Skip to main content
SpringerLink
Log in

The Joys and Perils of Flexible Fitting

  • Chapter
  • First Online:
Protein Conformational Dynamics

Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 805))

Abstract

While performing their functions, biological macromolecules often form large, dynamically changing macromolecular assemblies. Only a relatively small number of such assemblies have been accessible to the atomic-resolution techniques X-ray crystallography and NMR. Electron microscopy in conjunction with image reconstruction has become the preferred alternative for revealing the structures of such macromolecular complexes. However, for most assemblies the achievable resolution is too low to allow accurate atomic modeling directly from the data. Yet, useful models often can be obtained by fitting atomic models of individual components into a low-resolution reconstruction of the entire assembly. Several algorithms for achieving optimal fits in this context were developed recently, many allowing considerable degrees of flexibility to account for binding-induced conformational changes of the assembly components. This chapter describes the advantages and potential pitfalls of these methods and puts them into perspective with alternative approaches such as iterative modular fitting of rigid-body domains.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ahmed A, Tama F (2013) Consensus among multiple approaches as a reliability measure for flexible fitting into cryo-EM data. J Struct Biol 182:67–77

    Article  CAS  PubMed  Google Scholar 

  2. Ahmed A, Whitford PC, Sanbonmatsu KY, Tama F (2012) Consensus among flexible fitting approaches improves the interpretation of cryo-EM data. J Struct Biol 177:561–570

    Article  PubMed Central  PubMed  Google Scholar 

  3. Alber F, Dokudovskaya S, Veenhoff LM, Zhang W, Kipper J, Devos D, Suprapto A, Karni-Schmidt O, Williams R et al (2007) Determining the architectures of macromolecular assemblies. Nature 450:683–694

    Article  CAS  PubMed  Google Scholar 

  4. Allen GS, Stokes DL (2013) Modeling, docking, and fitting of atomic structures to 3D maps from cryo-electron microscopy. Methods Mol Biol 955:229–241

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  5. Bammes BE, Rochat RH, Jakana J, Chen DH, Chiu W (2012) Direct electron detection yields cryo-EM reconstructions at resolutions beyond 3/4 Nyquist frequency. J Struct Biol 177:589–601

    Article  PubMed Central  PubMed  Google Scholar 

  6. Britton KL, Baker PJ, Rice DW, Stillman TJ (1992) Structural relationship between the hexameric and tetrameric family of glutamate dehydrogenases. Eur J Biochem 209:851–859

    Article  CAS  PubMed  Google Scholar 

  7. Brown JH, Volkmann N, Jun G, Henschen-Edman AH, Cohen C (2000) The crystal structure of modified bovine fibrinogen. Proc Natl Acad Sci USA 97:85–90

    Article  CAS  PubMed  Google Scholar 

  8. Brünger AT (1992) Free R-value – a novel statistical quantity for assessing the accuracy of crystal-structures. Nature 355:472–475

    Article  PubMed  Google Scholar 

  9. Campbell MG, Cheng A, Brilot AF, Moeller A, Lyumkis D, Veesler D, Pan J, Harrison SC, Potter CS et al (2012) Movies of ice-embedded particles enhance resolution in electron cryo-microscopy. Structure 20:1823–1828

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  10. Campos M, Francetic O, Nilges M (2011) Modeling pilus structures from sparse data. J Struct Biol 173:436–444

    Article  CAS  PubMed  Google Scholar 

  11. Chacon P, Wriggers W (2002) Multi-resolution contour-based fitting of macromolecular structures. J Mol Biol 317:375–384

    Article  CAS  PubMed  Google Scholar 

  12. Chapman MS (1995) Restrained real-space macromolecular atomic refinement using a new resolution-dependent electron density function. Acta Crystallogr A51:69–80

    Article  CAS  Google Scholar 

  13. Chapman MS, Trzynka A, Chapman BK (2013) Atomic modeling of cryo-electron microscopy reconstructions – joint refinement of model and imaging parameters. J Struct Biol 182(1):10–21

    Article  CAS  PubMed  Google Scholar 

  14. Chen JZ, Furst J, Chapman MS, Grigorieff N (2003) Low-resolution structure refinement in electron microscopy. J Struct Biol 144:144–151

    Article  PubMed  Google Scholar 

  15. Cong Y, Baker ML, Jakana J, Woolford D, Miller EJ, Reissmann S, Kumar RN, Redding-Johanson AM, Batth TS et al (2010) 4.0-Å resolution cryo-EM structure of the mammalian chaperonin TRiC/CCT reveals its unique subunit arrangement. Proc Natl Acad Sci USA 107:4967–4972

