Osmotic virial coefficients for model protein and colloidal solutions: Importance of ensemble constraints in the analysis of light scattering data

Abstract

Protein-protein interactions in solution may be quantified by the osmotic second virial coefficient (OSVC), which can be measured by various experimental techniques including light scattering. Analysis of Rayleigh light scattering measurements from such experiments requires identification of a scattering volume and the thermodynamic constraints imposed on that volume, i.e., the statistical mechanical ensemble in which light scattering occurs. Depending on the set of constraints imposed on the scattering volume, one can obtain either an apparent OSVC, A2,app, or the true thermodynamic OSVC, \documentclass[12pt]{minimal}\begin{document}${B_{22}^{osm}}$\end{document}B22osm, that is rigorously defined in solution theory [M. A. Blanco, E. Sahin, Y. Li, and C. J. Roberts, J. Chem. Phys. 134, 225103 (2011)10.1063/1.3596726]. However, it is unclear to what extent A2,app and \documentclass[12pt]{minimal}\begin{document}${B_{22}^{osm}}$\end{document}B22osm differ, which may have implications on the physical interpretation of OSVC measurements from light scattering experiments. In this paper, we use the multicomponent hard-sphere model and a well-known equation of state to directly compare A2,app and \documentclass[12pt]{minimal}\begin{document}${B_{22}^{osm}}$\end{document}B22osm. Our results from the hard-sphere equation of state indicate that A2,app underestimates \documentclass[12pt]{minimal}\begin{document}${B_{22}^{osm}}$\end{document}B22osm, but in a systematic manner that may be explained using fundamental thermodynamic expressions for the two OSVCs. The difference between A2,app and \documentclass[12pt]{minimal}\begin{document}${B_{22}^{osm}}$\end{document}B22osm may be quantitatively significant, but may also be obscured in experimental application by statistical uncertainty or non-steric interactions. Consequently, the two OSVCs that arise in the analysis of light scattering measurements do formally differ, but in a manner that may not be detectable in actual application.

Coarse-Grained Model for Colloidal Protein Interactions, B22, and Protein Cluster Formation

“…Experimentally, $B_{22}∕B_2^{HS}$ values for proteins typically lie between approximately ±10 unless one considers: (i) extremely highly charged proteins; or (ii) conditions corresponding to such strong protein–protein attractions/repulsions that they are thermodynamically unstable or highly metastable with respect to phase separation. 72,77 By inspection of Fig. 2, one can see that quantitatively reasonable B 22 profiles are obtained for 0.2 < ε cc /ε hp < 0.4, since values of ε cc outside that region provides either too large or too small B 22 values at very long screening lengths, conditions that correspond to essentially just protein, water, and counterions needed for electronegativity (i.e.…”

Recent applications of light scattering measurement in the biological and biopharmaceutical sciences

“…Although a more rigorous interpretation of A 2 has been presented [3, 4], it is not obvious whether or when the distinction between the more rigorous interpretation and the conventional one is qualitatively or quantitatively significant in aqueous solutions of macromolecules. We shall therefore adopt the conventional interpretation of A 2 for the present review.…”

McMillan-Mayer theory of solutions revisited: Simplifications and extensions

“…We find the virial series for the osmotic pressure π = p(c A , μ B , T) − p B (μ B , T) by differentiating the series (33) for the semi-grand potentialF with respect to volume (see the first thermodynamic relation in (15)). For p we thus have to…”

“…This is an example of MMII above. Equation (1) has long been used 15,[25][26][27][28][29][30][31][32][33][34] by polymer, biopolymer, and colloid solution researchers to obtain molecular weights of macromolecules (from the first virial term c A k B T) and to study macromolecule solute-solute interactions (using the second virial term). The osmotic second virial coefficient has also been used in discussions of the hydrophobic interaction of small nonpolar solutes in water, [35][36][37][38][39] and we give an example in Sec.…”

“…24,33,and 44) who, in order to discuss light scattering from multicomponent dilute solutions, introduced a constant pressure ensemble which is grand with respect to the solutes but not with respect to the solvent. The semi-grand canonical ensemble we employ, grand with respect to the solvent, was introduced by Hill.…”