Hybrid Methods for Modeling Protein Structures Using Molecular Dynamics Simulations and Small-Angle X-Ray Scattering Data

  • Toru Ekimoto
  • Mitsunori IkeguchiEmail author
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 1105)


Small-angle X-ray scattering (SAXS) is an efficient experimental tool to measure the overall shape of macromolecular structures in solution. However, due to the low resolution of SAXS data, high-resolution data obtained from X-ray crystallography or NMR and computational methods such as molecular dynamics (MD) simulations are complementary to SAXS data for understanding protein functions based on their structures at atomic resolution. Because MD simulations provide a physicochemically proper structural ensemble for flexible proteins in solution and a precise description of solvent effects, the hybrid analysis of SAXS and MD simulations is a promising method to estimate reasonable solution structures and structural ensembles in solution. Here, we review typical and useful in silico methods for modeling three dimensional protein structures, calculating theoretical SAXS profiles, and analyzing ensemble structures consistent with experimental SAXS profiles. We also review two examples of the hybrid analysis, termed MD-SAXS method in which MD simulations are carried out without any knowledge of experimental SAXS data, and the experimental SAXS data are used only to assess the consistency of the solution model from MD simulations with those observed in experiments. One example is an investigation of the intrinsic dynamics of EcoO109I using the computational method to obtain a theoretical profile from the trajectory of an MD simulation. The other example is a structural investigation of the vitamin D receptor ligand-binding domain using snapshots generated by MD simulations and assessment of the snapshots by experimental SAXS data.


Small-angle X-ray scattering Molecular dynamics simulation Solution structure Coarse-grained model MD-SAXS Endonuclease Vitamin D receptor 



This work was financially supported by Innovative Drug Discovery Infrastructure through Functional Control of Biomolecular Systems, Priority Issue 1 in Post-K Supercomputer Development from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) to M.I. (Project ID: hp150269, hp160223, hp170255, and hp180191); by Basis for Supporting Innovative Drug Discovery and Life Science Research (BINDS) (Project ID: JP17am0101109) from Japan Agency for Medical Research and Development (AMED) to M.I.; and by RIKEN Dynamic Structural Biology Project to M.I. We further thank collaborators, Dr. Tomotaka Oroguchi (Keio Univ.), Prof. Hiroshi Hashimoto (Univ. of Shizuoka), Prof. Toshiyuki Shimizu (Tokyo Univ.), Prof. Mamoru Sato (Yokohama City Univ.), Dr. Yasuaki Anami (Univ. of Texas), Dr. Nobutaka Shimizu (KEK), Dr. Daichi Egawa (Showa Pharmaceutical Univ.), Dr. Toshimasa Itoh (Showa Pharmaceutical Univ.), and Prof. Keiko Yamamoto (Showa Pharmaceutical Univ.).


  1. Abraham MJ, Murtola T, Schulz R, Pall S, Smith JC, Hess B, Lindahl E (2015) GROMACS: high performance molecular simulations through multi-level parallelism from laptops to supercomputers. SoftwareX 1-2:19–25CrossRefGoogle Scholar
  2. Alva V, Nam SZ, Söding J, Lupas AN (2016) The MPI bioinformatics toolkit as an integrative platform for advanced protein sequence and structure analysis. Nuc Acid Res 44:W410–W415CrossRefGoogle Scholar
