Cited by 10Enzyme Structure and FunctionProtein Structure and DynamicsAdvanced Electron Microscopy Techniques and Applications

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Fitting high-resolution electron density maps from atomic models to solution scattering data

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Chamberlain, Sarah R., Moore, Stephen, Grant, Thomas D.·2023·Biophysical Journal

Published version of a preprint

Abstract

Solution scattering techniques, such as small- and wide-angle X-ray scattering (SWAXS), provide valuable insights into the structure and dynamics of biological macromolecules in solution. In this study, we present an approach to accurately predict solution X-ray scattering profiles at wide angles from atomic models by generating high-resolution electron density maps. Our method accounts for the excluded volume of bulk solvent by calculating unique adjusted atomic volumes directly from the atomic coordinates. This approach eliminates the need for one of the free fitting parameters commonly used in existing algorithms, resulting in improved accuracy of the calculated SWAXS profile. An implicit model of the hydration shell is generated that uses the form factor of water. Two parameters, namely the bulk solvent density and the mean hydration shell contrast, are adjusted to best fit the data. Results using eight publicly available SWAXS profiles show high-quality fits to the data. In each case, the optimized parameter values show small adjustments demonstrating that the default values are close to the true solution. Disabling parameter optimization produces significantly more accurate predicted scattering profiles compared to the leading software. The algorithm is computationally efficient, comparable to the leading software and up to 10 times faster for large molecules. The algorithm is encoded in a command line script called denss.pdb2mrc.py and is available open source as part of the DENSS v1.7.0 software package. In addition to improving the ability to compare atomic models to experimental SWAXS data, these developments pave the way for increasing the accuracy of modeling algorithms using SWAXS data and decreasing the risk of overfitting.

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Research works printed but not linked: 58

