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Elastic Network Models: Theoretical and Empirical Foundations

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Biomolecular Simulations

Part of the book series: Methods in Molecular Biology ((MIMB,volume 924))

Abstract

Fifteen years ago, Monique Tirion showed that the low-frequency normal modes of a protein are not significantly altered when nonbonded interactions are replaced by Hookean springs, for all atom pairs whose distance is smaller than a given cutoff value. Since then, it has been shown that coarse-grained versions of Tirion’s model are able to provide fair insights on many dynamical properties of biological macromolecules. In this chapter, theoretical tools required for studying these so-called Elastic Network Models are described, focusing on practical issues and, in particular, on possible artifacts. Then, an overview of some typical results that have been obtained by studying such models is given.

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References

  1. Tirion M (1996) Low-amplitude elastic motions in proteins from a single-parameter atomic analysis. Phys Rev Lett 77:1905–1908

    Article  PubMed  CAS  Google Scholar 

  2. Noguti T, Go N (1982) Collective variable description of small-amplitude conformational fluctuations in a globular protein. Nature 296:776–778

    Article  PubMed  CAS  Google Scholar 

  3. Go N, Noguti T, Nishikawa T (1983) Dynamics of a small globular protein in terms of low-frequency vibrational modes. Proc Natl Acad Sci USA 80:3696–3700

    Article  PubMed  CAS  Google Scholar 

  4. Levitt M, Sander C, Stern P (1983) Normal-mode dynamics of a protein: bovine pancreatic trypsin inhibitor. Int J Quant Chem 10:181–199

    CAS  Google Scholar 

  5. Bahar I, Atilgan AR, Erman B (1997) Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential. Fold Des 2:173–181

    Article  PubMed  CAS  Google Scholar 

  6. Hinsen K (1998) Analysis of domain motions by approximate normal mode calculations. Proteins 33:417–429

    Article  PubMed  CAS  Google Scholar 

  7. Micheletti C, Lattanzi G, Maritan A (2002) Elastic properties of proteins: insight on the folding process and evolutionary selection of native structures. J Mol Biol 321:909–921

    Article  PubMed  CAS  Google Scholar 

  8. Kondrashov D, Van Wynsberghe A, Bannen R, Cui Q, Phillips G (2007) Protein structural variation in computational models and crystallographic data. Structure 15:169–177

    Article  PubMed  CAS  Google Scholar 

  9. Bahar I, Cui Q (eds) (2005) Normal mode analysis: theory and applications to biological and chemical systems. C&H/CRC Mathematical and Computational Biology Series, vol. 9. CRC press, Boca Raton

    Google Scholar 

  10. Tama F, Sanejouand YH (2001) Conformational change of proteins arising from normal mode calculations. Prot Engineering 14:1–6

    Article  CAS  Google Scholar 

  11. Krebs WG, Alexandrov V, Wilson CA, Echols N, Yu H, Gerstein M (2002) Normal mode analysis of macromolecular motions in a database framework: developing mode concentration as a useful classifying statistic. Proteins 48:682–695

    Article  PubMed  CAS  Google Scholar 

  12. Delarue M, Sanejouand Y-H (2002) Simplified normal modes analysis of conformational transitions in DNA-dependant polymerases: the elastic network model. J Mol Biol 320:1011–1024

    Article  PubMed  CAS  Google Scholar 

  13. Valadie H, Lacapere J-J, Sanejouand Y-H, Etchebest C (2003) Dynamical properties of the MscL of Escherichia coli: a normal mode analysis. J Mol Biol 332:657–674

    Article  PubMed  CAS  Google Scholar 

  14. Suhre K, Sanejouand Y-H (2004) Elnémo: a normal mode server for protein movement analysis and the generation of templates for molecular replacement. Nucl Ac Res 32:W610–W614

    Article  CAS  Google Scholar 

  15. Tama F, Brooks III C (2002) The mechanism and pathway of pH induced swelling in cowpea chlorotic mottle virus. J Mol Biol 318:733–747

    Article  PubMed  CAS  Google Scholar 

  16. Tama F, Valle M, Frank J, Brooks III CL (2003) Dynamic reorganization of the functionally active ribosome explored by normal mode analysis and cryo-electron microscopy. Proc Natl Acad Sci USA 100:9319–9323

    Article  PubMed  CAS  Google Scholar 

  17. Tirion M, ben Avraham D, Lorenz M, Holmes K (1995) Normal modes as refinement parameters for the F-actin model. Biophys J 68:5–12

    Google Scholar 

  18. Suhre K, Sanejouand Y-H (2004) On the potential of normal mode analysis for solving difficult molecular replacement problems. Act Cryst D 60:796–799

    Article  Google Scholar 

  19. Delarue M, Dumas P (2004) On the use of low-frequency normal modes to enforce collective movements in refining macromolecular structural models. Proc Natl Acad Sci USA 101:6957–6962

    Article  PubMed  CAS  Google Scholar 

  20. Tama F, Miyashita O, Brooks III CL (2004) Flexible multi-scale fitting of atomic structures into low-resolution electron density maps with elastic network normal mode analysis. J Mol Biol 337:985–999

