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

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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.

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References

  • 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 346:132–138

    Article  CAS  Google Scholar 

  • Blaak R (1998) Exact analytic expression for a subset of fourth virial coefficients of polydisperse hard sphere mixtures. Mol Phys 95:695–699

    Article  CAS  Google Scholar 

  • 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 134:225103–225114

    Article  Google Scholar 

  • Bonneté F, Vivarès D, Colloc’h CRN (2001) Interactions in solution and crystallization of Aspergillus flavis urate oxidase. J Cryst Growth 232:330–339

    Article  Google Scholar 

  • Cantor CR, Schimmel PR (1980) Biophysical chemistry. Freeman, San Francisco

    Google Scholar 

  • Chen SH (1986) Small angle neutron scattering studies of the structure and interaction of the micellar and microemulsion systems. Annu Rev Phys Chem 37:351–399

    Article  CAS  Google Scholar 

  • 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 120:106–113

    Article  CAS  Google Scholar 

  • Ferens FG, Patel TR, Oriss G, Court DA, Stetefeld J (2019) A cholesterol analog induces an oligomeric reorganization of VDAC. Biophys J 116:847–859

    Article  CAS  Google Scholar 

  • George A, Wilson WW (1994) Predicting protein crystallization from a dilute solution property. Acta Cryst D 50:361–365

    Article  CAS  Google Scholar 

  • Hayter JB, Penfold J (1983) Determination of micelle structure and charge by neutron small angle scattering. J Colloid Polym Sci 261:1022–1030

    Article  CAS  Google Scholar 

  • Hill TL (1959) Theory of solutions. II. Osmotic pressure virial expansion and light scattering in two component solutions. J Chem Phys 30:93–97

    Article  CAS  Google Scholar 

  • 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 114:3776–3783

    Article  CAS  Google Scholar 

  • Kirkwood JG, Goldberg RJ (1950) Light scattering arising from composition fluctuations in multi-component systems. J Chem Phys 18:54–57

    Article  CAS  Google Scholar 

  • 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 36:1277–1282

    Article  CAS  Google Scholar 

  • McMillan WG, Mayer JE (1945) The statistical thermodynamics of multicomponent systems. J Chem Phys 13:276–305

    Article  CAS  Google Scholar 

  • 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 46:5319–5331

    Article  CAS  Google Scholar 

  • Muschol M, Rosenberger F (1995) Interactions in undersaturated and supersaturated lysozyme solutions: static and dynamic light scattering results. J Chem Phys 103:10424–10432

    Article  CAS  Google Scholar 

  • 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 4:2411–2423

    Article  CAS  Google Scholar 

  • 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 426:57–61

    Article  CAS  Google Scholar 

  • Rosenbaum DF, Zukoski CF (1996) Protein interactions and crystallization. J Cryst Growth 169:752–758

    Article  CAS  Google Scholar 

  • 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 00:4830–4848

    Google Scholar 

  • 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 435:159–165

    Article  CAS  Google Scholar 

  • Stockmayer WH (1950) Light scattering in multi-component systems. J Chem Phys 18:58–61

    Article  CAS  Google Scholar 

  • Tanford C (1954) Physical chemistry of macromolecules. Wiley, New York

    Google Scholar 

  • Tanford C, Swanson SA, Shore WS (1955) Hydrogen ion equilibria of bovine serum albumin. J Am Chem Soc 77:6414–6421

    Article  CAS  Google Scholar 

  • Van Holde KE (1985) Physical biochemistry. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • 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 D58:470–472

    Google Scholar 

  • Wills PR, Winzor DJ (2017) Rigorous analysis of static light scattering measurements on buffered protein solutions. Biophys Chem 228:108–113

    Article  CAS  Google Scholar 

  • 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 490:55–65

    Article  CAS  Google Scholar 

  • 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 128:46–55

    Article  CAS  Google Scholar 

  • Wu D, Minton AP (2013) Quantitative characterization of the interaction between sucrose and native proteins via static light scattering. J Phys Chem B 117:111–117

    Article  CAS  Google Scholar 

  • Wu D, Minton AP (2015) Quantitative characterization of nonspecific self- and hetero-interactions of proteins via static light scattering. J Phys Chem B 119:1891–1898

    Article  CAS  Google Scholar 

  • 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 111:251–259

    Article  CAS  Google Scholar 

  • Zimm BH (1948) The scattering of light and the radial distribution function of high polymer solutions. J Chem Phys 16(1948):1093–1099

    Article  CAS  Google Scholar 

Download references

Acknowledgements

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

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Authors and Affiliations

  1. Department of Chemistry and Biochemistry, Alberta RNA Research and Training Institute, University of Lethbridge, 4401 University Drive, Lethbridge, AB, T1K 3M4, Canada

    Tyler Mrozowich & Trushar R. Patel

  2. School of Chemistry and Molecular Biosciences, University of Queensland, Brisbane, QLD, 4072, Australia

    Donald J. Winzor

  3. National Centre for Macromolecular Hydrodynamics, School of Biosciences, University of Nottingham, Sutton Bonington Campus, Nottingham, LE12 5RD, UK

    David J. Scott

  4. ISIS Spallation Neutron and Muon Source, Rutherton Appleton Research Complex at Harwell, Harwell, OX11 OFA, UK

    David J. Scott

  5. Department of Microbiology, Immunology and Infectious Disease, Cumming School of Medicine, University of Calgary, Calgary, T2N 1N4, AB, Canada

    Trushar R. Patel

  6. Li Ka Shing Institute of Virology and Discovery Lab, University of Alberta, Edmonton, AB, T6G 2E1, Canada

    Trushar R. Patel

Authors
  1. Tyler Mrozowich
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  2. Donald J. Winzor
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  3. David J. Scott
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  4. Trushar R. Patel
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Correspondence to David J. Scott or Trushar R. Patel.

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Mrozowich, T., Winzor, D.J., Scott, D.J. et al. Experimental determination of second virial coefficients by small-angle X-ray scattering: a problem revisited. Eur Biophys J 48, 781–787 (2019). https://doi.org/10.1007/s00249-019-01404-0

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  • DOI: https://doi.org/10.1007/s00249-019-01404-0

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