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. 1994 Jun;3(6):936–943. doi: 10.1002/pro.5560030608

Harmonic and anharmonic aspects in the dynamics of BPTI: a normal mode analysis and principal component analysis.

S Hayward 1, A Kitao 1, N Go 1
PMCID: PMC2142881  PMID: 7520795

Abstract

A comparison is made between a 200-ps molecular dynamics simulation in vacuum and a normal mode analysis on the protein bovine pancreatic trypsin inhibitor (BPTI) in order to elucidate the dual aspects of harmonicity and anharmonicity in the dynamics of proteins. The molecular dynamics trajectory is analyzed using principal component analysis, an effective harmonic analysis suited for comparison with the results from the normal mode analysis. The results suggest that the first principal component shows qualitatively different behavior from higher principal components and is associated with apparent barrier crossing events on an anharmonic conformational energy surface. The higher principal components appear to have probability distributions that are well approximated by Gaussians, indicating harmonicity. Eliminating the contribution from the first principal component reveals a great deal of correspondence between the 2 methods. This correspondence, however, involves a factor of 2, as the variances of the distribution of the higher principal components are, on average, roughly twice those found from the normal mode analysis. A model is proposed to reconcile these results with those from previous analyses.

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Selected References

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

  1. Amadei A., Linssen A. B., Berendsen H. J. Essential dynamics of proteins. Proteins. 1993 Dec;17(4):412–425. doi: 10.1002/prot.340170408. [DOI] [PubMed] [Google Scholar]
  2. Austin R. H., Beeson K. W., Eisenstein L., Frauenfelder H., Gunsalus I. C. Dynamics of ligand binding to myoglobin. Biochemistry. 1975 Dec 2;14(24):5355–5373. doi: 10.1021/bi00695a021. [DOI] [PubMed] [Google Scholar]
  3. Brooks B., Karplus M. Harmonic dynamics of proteins: normal modes and fluctuations in bovine pancreatic trypsin inhibitor. Proc Natl Acad Sci U S A. 1983 Nov;80(21):6571–6575. doi: 10.1073/pnas.80.21.6571. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Elber R., Karplus M. Multiple conformational states of proteins: a molecular dynamics analysis of myoglobin. Science. 1987 Jan 16;235(4786):318–321. doi: 10.1126/science.3798113. [DOI] [PubMed] [Google Scholar]
  5. Go N., Noguti T., Nishikawa T. Dynamics of a small globular protein in terms of low-frequency vibrational modes. Proc Natl Acad Sci U S A. 1983 Jun;80(12):3696–3700. doi: 10.1073/pnas.80.12.3696. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Hayward S., Kitao A., Hirata F., Go N. Effect of solvent on collective motions in globular protein. J Mol Biol. 1993 Dec 20;234(4):1207–1217. doi: 10.1006/jmbi.1993.1671. [DOI] [PubMed] [Google Scholar]
  7. Horiuchi T., Go N. Projection of Monte Carlo and molecular dynamics trajectories onto the normal mode axes: human lysozyme. Proteins. 1991;10(2):106–116. doi: 10.1002/prot.340100204. [DOI] [PubMed] [Google Scholar]
  8. Ikura M., Clore G. M., Gronenborn A. M., Zhu G., Klee C. B., Bax A. Solution structure of a calmodulin-target peptide complex by multidimensional NMR. Science. 1992 May 1;256(5057):632–638. doi: 10.1126/science.1585175. [DOI] [PubMed] [Google Scholar]
  9. Kidera A., Go N. Normal mode refinement: crystallographic refinement of protein dynamic structure. I. Theory and test by simulated diffraction data. J Mol Biol. 1992 May 20;225(2):457–475. doi: 10.1016/0022-2836(92)90932-a. [DOI] [PubMed] [Google Scholar]
  10. Kidera A., Go N. Refinement of protein dynamic structure: normal mode refinement. Proc Natl Acad Sci U S A. 1990 May;87(10):3718–3722. doi: 10.1073/pnas.87.10.3718. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. 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]
  12. Mozzarelli A., Rivetti C., Rossi G. L., Henry E. R., Eaton W. A. Crystals of haemoglobin with the T quaternary structure bind oxygen noncooperatively with no Bohr effect. Nature. 1991 May 30;351(6325):416–419. doi: 10.1038/351416a0. [DOI] [PubMed] [Google Scholar]
  13. Noguti T., Go N. Structural basis of hierarchical multiple substates of a protein. I: Introduction. Proteins. 1989;5(2):97–103. doi: 10.1002/prot.340050203. [DOI] [PubMed] [Google Scholar]
  14. Noguti T., Go N. Structural basis of hierarchical multiple substates of a protein. III: Side chain and main chain local conformations. Proteins. 1989;5(2):113–124. doi: 10.1002/prot.340050205. [DOI] [PubMed] [Google Scholar]
  15. Noguti T., Go N. Structural basis of hierarchical multiple substates of a protein. V: Nonlocal deformations. Proteins. 1989;5(2):132–138. doi: 10.1002/prot.340050207. [DOI] [PubMed] [Google Scholar]
  16. Tilton R. F., Jr, Dewan J. C., Petsko G. A. Effects of temperature on protein structure and dynamics: X-ray crystallographic studies of the protein ribonuclease-A at nine different temperatures from 98 to 320 K. Biochemistry. 1992 Mar 10;31(9):2469–2481. doi: 10.1021/bi00124a006. [DOI] [PubMed] [Google Scholar]

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