  3. Anami Y, Shimizu N, Ekimoto T, Egawa D, Itoh T, Ikeguchi M, Yamamoto K (2016) Apo- and antagonist-binding structures of vitamin D receptor ligand-binding domain revealed by hybrid approach combining small-angle x-ray scattering and molecular dynamics. J Med Chem 59:7888–7900PubMedCrossRefPubMedCentralGoogle Scholar
  4. Beauchamp KA, Lin YS, Das R, Pande VS (2012) Are protein force fields getting better? A systematic benchmark on 524 diverse NMR measurements. J Chem Theory Comput 8:1409–1414PubMedPubMedCentralCrossRefGoogle Scholar
  5. Bernado P (2010) Effect of interdomain dynamics on the structure determination of modular proteins by small-angle scattering. Eur Biophys J 39:769–780PubMedCrossRefPubMedCentralGoogle Scholar
  6. Bernado P, Svergun DI (2012) Structural analysis of intrinsically disordered proteins by small-angle x-ray scattering. Mol Bio Syst 8:151–167Google Scholar
  7. Bernado P, Mylonas E, Petoukhov MV, Blackledge M, Svergun DI (2007) Structural characterization of flexible proteins using small-angle x-ray scattering. J Am Chem Soc 129:5656–5664PubMedPubMedCentralCrossRefGoogle Scholar
  8. Boldon L, Laliberte F, Liu L (2015) Review of the fundamental theories behind small angle x-ray scattering, molecular dynamics simulations, and relevant integrated application. Nano Rev 6:25661PubMedCrossRefPubMedCentralGoogle Scholar
  9. Case DA, Cerutti DS, Cheatham TE III, Darden TA, Duke RE, Giese TJ, Gohlke H, Goetz AW, Greene D, Homeyer N, Izadi S, Kovalenko A, Lee TS, LeGrand S, Li P, Lin C, Liu J, Luchko T, Luo R, Mermelstein D, Merz KM, Monard G, Nguyen H, Omelyan I, Onufriev A, Pan F, Qi R, Roe DR, Roitberg A, Sagui C, Simmerling CL, Botello-Smith WM, Swails J, Walker RC, Wang J, Wolf RM, Wu X, Xiao L, York DM, Kollman PA (2017) AMBER 2017 University of California, San FranciscoGoogle Scholar
  10. Chen P, Hub JS (2015) Interpretation of solution x-ray scattering by explicit-solvent molecular dynamics. Biophys J 108:2573–2584PubMedPubMedCentralCrossRefGoogle Scholar
  11. dos Reis MA, Apricio R, Zhang Y (2011) Improving protein template recognition by using small-angle x-ray scattering profiles. Biophys J 101:2770–2781PubMedPubMedCentralCrossRefGoogle Scholar
  12. Dror RO, Dirks RM, Grossman JP, Xu H, Shaw DE (2012) Biomolecular simulation: a computational microscope for molecular biology. Annu Rev Biophys 41:429–452PubMedCrossRefPubMedCentralGoogle Scholar
  13. Fiser A (2010) Template-based protein structure modeling. Methods Mol Biol 673:73–94PubMedPubMedCentralCrossRefGoogle Scholar
  14. Förster F, Webb B, Krukenberg KA, Tsuruta H, Agard DA, Sali A (2008) Integration of small angle x-ray scattering data into structural modeling of proteins and their assemblies. J Mol Biol 382:1089–1106PubMedPubMedCentralCrossRefGoogle Scholar
  15. Goh BC, Hadden JA, Bernardi RC, Singharoy A, McGreevy R, Rudack T, Cassidy CK, Schulten K (2016) Computational methodologies for real-space structural refinement of large macromolecular complexes. Annu Rev Biophys 45:253–278PubMedPubMedCentralCrossRefGoogle Scholar
  16. Gorba C, Tama F (2010) Normal mode flexible fitting of high-resolution structures of biological molecules toward SAXS data. Bioinform Biol Insights 4:43–54PubMedPubMedCentralCrossRefGoogle Scholar
  17. Grishaev A, Wu J, Trewhella J, Bax A (2005) Refinement of multidomain protein structures by combination of solution small-angle x-ray scattering and NMR data. J Am Chem Soc 127:16621–16628PubMedPubMedCentralCrossRefGoogle Scholar