  1. Grant, 2011, Small angle X-ray scattering as a complementary tool for high-throughput structural studies, Biopolymers, 95, 517, 10.1002/bip.21630 · DOI
  2. Mertens, 2017, Combining NMR and small angle X-ray scattering for the study of biomolecular structure and dynamics, Arch. Biochem. Biophys., 628, 33, 10.1016/j.abb.2017.05.005 · DOI
  3. Vestergaard, 2005, The SAXS solution structure of RF1 differs from its crystal structure and is similar to its ribosome bound cryo-EM structure, Mol. Cell, 20, 929, 10.1016/j.molcel.2005.11.022 · DOI
  4. Kim, 2017, Cross-Validation of Data Compatibility Between Small Angle X-ray Scattering and Cryo-Electron Microscopy, J. Comput. Biol., 24, 13, 10.1089/cmb.2016.0139 · DOI
  5. Chacón, 1998, Low-resolution structures of proteins in solution retrieved from X-ray scattering with a genetic algorithm, Biophys. J., 74, 2760, 10.1016/S0006-3495(98)77984-6 · DOI
  6. Svergun, 1999, Restoring low resolution structure of biological macromolecules from solution scattering using simulated annealing, Biophys. J., 76, 2879, 10.1016/S0006-3495(99)77443-6 · DOI
  7. Franke, 2009, DAMMIF, a program for rapid ab-initio shape determination in small-angle scattering, J. Appl. Crystallogr., 42, 342, 10.1107/S0021889809000338 · DOI · Paper page
  8. Grant, 2018, Ab initio electron density determination directly from solution scattering data, Nat. Methods, 15, 191, 10.1038/nmeth.4581 · DOI
  9. Cooley, 1965, An algorithm for the machine calculation of complex Fourier series, Math. Comput., 19, 297, 10.1090/S0025-5718-1965-0178586-1 · DOI · Paper page
  10. Makowski, 2010, Characterization of proteins with wide-angle X-ray solution scattering (WAXS), J. Struct. Funct. Genom., 11, 9, 10.1007/s10969-009-9075-x · DOI
  11. Petoukhov, 2005, Global rigid body modeling of macromolecular complexes against small-angle scattering data, Biophys. J., 89, 1237, 10.1529/biophysj.105.064154 · DOI
  12. Schneidman-Duhovny, 2012, Integrative structural modeling with small angle X-ray scattering profiles, BMC Struct. Biol., 12, 17, 10.1186/1472-6807-12-17 · DOI
  13. Chen, 2015, Interpretation of solution x-ray scattering by explicit-solvent molecular dynamics, Biophys. J., 108, 2573, 10.1016/j.bpj.2015.03.062 · DOI
  14. Bernadó, 2007, Structural characterization of flexible proteins using small-angle X-ray scattering, J. Am. Chem. Soc., 129, 5656, 10.1021/ja069124n · DOI
  15. Svergun, 1995, CRYSOL - a Program to Evaluate X-ray Solution Scattering of Biological Macromolecules from Atomic Coordinates, J. Appl. Crystallogr., 28, 768, 10.1107/S0021889895007047 · DOI
  16. Schneidman-Duhovny, 2010, FoXS: a web server for rapid computation and fitting of SAXS profiles, Nucleic Acids Res., 38, W540, 10.1093/nar/gkq461 · DOI
  17. Bardhan, 2009, SoftWAXS: a computational tool for modeling wide-angle X-ray solution scattering from biomolecules, J. Appl. Crystallogr., 42, 932, 10.1107/S0021889809032919 · DOI
  18. Grudinin, 2017, Pepsi-SAXS: an adaptive method for rapid and accurate computation of small-angle X-ray scattering profiles, Acta Crystallogr. D Struct. Biol., 73, 449, 10.1107/S2059798317005745 · DOI
  19. Poitevin, 2011, AquaSAXS: a web server for computation and fitting of SAXS profiles with non-uniformally hydrated atomic models, Nucleic Acids Res., 39, W184, 10.1093/nar/gkr430 · DOI
  20. Knight, 2015, WAXSiS: a web server for the calculation of SAXS/WAXS curves based on explicit-solvent molecular dynamics, Nucleic Acids Res., 43, W225, 10.1093/nar/gkv309 · DOI
  21. Nguyen, 2014, Accurate small and wide angle x-ray scattering profiles from atomic models of proteins and nucleic acids, J. Chem. Phys., 141, 22D508, 10.1063/1.4896220 · DOI
  22. Virtanen, 2011, Modeling the hydration layer around proteins: applications to small- and wide-angle x-ray scattering, Biophys. J., 101, 2061, 10.1016/j.bpj.2011.09.021 · DOI
  23. Debye, 1915, Zerstreuung von Röntgenstrahlen, Ann. Phys., 351, 809, 10.1002/andp.19153510606 · DOI
  24. Schneidman-Duhovny, 2013, Accurate SAXS profile computation and its assessment by contrast variation experiments, Biophys. J., 105, 962, 10.1016/j.bpj.2013.07.020 · DOI
  25. Yang, 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, 10.1016/j.bpj.2009.03.036 · DOI
  26. Stovgaard, 2010, Calculation of accurate small angle X-ray scattering curves from coarse-grained protein models, BMC Bioinf., 11, 429, 10.1186/1471-2105-11-429 · DOI
  27. Zheng, 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, 10.1016/j.bpj.2011.11.003 · DOI
  28. Pavlov, 1983, Improved technique for calculating X-ray scattering intensity of biopolymers in solution: Evaluation of the form, volume, and surface of a particle, Biopolymers, 22, 1507, 10.1002/bip.360220607 · DOI
  29. Köfinger, 2013, Atomic-resolution structural information from scattering experiments on macromolecules in solution, Phys. Rev. E - Stat. Nonlinear Soft Matter Phys., 87, 10.1103/PhysRevE.87.052712 · DOI
  30. Berlin, 2014, Hierarchical O(N) computation of small-angle scattering profiles and their associated derivatives, J. Appl. Crystallogr., 47, 755, 10.1107/S1600576714004671 · DOI
  31. Cromer, 1968, X-ray scattering factors computed from numerical Hartree-Fock wave functions, Acta Crystallogr., Sect. A, 24, 321, 10.1107/S0567739468000550 · DOI
