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Experimental determination of second virial coefficients by small-angle X-ray scattering: a problem revisited

  • Tyler Mrozowich
  • Donald J. Winzor
  • David J. ScottEmail author
  • Trushar R. PatelEmail author
Original Article

Abstract

This investigation examines the validity of employing single-solute theory to interpret SAXS measurements on buffered protein solutions—the current practice despite the necessity to regard the buffer components as additional non-scattering solutes rather than as part of the solvent. The present study of bovine serum albumin in phosphate-buffered saline supplemented with 20–100 g/L sucrose as small cosolute has certainly verified the prediction that the experimentally obtained second virial coefficient should contain protein–cosolute contributions. Nevertheless, the second virial coefficient determined for protein solutions supplemented with high cosolute concentrations on the basis of single-solute theory remains a valid means for identifying conditions conducive to protein crystallization, because the return of a slightly negative second virial coefficient based on single-solute theory \(A_{2}^{\text{app}}\) still establishes the existence of slightly associative interactions between protein molecules, irrespective of the molecular source–protein self-interactions and/or protein–cosolute contributions.

Keywords

Small-angle X-ray scattering Thermodynamic nonideality Second virial coefficients Bovine serum albumin Small cosolute effects 

Notes

Acknowledgements

TM is supported by the NSERC Discovery Grant to TRP (RGPIN-2017-04003). TRP is a Canada Research Chair in RNA & Protein Biophysics.