    Article  CAS  PubMed  Google Scholar 

  16. Darnault C, Volbeda A, Kim EJ, Legrand P, Vernede X, Lindahl PA, Fontecilla-Camps JC (2003) Ni-Zn-[Fe4-S4] and Ni-Ni-[Fe4-S4] clusters in closed and open subunits of acetyl-CoA synthase/carbon monoxide dehydrogenase. Nat Struct Biol 10:271–279

    Article  CAS  PubMed  Google Scholar 

  17. DiMaio F, Tyka MD, Baker ML, Chiu W, Baker D (2009) Refinement of protein structures into low-resolution density maps using Rosetta. J Mol Biol 392:181–190

    Article  CAS  PubMed  Google Scholar 

  18. DiMaio F, Zhang J, Chiu W, Baker D (2013) Cryo-EM model validation using independent map reconstructions. Protein Sci 22:865–868

    Article  CAS  PubMed  Google Scholar 

  19. Dorset DL (1997) Direct phase determination in protein electron crystallography: the pseudo-atom approximation. Proc Natl Acad Sci USA 94:1791–1794

    Article  CAS  PubMed  Google Scholar 

  20. Fabiola F, Korostelev A, Chapman MS (2006) Bias in cross-validated free R factors: mitigation of the effects of non-crystallographic symmetry. Acta Crystallogr D62:227–238

    CAS  Google Scholar 

  21. Falkner B, Schröder GF (2013) Cross-validation in cryo-EM-based structural modeling. Proc Natl Acad Sci USA 110:8930–8935

    Article  CAS  PubMed  Google Scholar 

  22. Fisher RA (1921) On the ‘probable error’ of a coefficient of correlation deduced from a small sample. Metron 1:1–32

    Google Scholar 

  23. Fujiyoshi Y, Unwin N (2008) Electron crystallography of proteins in membranes. Curr Opin Struct Biol 18:587–592

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  24. Gao H, Frank J (2005) Molding atomic structures into intermediate-resolution cryo-EM density maps of ribosomal complexes using real-space refinement. Structure 13:401–406

    Article  PubMed  Google Scholar 

  25. Gao H, Sengupta J, Valle M, Korostelev A, Eswar N, Stagg SM, Van Roey P, Agrawal RK, Harvey SC et al (2003) Study of the structural dynamics of the E coli 70S ribosome using real-space refinement. Cell 113:789–801

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  27. Grigorieff N (2013) Direct detection pays off for electron cryo-microscopy. Elife 2:e00573

    Article  PubMed Central  PubMed  Google Scholar 

  28. Grigorieff N, Harrison SC (2011) Near-atomic resolution reconstructions of icosahedral viruses from electron cryo-microscopy. Curr Opin Struct Biol 21:265–273

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  29. Hanein D, Volkmann N (2011) Correlative light-electron microscopy. Adv Protein Chem Struct Biol 82:91–99

    Article  CAS  PubMed  Google Scholar 

  30. Hanein D, Volkmann N, Goldsmith S, Michon AM, Lehman W, Craig R, DeRosier D, Almo S, Matsudaira P (1998) An atomic model of fimbrin binding to F-actin and its implications for filament crosslinking and regulation. Nat Struct Biol 5:787–792

    Article  CAS  PubMed  Google Scholar 

  31. Hayward S (1999) Structural principles governing domain motions in proteins. Proteins 36:425–435

    Article  CAS  PubMed  Google Scholar 

  32. Hayward S, Berendsen HJ (1998) Systematic analysis of domain motions in proteins from conformational change: new results on citrate synthase and T4 lysozyme. Proteins 30:144–154

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  34. Hinsen K, Thomas A, Field MJ (1999) Analysis of domain motions in large proteins. Proteins 34:369–382

    Article  CAS  PubMed  Google Scholar 

  35. Hoenger A, Sack S, Thormahlen M, Marx A, Muller J, Gross H, Mandelkow E (1998) Image reconstructions of microtubules decorated with monomeric and dimeric kinesins: comparison with x-ray structure and implications for motility. J Cell Biol 141:419–430

    Article  CAS  PubMed  Google Scholar 

  36. Jolley CC, Wells SA, Fromme P, Thorpe MF (2008) Fitting low-resolution cryo-EM maps of proteins using constrained geometric simulations. Biophys J 94:1613–1621

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  37. Jones TA, Zou J-Y, Cowan SW, Kjeldgaard M (1991) Improved methods for the building of protein models in electron density maps and the location of errors in these models. Acta Crystallogr A 47:110–119

