(308e) Osmotic Virial Coefficients of Protein Solutions: Effect of Differing Ensemble Constraints and Connection to Experiment

The so-called second osmotic virial coefficient is often used to describe or quantify intermolecular interactions in macromolecular systems such as colloidal fluids containing proteins, surfactants, and synthetic colloids[1]. In this context, the second osmotic virial coefficient approximates the manner in which the osmotic pressure varies with the concentration of a particular colloidal species, such as the concentration of protein in the case of a protein-electrolyte solution. Many experimental methods, including laser light scattering, osmometry, ultracentrifugation, and self-interaction chromatography seek to provide measurements of this osmotic virial coefficient[2,3]. Unfortunately, the virial coefficients yielded by these experimental methods have subtle, yet important, differences that are connected to the thermodynamic constraints or statistical mechanical ensemble associated with each method. Furthermore, the multicomponent nature of the solvent is often neglected in the underlying theoretical analysis connecting experimental measurements to the osmotic virial coefficient and other thermodynamic quantities. The formally differing virial coefficients that result from these analysis are often treated as though they are identical, which can lead to misinterpretation of experimental data. The nature and magnitude of these differences is poorly understood at present.

To address these deficiencies in present connections between osmotic thermodynamics and experimental techniques, we revisit the relevant definitions of the virial coefficients in the context of Kirkwood-Buff solution theory [4] and identify the mathematical differences between the various virial coefficients in different ensembles or under different constraints. Additionally, we point out connections between the osmotic virial coefficient and thermodynamic stability criteria, which may assist in understanding phase transitions in protein solutions[5]. We model a fluid containing solvent, protein, and co-solvent (e.g., electrolyte) as a mixture of hard-spheres using the BMCSL equation of state [6] and perturbations thereto and compute the osmotic virial coefficient as a function of protein size, co-solvent molality, and system pressure and, in doing so, quantify the various thermodynamic contributions to the virial coefficient, some of which are neglected in traditional analyses. These differences are highlighted and discussed in the context of various experimental techniques, which will allow for better understanding and integration of data from the differing techniques.

[1] B.L. Neal, D. Asthagiri, and A.M. Lenhoff, Biophys. J., 75:2469 (1998)

[2] P.M. Tessier, A.M. Lenhoff, and S.I. Sandler, Biophys. J., 82:1620 (2002)

[3] W.H. Stockmayer, J. Chem. Phys., 18:58 (1950)

[4] J.G. Kirkwood and F.P. Buff, J. Chem. Phys., 19:774 (1951)

[5] S. Ruppert, S.I. Sandler, and A.M. Lenhoff, Biotechnol. Prog., 17:182 (2001)

[6] T. Boublik, J. Chem. Phys., 53:471 (1970), G.A. Mansoori, N.F. Carnahan, K.E. Starling, and T.W. Leland Jr., J. Chem. Phys., 54:1523 (1971)