  18. Grishaev A, Guo L, Irving T, Bax A (2010) Improved fitting of solution x-ray scattering data to macromolecular structures and structural ensembles by explicit water modeling. J Am Chem Soc 132:15484–15486PubMedPubMedCentralCrossRefGoogle Scholar
  19. Hamelberg D, Mongan J, McCammon JA (2004) Accelerated molecular dynamics: a promising and efficient simulation method for biomolecules. J Chem Phys 120:11919–11929PubMedCrossRefPubMedCentralGoogle Scholar
  20. Hammel M (2012) Validation of macromolecular flexibility in solution by small-angle x-ray scattering (SAXS). Eur Biophys J 41:789–799PubMedPubMedCentralCrossRefGoogle Scholar
  21. Harrigan MP, Sultan MM, Hemandez CX, Husic BE, Eastman P, Schwantes CR, Beauchamp KA, McGibbon RT, Pande VS (2017) MSMBuilder: statistical models for biomolecular dynamics. Biophys J 112:10–15PubMedPubMedCentralCrossRefGoogle Scholar
  22. Hura GL, Menon AL, Hammel M, Rambo RP, Poole FL, 2nd, Tsutakawa SE, Jenny FE, Jr., Classen S, Frankel KA, Hopkins RC, Yang Sj, Scott JW, Dillard BD, Adams MW, Tainer, JA (2009) Robust, high-throughput solution structural analysis by small angle X-ray scattering (SAXS). Nat Methods 6(8):606–612PubMedPubMedCentralCrossRefGoogle Scholar
  23. Jacques DA, Guss JM, Svergun DI, Trewhella J (2012) Publication guidelines for structural modeling of small-angle scattering data from biomolecules in solution. Acta Cryst D 68:620–626CrossRefGoogle Scholar
  24. Kiefer F, Arnold K, Kunzli M, Bordoli L, Schwede T (2009) The SWISS-MODEL repository and associated resources. Nuc Acid Res 37:D387–D392CrossRefGoogle Scholar
  25. Kikhney AG, Svergun DI (2015) A practical guide to small angle x-ray scattering (SAXS) of flexible and intrinsically disordered proteins. FEBS Lett 589:2570–2577PubMedCrossRefPubMedCentralGoogle Scholar
  26. Kim DE, Chivian D, Baker D (2004) Protein structure prediction and analysis using the Robetta server. Nuc Acid Res 32:W526–W531CrossRefGoogle Scholar
  27. Kimanius D, Pettersson I, Schluchebier G, Lindahl E, Andersson M (2015) SAXS-guided metadynamics. J Chem Theory Comput 11:3491–3498PubMedCrossRefPubMedCentralGoogle Scholar
  28. Knight CJ, Hub JS (2015) WAXSiS: a web server for the calculation of SAXS/WAXS curves based on explicit-solvent molecular dynamics. Nuc Acid Res 43:W225–W230CrossRefGoogle Scholar
  29. Kobayashi C, Jung J, Matunaga Y, Mori T, Ando T, Tamura K, Kamiya M, Sugita Y (2017) GENESIS 1.1: a hybrid-parallel molecular dynamics simulator with enhanced sampling algorithms on multiple computational platforms. J Comput Chem 38:2193–2206PubMedCrossRefPubMedCentralGoogle Scholar
  30. Köfinger J, Hummer G (2013) Atomic-resolution structural information from scattering experiments on macromolecules in solution. Phys Rev E 87:052712CrossRefGoogle Scholar
  31. Kojima M, Timchenko AA, Higo J, Ito K, Kihara H, Takahashi K (2004) Structural refinement by restrained molecular-dynamics algorithm with small-angle x-ray scattering constraints for a biomolecule. J Appl Cryst 37:103–109CrossRefGoogle Scholar
  32. Konarev PV, Volkov VV, Sokolova AV, Koch MHJ, Svergun DI (2003) PRIMUS – a windows-pc based system for small-angle scattering data analysis. J Appl Cryst 36:1277–1282CrossRefGoogle Scholar
  33. Kozakov D, Hall DR, Xia B, Porter KA, Padhorny D, Yueh C, Beglov D, Vajda S (2017) The ClusPro web server for protein-protein docking. Nat Protoc 12:255–278PubMedPubMedCentralCrossRefGoogle Scholar
  34. Lane TJ, Shukla D, Beauchamp KA, Pande VS (2013) To milliseconds and beyond: challenges in the simulation of protein folding. Curr Opin Struct Biol 23:58–65PubMedCrossRefGoogle Scholar