    Article  PubMed  CAS  Google Scholar 

  21. Hinsen K, Reuter N, Navaza J, Stokes DL, Lacapere JJ (2005) Normal mode-base fitting of atomic structure into electron density maps: application to sarcoplasmic reticulum Ca-ATPase. Biophys J 88:818–827

    Article  PubMed  CAS  Google Scholar 

  22. Mitra K, Schaffitzel C, Shaikh T, Tama F, Jenni S, Brooks 3rd C, Ban N, Frank J (2005) Structure of the E. coli protein-conducting channel bound to a translating ribosome. Nature 438:318–324

    Article  PubMed  CAS  Google Scholar 

  23. Suhre K, Navaza J, Sanejouand Y-H (2006) Norma: a tool for flexible fitting of high resolution protein structures into low resolution electron microscopy derived density maps. Act Cryst D 62:1098–1100

    Article  Google Scholar 

  24. Levitt M, Warshel A (1975) Computer simulation of protein folding. Nature 253:694–698

    Article  PubMed  CAS  Google Scholar 

  25. Taketomi H, Ueda Y, Go N (1975) Studies on protein folding, unfolding and fluctuations by computer simulation. I. The effect of specific amino acid sequence represented by specific inter-unit interactions. Int J Pept Prot Res 7:445–459

    CAS  Google Scholar 

  26. Shakhnovich E, Gutin A (1990) Enumeration of all compact conformations of copolymers with random sequence of links. J Chem Phys 93:5967

    Article  CAS  Google Scholar 

  27. Li H, Tang C, Wingreen N (1997) Nature of driving force for protein folding: a result from analyzing the statistical potential. Phys Rev lett 79:765–768

    Article  CAS  Google Scholar 

  28. Li H, Helling R, Tang C, Wingreen N (1996) Emergence of preferred structures in a simple model of protein folding. Science 273:666–669

    Article  PubMed  CAS  Google Scholar 

  29. Trinquier G, Sanejouand YH (1999) New protein-like properties of cubic lattice models. Phys Rev E 59:942–946

    Article  CAS  Google Scholar 

  30. He Y, Chen Y, Alexander P, Bryan P, Orban J (2008) NMR structures of two designed proteins with high sequence identity but different fold and function. Proc Natl Acad Sci USA 105:14412

    Article  PubMed  CAS  Google Scholar 

  31. Goldstein H (1950) Classical mechanics. Addison-Wesley, Reading, MA

    Google Scholar 

  32. Wilson E, Decius J, Cross P (1955) Cross molecular vibrations. McGraw-Hill, New York

    Google Scholar 

  33. Sanejouand Y-H (1990) Ph.D. Thesis. Université de Paris XI, Orsay, France

    Google Scholar 

  34. Levy R, Perahia D, Karplus M (1982) Molecular dynamics of an alpha-helical polypeptide: temperature dependance and deviation from harmonic behavior. Proc Natl Acad Sci USA 79:1346–1350

    Article  PubMed  CAS  Google Scholar 

  35. Elber R, Karplus M (1987) Multiple conformational states of proteins: a molecular dynamics analysis of myoglobin. Science 235:318–321

    Article  PubMed  CAS  Google Scholar 

  36. Brooks B, Karplus M (1983) Harmonic dynamics of proteins: normal modes and fluctuations in bovine pancreatic trypsin inhibitor. Proc Natl Acad Sci USA 80:6571–6575

    Article  PubMed  CAS  Google Scholar 

  37. Lazaridis T, Karplus M (1999) Effective energy function for proteins in solution. Proteins 35:133–152

    Article  PubMed  CAS  Google Scholar 

  38. Haliloglu T, Bahar I, Erman B (1997) Gaussian dynamics of folded proteins. Phys Rev lett 79:3090–3093

    Article  CAS  Google Scholar 

  39. Atilgan A, Durell S, Jernigan R, Demirel M, Keskin O, Bahar I (2001) Anisotropy of fluctuation dynamics of proteins with an elastic network model. Biophys J 80:505–515

    Article  PubMed  CAS  Google Scholar 

  40. Hinsen K, Kneller G (1999) A simplified force field for describing vibrational protein dynamics over the whole frequency range. J Chem Phys 111:10766

    Article  CAS  Google Scholar 

  41. Kundu S, Melton J, Sorensen D, Phillips Jr G (2002) Dynamics of proteins in crystals: comparison of experiment with simple models. Biophys J 83:723–732

    Article  PubMed  CAS  Google Scholar 

  42. Nicolay S, Sanejouand Y-H (2006) Functional modes of proteins are among the most robust. Phys Rev Lett 96:078104

    Article  PubMed  CAS  Google Scholar 

  43. Miyazawa S, Jernigan R (1985) Estimation of effective inter-residue contact energies from protein crystal structures: quasi-chemical approximation. Macromolecules 18:534–552

    Article  CAS  Google Scholar 

  44. Miyazawa S, Jernigan R (1996) Residue-residue potentials with a favorable contact pair term and an unfavorable high packing density term for simulation and threading. J Mol Biol 256:623–644

