Accounting for thermodynamic non-ideality in the Guinier region of small-angle scattering data of proteins.

David J Scott

doi:10.1007/s12551-016-0235-5

Abstract

Hydrodynamic studies of the solution properties of proteins and other biological macromolecules are often hard to interpret when the sample is present at a reasonably concentrated solution. The reason for this is that solutions exhibit deviations from ideal behaviour which is manifested as thermodynamic non-ideality. The range of concentrations at which this behaviour typically is exhibited is as low as 1–2 mg/ml, well within the range of concentrations used for their analysis by techniques such as small-angle scattering. Here we discuss thermodynamic non-ideality used previously used in the context of light scattering and sedimentation equilibrium analytical ultracentrifugation and apply it to the Guinier region of small-angle scattering data. The results show that there is a complementarity between the radially averaged structure factor derived from small-angle X-ray scattering/small-angle neutron scattering studies and the second virial coefficient derived from sedimentation equilibrium analytical ultracentrifugation experiments.

Highlights

The technique of small-angle scattering by X-rays and neutrons is enjoying a resurgence due to better sources and much improved data analysis
The main feature of this concentration regime is the effect of inter-particle interference whereby the molecules under study can no longer be treated as isolated particles, but exhibit some scattering between molecules. This effect can be interpreted as thermodynamic nonideality and as such be treated in a similar manner to that observed in light scattering and sedimentation equilibrium analytical ultracentrifugation
Whether Rg increases or decreases depends on the sign of the term g(r), i.e. the pair correlation function, at low angles. This predicts that for replusive interactions both Rg and I(0) will fall with decreasing protein concentration and that for attractive interactions, I(0) will rise with increasing protein concentration, whereas Rg will fall in the dilute regime for which the structure factor is term is smaller than the form factor term: a situation seen experimentally when measurements are made over a range of concentrations (Rubinson et al 2008)

Summary

Introduction

The technique of small-angle scattering by X-rays and neutrons is enjoying a resurgence due to better sources and much improved data analysis. Whether Rg increases or decreases depends on the sign of the term g(r), i.e. the pair correlation function, at low angles This predicts that for replusive interactions both Rg and I(0) will fall with decreasing protein concentration and that for attractive interactions, I(0) will rise with increasing protein concentration, whereas Rg will fall in the dilute regime for which the structure factor is term is smaller than the form factor term: a situation seen experimentally when measurements are made over a range of concentrations (Rubinson et al 2008). At high co-solute concentrations, such as studies of unfolded protein at 4– 6 M urea, this term B23c3 will have a considerable effect upon the nature of the scattering curve through the structure factor term (Scott et al 2013) Such changes have previously been ascribed to aggregation, and as such great care is needed in the interpretation of non-ideal data in the Guinier region

Conclusions

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