  35. Lau AY, Roux B (2007) The free energy landscapes governing conformational changes in a glutamate receptor ligand-binding domain. Structure 15:1203–1214PubMedPubMedCentralCrossRefGoogle Scholar
  36. Lindorff-Larsen K, Maragakis P, Piana S, Eastwood MP, Dror RO, Shaw DE (2012) Systematic validation of protein force fields against experimental data. PLoS One 7:e32131PubMedPubMedCentralCrossRefGoogle Scholar
  37. Liu H, Morris RJ, Hexemer A, Grandison S, Zwart PH (2012) Computation of small-angle scattering profiles with three-dimensional Zernike polynomials. Acta Cryst A68:278–285CrossRefGoogle Scholar
  38. Marchi M (2016) A first principle particle mesh method for solution SAXS of large bio-molecular systems. J Chem Phys 145:045101PubMedCrossRefPubMedCentralGoogle Scholar
  39. Moras D, Gronemeyer H (1998) The nuclear receptor ligand-binding domain: structure and function. Curr Opin Cell Biol 10:384–391PubMedCrossRefPubMedCentralGoogle Scholar
  40. Morimoto Y, Nakagawa T, Kojima M (2013) Small-angle x-ray scattering constraints and local geometry like secondary structures can construct a coarse-grained protein model at amino acid residue resolution. Biochem Biophys Res Commun 431:65–69PubMedCrossRefPubMedCentralGoogle Scholar
  41. Nguyen HT, Pabit SA, Meisburger SP, Pollack L, Case DA (2014) Accurate small and wide angle x-ray scattering profiles from atomic models of proteins and nucleic acids. J Chem Phys 141:22D508PubMedPubMedCentralCrossRefGoogle Scholar
  42. Ohmura I, Morimoto G, Ohno Y, Hasegawa A, Taiji M (2014) MDGRAPE-4: a special-purpose computer system for molecular dynamics simulations. Philos Trans A Math Phys Eng Sci 372:20130387PubMedPubMedCentralCrossRefGoogle Scholar
  43. Oroguchi T, Ikeguchi M (2011) Effects of ionic strength on SAXS data for proteins revealed by molecular dynamics simulations. J Chem Phys 134:025102-1-14PubMedCrossRefGoogle Scholar
  44. Oroguchi T, Ikeguchi M (2012) MD-SAXS method with nonspherical boundaries. Chem Phys Lett 541:117–121CrossRefGoogle Scholar
  45. Oroguchi T, Hashimoto H, Shimizu T, Sato M, Ikeguchi M (2009) Intrinsic dynamics of restriction endonuclease EcoO109I studied by molecular dynamics simulations and x-ray scattering data analysis. Biophys J 96:2808–2822PubMedPubMedCentralCrossRefGoogle Scholar
  46. Park S, Bardhan JP, Roux B, Makowski L (2009) Simulated x-ray scattering of protein solutions using explicit-solvent models. J Chem Phys 130:134114-1-8PubMedPubMedCentralCrossRefGoogle Scholar
  47. Pelikan M, Hura GL, Hammel M (2009) Structure and flexibility within proteins as identified through small angle x-ray scattering. Gen Physiol Biophys 28:174–189PubMedPubMedCentralCrossRefGoogle Scholar
  48. Petoukhov MV, Svergun DI (2005) Global rigid body modelling of macromolecular complexes against small-angle scattering data. Biophys J 89:1237–1250PubMedPubMedCentralCrossRefGoogle Scholar
  49. Petoukhov MV, Franke D, Shkumatov AV, Tria G, Kikhney AG, Gajda M, Gorba C, Mertens HDT, Konarev PV, Svergun DI (2012) New developments in the ATSAS program package for small-angle scattering data analysis. J Appl Cryst 45:342–350CrossRefGoogle Scholar
  50. Phillips JC, Braun R, Wang W, Gumbart J, Tajkhorshid E, Villa E, Chipot C, Skeel RD, Kale L, Schulten K (2005) Scalable molecular dynamics with NAMD. J Comput Chem 26:1781–1802PubMedPubMedCentralCrossRefGoogle Scholar
  51. Piana S, Laio A (2007) A bias-exchange approach to protein folding. J Phys Chem B 111: 4553–4559PubMedCrossRefPubMedCentralGoogle Scholar
