. Smith J., Kuczera K., Karplus M. Dynamics of myoglobin: comparison of simulation results with neutron scattering spectra. Proc Natl Acad Sci U S A. 1990 Feb;87(4):1601–1605. doi: 10.1073/pnas.87.4.1601. [DOI] [PMC free article] [PubMed] [Google Scholar]
  37. Tama F., Gadea F. X., Marques O., Sanejouand Y. H. Building-block approach for determining low-frequency normal modes of macromolecules. Proteins. 2000 Oct 1;41(1):1–7. doi: 10.1002/1097-0134(20001001)41:1<1::aid-prot10>3.0.co;2-p. [DOI] [PubMed] [Google Scholar]
  38. Tama F., Sanejouand Y. H. Conformational change of proteins arising from normal mode calculations. Protein Eng. 2001 Jan;14(1):1–6. doi: 10.1093/protein/14.1.1. [DOI] [PubMed] [Google Scholar]
  39. Thomas A., Field M. J., Perahia D. Analysis of the low-frequency normal modes of the R state of aspartate transcarbamylase and a comparison with the T state modes. J Mol Biol. 1996 Aug 23;261(3):490–506. doi: 10.1006/jmbi.1996.0478. [DOI] [PubMed] [Google Scholar]
  40. Thomas A., Hinsen K., Field M. J., Perahia D. Tertiary and quaternary conformational changes in aspartate transcarbamylase: a normal mode study. Proteins. 1999 Jan 1;34(1):96–112. doi: 10.1002/(sici)1097-0134(19990101)34:1<96::aid-prot8>3.0.co;2-0. [DOI] [PubMed] [Google Scholar]
  41. Tidor B., Karplus M. The contribution of vibrational entropy to molecular association. The dimerization of insulin. J Mol Biol. 1994 May 6;238(3):405–414. doi: 10.1006/jmbi.1994.1300. [DOI] [PubMed] [Google Scholar]
  42. Tirion MM. Large Amplitude Elastic Motions in Proteins from a Single-Parameter, Atomic Analysis. Phys Rev Lett. 1996 Aug 26;77(9):1905–1908. doi: 10.1103/PhysRevLett.77.1905. [DOI] [PubMed] [Google Scholar]
  43. Toyoshima C., Nakasako M., Nomura H., Ogawa H. Crystal structure of the calcium pump of sarcoplasmic reticulum at 2.6 A resolution. Nature. 2000 Jun 8;405(6787):647–655. doi: 10.1038/35015017. [DOI] [PubMed] [Google Scholar]
  44. Toyoshima C., Sasabe H., Stokes D. L. Three-dimensional cryo-electron microscopy of the calcium ion pump in the sarcoplasmic reticulum membrane. Nature. 1993 Apr 1;362(6419):467–471. doi: 10.1038/362469a0. [DOI] [PubMed] [Google Scholar]
  45. Zhang M., Tanaka T., Ikura M. Calcium-induced conformational transition revealed by the solution structure of apo calmodulin. Nat Struct Biol. 1995 Sep;2(9):758–767. doi: 10.1038/nsb0995-758. [DOI] [PubMed] [Google Scholar]
  46. Zhang P., Toyoshima C., Yonekura K., Green N. M., Stokes D. L. Structure of the calcium pump from sarcoplasmic reticulum at 8-A resolution. Nature. 1998 Apr 23;392(6678):835–839. doi: 10.1038/33959. [DOI] [PubMed] [Google Scholar]
  47. Zhou Y., Morais-Cabral J. H., Kaufman A., MacKinnon R. Chemistry of ion coordination and hydration revealed by a K+ channel-Fab complex at 2.0 A resolution. Nature. 2001 Nov 1;414(6859):43–48. doi: 10.1038/35102009. [DOI] [PubMed] [Google Scholar]
  48. von Hippel P. H., Bear D. G., Morgan W. D., McSwiggen J. A. Protein-nucleic acid interactions in transcription: a molecular analysis. Annu Rev Biochem. 1984;53:389–446. doi: 10.1146/annurev.bi.53.070184.002133. [DOI] [PubMed] [Google Scholar]

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