References

  1. Attri AK, Minton AP (2005) Composition gradient static light scattering: a new technique for rapid detection and quantitative characterization of reversible macromolecular interactions in solution. Anal Biochem 346:132–138CrossRefGoogle Scholar
  2. Blaak R (1998) Exact analytic expression for a subset of fourth virial coefficients of polydisperse hard sphere mixtures. Mol Phys 95:695–699CrossRefGoogle Scholar
  3. Blanco MA, Sahin E, Li Y, Roberts CJ (2011) Re-examining protein-protein and protein-solvent interactions from Kirkwood-Buff analysis of light scattering in multi-component solutions. J Chem Phys 134:225103–225114CrossRefGoogle Scholar
  4. Bonneté F, Vivarès D, Colloc’h CRN (2001) Interactions in solution and crystallization of Aspergillus flavis urate oxidase. J Cryst Growth 232:330–339CrossRefGoogle Scholar
  5. Cantor CR, Schimmel PR (1980) Biophysical chemistry. Freeman, San FranciscoGoogle Scholar
  6. Chen SH (1986) Small angle neutron scattering studies of the structure and interaction of the micellar and microemulsion systems. Annu Rev Phys Chem 37:351–399CrossRefGoogle Scholar
  7. Deszczynski M, Harding SE, Winzor DJ (2006) Negative second virial coefficients as predictors of protein crystal growth: evidence from sedimentation equilibrium studies that refute the designation of those parameters as osmotic second virial coefficients. Biophys Chem 120:106–113CrossRefGoogle Scholar
  8. Ferens FG, Patel TR, Oriss G, Court DA, Stetefeld J (2019) A cholesterol analog induces an oligomeric reorganization of VDAC. Biophys J 116:847–859CrossRefGoogle Scholar
  9. George A, Wilson WW (1994) Predicting protein crystallization from a dilute solution property. Acta Cryst D 50:361–365CrossRefGoogle Scholar
  10. Hayter JB, Penfold J (1983) Determination of micelle structure and charge by neutron small angle scattering. J Colloid Polym Sci 261:1022–1030CrossRefGoogle Scholar
  11. Hill TL (1959) Theory of solutions. II. Osmotic pressure virial expansion and light scattering in two component solutions. J Chem Phys 30:93–97CrossRefGoogle Scholar
  12. Ianeselli L, Zhang F, Skoda MWA, Jacobs RA, Martin S, Callow S, Prévost S, Schreiber F (2010) Protein-protein interactions in ovalbumin solutions studies by small-angle scattering: effect of ionic strength and chemical nature of cations. J Phys Chem B 114:3776–3783CrossRefGoogle Scholar
  13. Kirkwood JG, Goldberg RJ (1950) Light scattering arising from composition fluctuations in multi-component systems. J Chem Phys 18:54–57CrossRefGoogle Scholar
  14. 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
  15. McMillan WG, Mayer JE (1945) The statistical thermodynamics of multicomponent systems. J Chem Phys 13:276–305CrossRefGoogle Scholar
  16. Meier MA, Moya A, Krahn N, McDougall M, McRae EK, Booy EP, Patel TR, McKenna SA, Stetefeld J (2018) Structure and hydrodynamics of a DNA G-quadruplex with a cytosine bulge. Nucleic Acids Res 46:5319–5331CrossRefGoogle Scholar
  17. Muschol M, Rosenberger F (1995) Interactions in undersaturated and supersaturated lysozyme solutions: static and dynamic light scattering results. J Chem Phys 103:10424–10432CrossRefGoogle Scholar
  18. Pace CN, Vajdos F, Fee L, Grimsley G, Gray T (1995) How to measure and predict the molar absorption coefficient of a protein. Protein Sci 4:2411–2423CrossRefGoogle Scholar
  19. Receveur V, Durand D, Desmadril BM, Calmettes P (1998) Repulsive interparticle interactions in a denatured protein solution revealed by small angle neutron scattering. FEBS Lett 426:57–61CrossRefGoogle Scholar
  20. Rosenbaum DF, Zukoski CF (1996) Protein interactions and crystallization. J Cryst Growth 169:752–758CrossRefGoogle Scholar
  21. Sahin E, Grillo O, Perkins MD, Roberts CJ (2011) Comparative affects of pH and ionic strength on protein-protein interactions, unfolding and aggregation of IgG1 antibodies. J Pharm Sci 00:4830–4848Google Scholar
  22. Scott DJ, Patel TR, Winzor DJ (2013) A potential for overestimating the absolute magnitudes of second virial coefficients by small-angle X-ray scattering. Anal Biochem 435:159–165CrossRefGoogle Scholar
  23. Stockmayer WH (1950) Light scattering in multi-component systems. J Chem Phys 18:58–61CrossRefGoogle Scholar
  24. Tanford C (1954) Physical chemistry of macromolecules. Wiley, New YorkGoogle Scholar
  25. Tanford C, Swanson SA, Shore WS (1955) Hydrogen ion equilibria of bovine serum albumin. J Am Chem Soc 77:6414–6421CrossRefGoogle Scholar
  26. Van Holde KE (1985) Physical biochemistry. Prentice Hall, Englewood CliffsGoogle Scholar
  27. Vivarès D, Bonneté F (2002) X-ray scattering studies of Aspergillus flavus urate oxidase: towards a better understanding of PEG effects on the crystallization of large proteins. Acta Cryst D58:470–472Google Scholar
  28. Wills PR, Winzor DJ (2017) Rigorous analysis of static light scattering measurements on buffered protein solutions. Biophys Chem 228:108–113CrossRefGoogle Scholar
  29. Wills PR, Scott DJ, Winzor DJ (2015) The osmotic second virial coefficient for protein self-interaction: use and misuse to describe thermodynamic nonideality. Anal Biochem 490:55–65CrossRefGoogle Scholar
  30. Winzor DJ, Deszczynski M, Harding SE, Wills PR (2007) Nonequivalence of second virial coefficients from sedimentation equilibrium and static light scattering studies of protein solutions. Biophys Chem 128:46–55CrossRefGoogle Scholar
  31. Wu D, Minton AP (2013) Quantitative characterization of the interaction between sucrose and native proteins via static light scattering. J Phys Chem B 117:111–117CrossRefGoogle Scholar
  32. Wu D, Minton AP (2015) Quantitative characterization of nonspecific self- and hetero-interactions of proteins via static light scattering. J Phys Chem B 119:1891–1898CrossRefGoogle Scholar
  33. Zhang F, Skoda MWA, Jacobs RMJ, Martin RA, Martin CM, Schreiber F (2007) Protein interaction studied by SAXS: effect of ionic strength and protein concentration for BSA in aqueous solutions. J Phys Chem B 111:251–259CrossRefGoogle Scholar
  34. Zimm BH (1948) The scattering of light and the radial distribution function of high polymer solutions. J Chem Phys 16(1948):1093–1099CrossRefGoogle Scholar

Copyright information

© European Biophysical Societies' Association 2019

Authors and Affiliations

  1. 1.Department of Chemistry and Biochemistry, Alberta RNA Research and Training InstituteUniversity of LethbridgeLethbridgeCanada
  2. 2.School of Chemistry and Molecular BiosciencesUniversity of QueenslandBrisbaneAustralia
  3. 3.National Centre for Macromolecular Hydrodynamics, School of BiosciencesUniversity of NottinghamNottinghamUK
  4. 4.ISIS Spallation Neutron and Muon Source, Rutherton Appleton Research Complex at HarwellHarwellUK
  5. 5.Department of Microbiology, Immunology and Infectious Disease, Cumming School of MedicineUniversity of CalgaryCalgaryCanada
  6. 6.Li Ka Shing Institute of Virology and Discovery LabUniversity of AlbertaEdmontonCanada

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