  52. Poitevin F, Orland H, Doniach S, Koehl P, Delarue M (2011) AquaSAXS: a web server for computation and fitting of SAXS profiles with non-uniformally hydrated atomic models. Nuc Acid Res 39:W184–W189CrossRefGoogle Scholar
  53. Pons C, D’Abramo M, Svergan DI, Orozco M, Bernado P, Fernandez-Recio J (2010) Structural characterization of protein-protein complexes by integrating computational docking with small-angle scattering data. J Mol Biol 403:217–230PubMedCrossRefPubMedCentralGoogle Scholar
  54. Rambo RP, Tainer JA (2013) Super-resolution in solution x-ray scattering and its applications to structural systems biology. Annu Rev Biophys 42:415–441PubMedCrossRefPubMedCentralGoogle Scholar
  55. Rauscher S, Gapsys V, Gajda MJ, Zweckstetter M, de Groot BL, Grumbmüller H (2015) Structural ensembles of intrinsically disordered proteins depend strongly on force field: a comparison to experiment. J Chem Theory Comput 11:5513–5524PubMedCrossRefPubMedCentralGoogle Scholar
  56. Ravikumar KM, Huang W, Yang S (2013) Fast-SAXS-pro: a unified approach to computing SAXS profiles of DNA, RNA, protein, and their complexes. J Chem Phys 138:024112-1-7Google Scholar
  57. Rochel N, Tocchini-Valentini G, Egea PF, Juntunen K, Garnier JM, Vihko P, Moras D (2001) Functional and structural characterization of the insertion region in the ligand binding domain of vitamin D nuclear receptor. Eur J Biochem 268:971–979PubMedCrossRefPubMedCentralGoogle Scholar
  58. Rochel N, Ciesielski F, Godet J, Moman E, Roessle M, Peluso-Iltis C, Moulin M, Haertlein M, Callow P, Mely Y, Svergun DI, Moras D (2011) Common architecture of nuclear receptor heterodimers on DNA direct repeat elements with different spacings. Nat Struct Mol Biol 18:564–570PubMedCrossRefPubMedCentralGoogle Scholar
  59. Rozycki B, Kim YC, Hummer G (2011) SAXS ensemble refinement of ESCRT-III CHMP3 conformational transitions. Structure 19:109–116PubMedPubMedCentralCrossRefGoogle Scholar
  60. Sali A, Blundell TL (1993) Comparative protein modelling by satisfaction of spatial restraints. J Mol Biol 234:779–815CrossRefGoogle Scholar
  61. Saunders MG, Voth GA (2013) Coarse-graining methods for computational biology. Annu Rev Biophys 42:73–93PubMedCrossRefPubMedCentralGoogle Scholar
  62. Scherer MK, Trendelkamp-Schroer B, Paul F, Perez-Hernandez G, Hoffmann M, Plattner N, Wehmeyer C, Prinz JH, Noe F (2015) PyEMMA2: a software package for estimation, validation, and analysis of Markov models. J Chem Theory Comput 11:5525–5542PubMedCrossRefPubMedCentralGoogle Scholar
  63. Schneidman-Duhobny D, Hammel M, Sali A (2011) Macromolecular docking restrained by a small angle x-ray scattering profile. J Struct Biol 173:461–471CrossRefGoogle Scholar
  64. Schneidman-Duhovny D, Kim SJ, Sali A (2012) Integrative structural modeling with small angle x-ray scattering profiles. BMC Struct Biol 12:7CrossRefGoogle Scholar
  65. Schneidman-Duhovny D, Hammel M, Tainer JA, Sali A (2013) Accurate SAXS profile computation and its assessment by contrast variation experiments. Biophys J 105:962–974PubMedPubMedCentralCrossRefGoogle Scholar
  66. Shaw DE, Deneroff MM, Dror RO, Kuskin JS, Larson RH, Salmon JK, Young C, Batson B, Bowers KJ, Chao JC (2008) Anton, a special-purpose machine for molecular dynamics simulation. Commun Acm 51:91–97CrossRefGoogle Scholar
  67. Stovgaard K, Andreetta C, Ferkinghoff-Borg J, Hamelryck T (2010) Calculation of accurate small angle x-ray scattering curves from coarse-grained protein models. BMC Bioinform 11:429CrossRefGoogle Scholar