    Article  PubMed  Google Scholar 

  38. Kovacs JA, Yeager M, Abagyan R (2008) Damped-dynamics flexible fitting. Biophys J 95:3192–3207

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  39. Kozielski F, Arnal I, Wade R (1998) A model of the microtuble-kinesin complex based on electron cryomicroscopy and X-ray crystallography. Curr Biol 8:191–198

    Article  CAS  PubMed  Google Scholar 

  40. Krebs WG, Gerstein M (2000) SURVEY AND SUMMARY: the morph server: a standardized system for analyzing and visualizing macromolecular motions in a database framework. Nucleic Acids Res 28:1665–1675

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  41. Liu H, Smith TJ, Lee WM, Mosser AG, Rueckert RR, Olson NH, Cheng RH, Baker TS (1994) Structure determination of an Fab fragment that neutralizes human rhinovirus 14 and analysis of the Fab-virus complex. J Mol Biol 240:127–137

    Article  CAS  PubMed  Google Scholar 

  42. Ludtke SJ, Baker ML, Chen DH, Song JL, Chuang DT, Chiu W (2008) De novo backbone trace of GroEL from single particle electron cryomicroscopy. Structure 16:441–448

    Article  CAS  PubMed  Google Scholar 

  43. Lunin VY, Lunina NL, Petrova TE, Vernoslova EA, Urzhumtsev AG, Podjarny AD (1995) On the ab initio solution of the phase problem for macromolecules at very low resolution: the few atoms model method. Acta Crystallogr D Biol Crystallogr 51:896–903

    Article  CAS  PubMed  Google Scholar 

  44. Milazzo AC, Leblanc P, Duttweiler F, Jin L, Bouwer JC, Peltier S, Ellisman M, Bieser F, Matis HS et al (2005) Active pixel sensor array as a detector for electron microscopy. Ultramicroscopy 104:152–159

    Article  CAS  PubMed  Google Scholar 

  45. Nalini V, Bax B, Driessen H, Moss DS, Lindley PF, Slingsby C (1994) Close packing of an oligomeric eye lens beta-crystallin induces loss of symmetry and ordering of sequence extensions. J Mol Biol 236:1250–1258

    Article  CAS  PubMed  Google Scholar 

  46. Norledge BV, Hay RE, Bateman OA, Slingsby C, Driessen HP (1997) Towards a molecular understanding of phase separation in the lens: a comparison of the X-ray structures of two high Tc gamma-crystallins, gammaE and gammaF, with two low Tc gamma-crystallins, gammaB and gammaD. Exp Eye Res 65:609–630

    Article  CAS  PubMed  Google Scholar 

  47. Norris GE, Anderson BF, Baker EN (1991) Molecular replacement solution of the structure of apolactoferrin, a protein displaying large-scale conformational change. Acta Crystallogr B47:998–1004

    Article  CAS  Google Scholar 

  48. Noske AB, Costin AJ, Morgan GP, Marsh BJ (2008) Expedited approaches to whole cell electron tomography and organelle mark-up in situ in high-pressure frozen pancreatic islets. J Struct Biol 161:298–313

    Article  PubMed Central  PubMed  Google Scholar 

  49. Pettersen EF, Goddard TD, Huang CC, Couch GS, Greenblatt DM, Meng EC, Ferrin TE (2004) UCSF Chimera–a visualization system for exploratory research and analysis. J Comput Chem 25:1605–1612

    Article  CAS  PubMed  Google Scholar 

  50. Pfaendtner J, Volkmann N, Hanein D, Dalhaimer P, Pollard TD, Voth GA (2012) Key structural features of the actin filament Arp2/3 complex branch junction revealed by molecular simulation. J Mol Biol 416:148–161

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  51. Rayment I, Holden HM, Whittaker M, Yohn CB, Lorenz M, Holmes KC, Milligan RA (1993) Structure of the actin-myosin complex and its implications for muscle contraction. Science 261:58–65

    Article  CAS  PubMed  Google Scholar 

  52. Rigort A, Bäuerlein FJ, Leis A, Gruska M, Hoffmann C, Laugks T, Böhm U, Eibauer M, Gnaegi H et al (2010) Micromachining tools and correlative approaches for cellular cryo-electron tomography. J Struct Biol 172:169–179

    Article  PubMed  Google Scholar 

  53. Robinson RC, Turbedsky K, Kaiser DA, Marchand JB, Higgs HN, Choe S, Pollard TD (2001) Crystal structure of Arp2/3 complex. Science 294:1679–1684

    Article  CAS  PubMed  Google Scholar 

  54. Roseman AM (2000) Docking structures of domains into maps from cryo-electron microscopy using local correlation. Acta Crystallogr D Biol Crystallogr 56:1332–1340