  32. Park, 2009, Simulated x-ray scattering of protein solutions using explicit-solvent models, J. Chem. Phys., 130, 134114, 10.1063/1.3099611 · DOI
  33. Fraser, 1978, An improved method for calculating the contribution of solvent to the X-ray diffraction pattern of biological molecules, J. Appl. Crystallogr., 11, 693, 10.1107/S0021889878014296 · DOI
  34. Bondi, 1964, van der Waals Volumes and Radii, J. Phys. Chem., 68, 441, 10.1021/j100785a001 · DOI
  35. Svergun, 1998, Protein hydration in solution: experimental observation by x-ray and neutron scattering, Proc. Natl. Acad. Sci. USA, 95, 2267, 10.1073/pnas.95.5.2267 · DOI
  36. Hsu, 2020, Integrating solvation shell structure in experimentally driven molecular dynamics using x-ray solution scattering data, J. Chem. Phys., 152, 204115, 10.1063/5.0007158 · DOI
  37. Grant, 2022, Describing small-angle scattering profiles by a limited set of intensities, J. Appl. Crystallogr., 55, 1116, 10.1107/S1600576722006598 · DOI
  38. Shannon, 1948, A mathematical theory of communication, The Bell system technical journal, 27, 379, 10.1002/j.1538-7305.1948.tb01338.x · DOI · Paper page
  39. Moore, 1980, Small-angle scattering. Information content and error analysis, J. Appl. Crystallogr., 13, 168, 10.1107/S002188988001179X · DOI
  40. Word, 1999, Asparagine and glutamine: using hydrogen atom contacts in the choice of side-chain amide orientation, J. Mol. Biol., 285, 1735, 10.1006/jmbi.1998.2401 · DOI
  41. Liebschner, 2019, Macromolecular structure determination using X-rays, neutrons and electrons: recent developments in Phenix, Acta Crystallogr. D Struct. Biol., 75, 861, 10.1107/S2059798319011471 · DOI · Paper page
  42. Berman, 2000, The Protein Data Bank, Nucleic Acids Res., 28, 235, 10.1093/nar/28.1.235 · DOI · Paper page
  43. Kikhney, 2020, SASBDB: Towards an automatically curated and validated repository for biological scattering data, Protein Sci., 29, 66, 10.1002/pro.3731 · DOI
  44. Diamond, 1974, Real-space refinement of the structure of hen egg-white lysozyme, J. Mol. Biol., 82, 371, 10.1016/0022-2836(74)90598-1 · DOI
  45. Virtanen, 2010, Modeling the hydration layer around proteins: HyPred, Biophys. J., 99, 1611, 10.1016/j.bpj.2010.06.027 · DOI
  46. Koehl, 2010, AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation, J. Chem. Phys., 132
  47. Nelder, 1965, A simplex method for function minimization, Comput. J., 7, 308
  48. Gao, 2012, Implementing the Nelder-Mead simplex algorithm with adaptive parameters, Comput. Optim. Appl., 51, 259, 10.1007/s10589-010-9329-3 · DOI
  49. Manalastas-Cantos, 2021, ATSAS 3.0: expanded functionality and new tools for small-angle scattering data analysis, J. Appl. Crystallogr., 54, 343, 10.1107/S1600576720013412 · DOI
  50. Korn, 2023, The preference signature of the SARS-CoV-2 Nucleocapsid NTD for its 5'-genomic RNA elements, Nat. Commun., 14, 3331, 10.1038/s41467-023-38882-y · DOI
  51. Weinert, 2017, Serial millisecond crystallography for routine room-temperature structure determination at synchrotrons, Nat. Commun., 8, 542, 10.1038/s41467-017-00630-4 · DOI
  52. Moore, 2014, The Effects of Thermal Disorder on the Solution-Scattering Profiles of Macromolecules, Biophys. J., 106, 1489, 10.1016/j.bpj.2014.02.016 · DOI
  53. Harris, 2020, Array programming with NumPy, Nature, 585, 357, 10.1038/s41586-020-2649-2 · DOI · Paper page
  54. Virtanen, 2020, SciPy 1.0: fundamental algorithms for scientific computing in Python, Nat. Methods, 17, 261, 10.1038/s41592-019-0686-2 · DOI · Paper page
  55. Frigo, 2005, The design and implementation of FFTW3, Proc. IEEE, 93, 216, 10.1109/JPROC.2004.840301 · DOI · Paper page
  56. Tolmachev, 2023, VkFFT-a performant, cross-platform and open-source GPU FFT library, IEEE Access, 11, 12039, 10.1109/ACCESS.2023.3242240 · DOI
  57. Nickolls, 2008, Scalable parallel programming with cuda: Is cuda the parallel programming model that application developers have been waiting for?, Queue, 6, 40, 10.1145/1365490.1365500 · DOI
  58. Nishino, 2017, CuPy: A NumPy-Compatible Library for NVIDIA GPU Calculations, 31st Conference on Neural Information Processing Systems, 151

Metadata

Authors
Chamberlain, S. R., Moore, S., & Grant, T. D.
Affiliations
University at Buffalo, State University of New York (US)
Corresponding author
Grant, Thomas D.
Venue
Biophysical Journal
Publisher
Elsevier BV
Published
2023-12
Volume
122
Issue
23
Pages
4567-4581
ISSN
0006-3495 (ISSN-L)
OpenAlex
W4388209650
Cited by
10
References
1
Citations by year
2026: 4 · 2025: 2 · 2024: 3 · 2023: 1
FWCI
0.74
Type
journal article
Language
en
Open access
Locations
  • Biophysical Journal (publishedVersion)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by)
  • PubMed Central (publishedVersion)
  • PubMed (publishedVersion)
  • PubMed Central (submittedVersion, cc-by)
Funders
  • National Institutes of Health
  • National Institute of General Medical Sciences (R01GM133998)
  • National Science Foundation (BioXFEL STC 1231306, MCB 1817862)
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Structural Biology › Enzyme Structure and Function
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Structural Biology › Advanced Electron Microscopy Techniques and Applications
Keywords
solution X-ray scattering, hydration shell

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