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

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, A(2,app), or the true thermodynamic OSVC, B(22)(osm), that is rigorously defined in solution theory M. A. Blanco, E. Sahin, Y. Li, and C. J. Roberts, J. Chem. Phys. 134, 225103 (2011)]. However, it is unclear to what extent A(2,app) and B(22)(osm) 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 A(2,app) and B(22)(osm). Our results from the hard-sphere equation of state indicate that A(2,app) underestimates B(22)(osm), but in a systematic manner that may be explained using fundamental thermodynamic expressions for the two OSVCs. The difference between A(2,app) and B(22)(osm) 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.