    Article  CAS  PubMed  Google Scholar 

  55. Rossmann MG (2000) Fitting atomic models into electron-microscopy maps. Acta Crystallogr D Biol Crystallogr 56:1341–1349

    Article  CAS  PubMed  Google Scholar 

  56. Rossmann MG, Arnold E, Erickson JW, Frankenberger EA, Griffith JP, Hecht HJ, Johnson JE, Kamer G, Luo M et al (1985) Structure of a human common cold virus and functional relationship to other picornaviruses. Nature 317:145–153

    Article  CAS  PubMed  Google Scholar 

  57. Rouiller I, Xu XP, Amann KJ, Egile C, Nickell S, Nicastro D, Li R, Pollard TD, Volkmann N, Hanein D (2008) The structural basis of actin filament branching by Arp2/3 complex. J Cell Biol 180:887–895

    Article  CAS  PubMed  Google Scholar 

  58. Rusu M, Birmanns S, Wriggers W (2008) Biomolecular pleiomorphism probed by spatial interpolation of coarse models. Bioinformatics 24:2460–2466

    Article  CAS  PubMed  Google Scholar 

  59. Schröder GF, Brünger AT, Levitt M (2007) Combining efficient conformational sampling with a deformable elastic network model facilitates structure refinement at low resolution. Structure 15:1630–1641

    Article  PubMed Central  PubMed  Google Scholar 

  60. Seul M, O’Gorman L, Sammon MJ (2000) Practical algorithms for image analysis: descriptions, examples, and code. Cambridge University Press, Cambridge

    Google Scholar 

  61. Shacham E, Sheehan B, Volkmann N (2007) Density-based score for selecting near-native atomic models of unknown structures. J Struct Biol 158:188–195

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  62. Shaikh TR, Hegerl R, Frank J (2003) An approach to examining model dependence in EM reconstructions using cross-validation. J Struct Biol 142:301–310

    Article  PubMed  Google Scholar 

  63. Smith CA, Rayment I (1996) X-ray structure of the magnesium(II).ADP.vanadate complex of the Dictyostelium discoideum myosin motor domain to 1.9 Å resolution. Biochemistry 35:5404–5417

    Article  CAS  PubMed  Google Scholar 

  64. Smith TJ, Olson NH, Cheng RH, Chase ES, Baker TS (1993) Structure of a human rhinovirus-bivalently bound antibody complex: implications for viral neutralization and antibody flexibility. Proc Natl Acad Sci USA 90:7015–7018

    Article  CAS  PubMed  Google Scholar 

  65. Smith TJ, Olson NH, Cheng RH, Liu H, Chase ES, Lee WM, Leippe DM, Mosser AG, Rueckert RR, Baker TS (1993) Structure of human rhinovirus complexed with Fab fragments from a neutralizing antibody. J Virol 67:1148–1158

    CAS  PubMed Central  PubMed  Google Scholar 

  66. Smith TJ, Peterson PE, Schmidt T, Fang J, Stanley CA (2001) Structures of bovine glutamate dehydrogenase complexes elucidate the mechanism of purine regulation. J Mol Biol 307:707–720

    Article  CAS  PubMed  Google Scholar 

  67. Studholme C, Hill DL, Hawkes DJ (1996) Automated 3-D registration of MR and CT images of the head. Med Image Anal 1:163–175

    Article  CAS  PubMed  Google Scholar 

  68. Suhre K, Navaza J, Sanejouand YH (2006) NORMA: a tool for flexible fitting of high-resolution protein structures into low-resolution electron-microscopy-derived density maps. Acta Crystallogr D Biol Crystallogr 62:1098–1100

    Article  PubMed  Google Scholar 

  69. Tama F, Miyashita O, Brooks 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  CAS  PubMed  Google Scholar 

  70. Tan RKZ, Devkota B, Harvey SC (2008) YUP.SCX: coaxing atomic models into medium resolution electron density maps. J Struct Biol 163:163–174

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  71. Topf M, Lasker K, Webb B, Wolfson H, Chiu W, Sali A (2008) Protein structure fitting and refinement guided by cryo-EM density. Structure 16:295–307

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  72. Trabuco LG, Villa E, Mitra K, Frank J, Schulten K (2008) Flexible fitting of atomic structures into electron microscopy maps using molecular dynamics. Structure 16:673–683

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  73. Vasishtan D, Topf M (2011) Scoring functions for cryoEM density fitting. J Struct Biol 174:333–343