  68. Sugita Y, Okamoto Y (1999) Replica-exchange molecular dynamics method for protein folding. Chem Phys Lett 314:141–151CrossRefGoogle Scholar
  69. Svergun DI (1999) Restoring low resolution structure of biological macromolecules from solution scattering using simulated annealing. Biophys J 77:2879–2886CrossRefGoogle Scholar
  70. Svergun DI, Koch MJH (2003) Small-angle scattering studies of biological macromolecules in solution. Rep Prog Phys 66:1735–1782CrossRefGoogle Scholar
  71. Svergun DI, Barberato C, Koch MJH (1995) CRYSOL – a program to evaluate x-ray solution scattering of biological macromolecules from atomic coordinates. J Appl Cryst 28:768–773CrossRefGoogle Scholar
  72. Svergun DI, Petoukhov MV, Koch MHJ (2001) Determination of domain structure of proteins from x-ray solution scattering. Biophys J 80:2946–2953PubMedPubMedCentralCrossRefGoogle Scholar
  73. Tria G, Mertens HD, Kachala M, Svefun DI (2015) Advanced ensemble modeling of flexible macromolecules using x-ray solution scattering. IUCrJ 26:207–217CrossRefGoogle Scholar
  74. Venditti V, Egner TK, Clore GM (2016) Hybrid approaches to structural characterization of conformational ensembles of complex macromolecular systems combining NMR residual dipolar couplings and solution x-ray scattering. Chem Rev 116:6305–6322PubMedPubMedCentralCrossRefGoogle Scholar
  75. Vestergaard B (2016) Analysis of biostructural changes, dynamics, and interactions – small-angle x-ray scattering to the rescue. Arch Biochem Biohys 602:69–79CrossRefGoogle Scholar
  76. Virtanen JJ, Makowski L, Sosnick TR, Freed KF (2011) Modeling the hydration layer around proteins: applications to small- and wide-angle x-ray scattering. Biophys J 101:2061–2069PubMedPubMedCentralCrossRefGoogle Scholar
  77. Weinan E, Vanden-Eijnden E (2010) Transition-path theory and path-finding algorithms for the study of rare events. Annu Rev Phys Chem 61:391–420CrossRefGoogle Scholar
  78. Wright PE, Dyson HJ (1999) Intrinsically unstructured proteins: re-assessing the protein structure-function paradigm. J Mol Biol 293:321–331PubMedCrossRefGoogle Scholar
  79. Yang S, Park S, Makowski L, Roux B (2009) A rapid coarse residue-based computational method for x-ray solution scattering characterization of protein folds and multiple conformational states of large protein complexes. Biophys J 96:4449–4463PubMedPubMedCentralCrossRefGoogle Scholar
  80. Yang S, Blachowicz L, Makowski L, Roux B (2010) Multidomain assembled states of Hck tyrosine kinase in solution. Proc Natl Acad Sci U S A 107:15757–15762PubMedPubMedCentralCrossRefGoogle Scholar
  81. Yang Z, Lasker K, Schneidman-Duhovny D, Webb B, Huang CC, Pettersen EF, Goddard TD, Meng EC, Sali A, Ferrin TE (2012) UCSF Chimera, MODELLER, and IMP: an integrated modeling system. J Struct Biol 179:269–278PubMedCrossRefPubMedCentralGoogle Scholar
  82. Zheng W, Tekpinar M (2011) Accurate flexible fitting of high-resolution protein structures to small-angle x-ray scattering data using a coarse-grained model with implicit hydration shell. Biophys J 101:2981–2991PubMedPubMedCentralCrossRefGoogle Scholar
  83. Zuckerman DM, Chong LT (2017) Weighted ensemble simulation: review of methodology, applications, and software. Annu Rev Biophys 46:43–57PubMedPubMedCentralCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Graduate School of Medical Life ScienceYokohama City UniversityTsurumikuJapan
  2. 2.Medical Sciences Innovation Hub Program, RIKENTsurumikuJapan

Personalised recommendations