    Article  PubMed  CAS  Google Scholar 

  45. Tama F (2000) Ph.D. Thesis. Université Paul Sabatier, Toulouse, France

    Google Scholar 

  46. Durand P, Trinquier G, Sanejouand YH (1994) A new approach for determining low-frequency normal modes in macromolecules. Biopolymers 34:759–771

    Article  CAS  Google Scholar 

  47. Tama F, Gadea F-X, Marques O, Sanejouand Y-H (2000) Building-block approach for determining low-frequency normal modes of macromolecules. Proteins 41:1–7

    Article  PubMed  CAS  Google Scholar 

  48. Kuriyan J, Weis W (1991) Rigid protein motion as a model for crystallographic temperature factors. Proc Natl Acad Sci USA 88:2773

    Article  PubMed  CAS  Google Scholar 

  49. Simonson T, Perahia D (1992) Normal modes of symmetric protein assemblies. Application to the tobacco mosaic virus protein disk. Biophys J 61:410–427

    CAS  Google Scholar 

  50. Hinsen K (2008) Structural flexibility in proteins: impact of the crystal environment. Bioinformatics 24:521

    Article  PubMed  CAS  Google Scholar 

  51. Riccardi D, Cui Q, Phillips Jr G (2009) Application of elastic network models to proteins in the crystalline state. Biophys J 96:464–475

    Article  PubMed  CAS  Google Scholar 

  52. Juanico B, Sanejouand Y-H, Piazza F, De Los Rios P (2007) Discrete breathers in nonlinear network models of proteins. Phys Rev Lett 99:238104

    Article  PubMed  CAS  Google Scholar 

  53. Sacquin-Mora S, Laforet E, Lavery R (2007) Locating the active sites of enzymes using mechanical properties. Proteins 67:350–359

    Article  PubMed  CAS  Google Scholar 

  54. Kraulis P (1991) Molscript: a program to produce both detailed and schematic plots of protein structures. J Appl Cryst 24:946–950

    Article  Google Scholar 

  55. Marques O, Sanejouand Y-H (1995) Hinge-bending motion in citrate synthase arising from normal mode calculations. Proteins 23:557–560

    Article  PubMed  CAS  Google Scholar 

  56. Lu M, Ma J (2005) The role of shape in determining molecular motions. Biophys J 89: 2395–2401

    Article  PubMed  CAS  Google Scholar 

  57. Tama F, Brooks C (2006) Symmetry, form, and shape: guiding principles for robustness in macromolecular machines. Annu Rev Biophys Biomol Struct 35:115–133

    Article  PubMed  CAS  Google Scholar 

  58. McCammon JA, Gelin BR, Karplus M, Wolynes P (1976) The hinge-bending mode in lysozyme. Nature 262:325–326

    Article  PubMed  CAS  Google Scholar 

  59. Harrison R (1984) Variational calculation of the normal modes of a large macromolecules: methods and some initial results. Biopolymers 23:2943–2949

    Article  PubMed  CAS  Google Scholar 

  60. Perahia D, Mouawad L (1995) Computation of low-frequency normal modes in macromolecules: improvements to the method of diagonalization in a mixed basis and application to hemoglobin. Comput Chem 19:241–246

    Article  PubMed  CAS  Google Scholar 

  61. Branden C, Tooze J et al (1991) Introduction to protein structure. Garland Publishing, New York

    Google Scholar 

  62. Gerstein M, Krebs W (1998) A database of macromolecular motions Nucl Acid Res 26:4280–4290

    CAS  Google Scholar 

  63. Diamond R (1990) On the use of normal modes in thermal parameter refinement: theory and application to the bovine pancreatic trypsin inhibitor. Acta Cryst A 46:425–435

    Article  Google Scholar 

  64. Kidera A, Go N (1990) Refinement of protein dynamic structure: normal mode refinement. Proc Natl Acad Sci USA 87:3718–3722

    Article  PubMed  CAS  Google Scholar 

  65. Sanejouand Y-H (1996) Normal-mode analysis suggests important flexibility between the two N-terminal domains of CD4 and supports the hypothesis of a conformational change in CD4 upon HIV binding. Prot Eng 9:671–677

    Article  CAS  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Nantes, Nantes, France

    Yves-Henri Sanejouand

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  1. Yves-Henri Sanejouand
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Correspondence to Yves-Henri Sanejouand .

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Editors and Affiliations

  1. DSIMB, UMR-S 665, INSERM, rue Alexandre Cabanel 6, Paris, 75015, France

    Luca Monticelli

  2. , Department of Applied Physics, Aalto University, Otakaari, AALTO, FI-00076, Finland

    Emppu Salonen

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Sanejouand, YH. (2013). Elastic Network Models: Theoretical and Empirical Foundations. In: Monticelli, L., Salonen, E. (eds) Biomolecular Simulations. Methods in Molecular Biology, vol 924. Humana Press, Totowa, NJ. https://doi.org/10.1007/978-1-62703-017-5_23

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  • DOI: https://doi.org/10.1007/978-1-62703-017-5_23

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  • Publisher Name: Humana Press, Totowa, NJ

  • Print ISBN: 978-1-62703-016-8

  • Online ISBN: 978-1-62703-017-5

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