    Article  CAS  PubMed  Google Scholar 

  74. Velazquez-Muriel JA, Valle M, Santamaria-Pang A, Kakadiaris IA, Carazo JM (2006) Flexible fitting in 3D-EM guided by the structural variability of protein superfamilies. Structure 14:1115–1126

    Article  CAS  PubMed  Google Scholar 

  75. Volkmann N (2002) A novel three-dimensional variant of the watershed transform for segmentation of electron density maps. J Struct Biol 138:123–129

    Article  CAS  PubMed  Google Scholar 

  76. Volkmann N, Hanein D (1999) Quantitative fitting of atomic models into observed densities derived by electron microscopy. J Struct Biol 125:176–184

    Article  CAS  PubMed  Google Scholar 

  77. Volkmann N, Hanein D (2003) Docking of atomic models into reconstructions from electron microscopy. Methods Enzymol 374:204–225

    CAS  PubMed  Google Scholar 

  78. Volkmann N, Hanein D (2009) Electron microscopy in the context of systems biology. In: Gu J, Bourne PE (eds) Structural bioinformatics. Wiley-Blackwell, New York, pp 143–170

    Google Scholar 

  79. Volkmann N (2009) Confidence intervals for fitting of atomic models into low-resolution densities. Acta Crystallogr D Biol Crystallogr 65:679–689

    Article  CAS  PubMed  Google Scholar 

  80. Volkmann N, Hanein D, Ouyang G, Trybus KM, DeRosier DJ, Lowey S (2000) Evidence for cleft closure in actomyosin upon ADP release. Nat Struct Biol 7:1147–1155

    Article  CAS  PubMed  Google Scholar 

  81. Wriggers W, Birmanns S (2001) Using situs for flexible and rigid-body fitting of multiresolution single-molecule data. J Struct Biol 133:193–202

    Article  CAS  PubMed  Google Scholar 

  82. Wriggers W, Milligan RA, McCammon JA (1999) Situs: a package for docking crystal structures into low-resolution maps from electron microscopy. J Struct Biol 125:185–195

    Article  CAS  PubMed  Google Scholar 

  83. Wüthrich K, Billeter M, Braun W (1983) Pseudo-structures for the 20 common amino acids for use in studies of protein conformations by measurements of intramolecular proton-proton distance constraints with nuclear magnetic resonance. J Mol Biol 169:949–961

    Article  PubMed  Google Scholar 

  84. Xia Z, Gardner DP, Gutell RR, Ren P (2010) Coarse-grained model for simulation of RNA three-dimensional structures. J Phys Chem B 114:13497–13506

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  85. Xu XP, Rouiller I, Slaughter BD, Egile C, Kim E, Unruh JR, Fan X, Pollard TD, Li R et al (2011) Three-dimensional reconstructions of Arp2/3 complex with bound nucleation promoting factors. EMBO J 31:236–247

    Article  PubMed  Google Scholar 

  86. Yonekura K, Maki-Yonekura S, Namba K (2003) Complete atomic model of the bacterial flagellar filament by electron cryomicroscopy. Nature 424:643–650

    Article  CAS  PubMed  Google Scholar 

  87. Zheng W (2011) Accurate flexible fitting of high-resolution protein structures into cryo-electron microscopy maps using coarse-grained pseudo-energy minimization. Biophys J 100:478–488

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  88. Zhu J, Cheng L, Fang Q, Zhou ZH, Honig B (2010) Building and refining protein models within cryo-electron microscopy density maps based on homology modeling and multiscale structure refinement. J Mol Biol 397:835–851

    Article  CAS  PubMed Central  PubMed  Google Scholar 

Download references

Acknowledgements

This work was supported by National Institutes of Health grant P01 GM066311.

Author information

Authors and Affiliations

  1. Bioinformatics and Systems Biology Program, Sanford-Burnham Medical Research Institute, 10901 N Torrey Pines Rd, La Jolla, CA, 92037, USA

    Niels Volkmann

Authors
  1. Niels Volkmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Niels Volkmann .

Editor information

Editors and Affiliations

  1. Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, People's Republic of China

    Ke-li Han

  2. The Scripps Research Institute, La Jolla, California, USA

    Xin Zhang

  3. Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, People's Republic of China

    Ming-jun Yang

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Volkmann, N. (2014). The Joys and Perils of Flexible Fitting. In: Han, Kl., Zhang, X., Yang, Mj. (eds) Protein Conformational Dynamics. Advances in Experimental Medicine and Biology, vol 805. Springer, Cham. https://doi.org/10.1007/978-3-319-02970-2_6

Download citation

Publish with us

Policies and ethics

Search

Navigation