Interpretation of negative second virial coefficients from non-attractive protein solution osmotic pressure data: An alternate perspective

- The second virial coefficient is related to solute-solvent interactions, hydration and ion binding.
- The predicted values agree with experimental values from literature.
- The ionic strength ratio of solute-bound solvent is critical in interpreting the second virial coefficient.
- The second virial coefficient relies critically on protein-ion binding.
- Protein-ion interaction is a critical parameter for understanding solubility, salting-in, salting-out, and crystallization.

A negative second virial coefficient has long been a predictor of potential protein crystallization and salting out. However, the assumption that this is due to attractive solute-solute interactions remains a source of debate. Here we reexamine the second virial coefficient from protein osmometry in terms of the free-solvent model. The free-solvent model has been shown to provide excellent predictions of the osmotic pressure of concentrated and crowded environments for aqueous protein solutions in moderate ionic strengths. The free-solvent model relies on two critical parameters, hydration and ion binding, both which can be determined independently of osmotic pressure data. Herein, the free-solvent model is mathematically represented as a virial expansion model and the second virial coefficient is expressed in terms of solute-solvent interactions, namely hydration and ion binding. Hydration and ion binding values are then used to estimate the second virial coefficient at various protein concentrations for three model proteins ovalbumin (OVA), bovine serum albumin (BSA), and hen egg lysozyme (HEL) in various monovalent salt aqueous solutions. The results show that the conditions for obtaining a negative second virial coefficient emerge when the ionic strength of the influenced region of the protein is higher than that of the bulk. This analysis suggests a plausible explanation as to why proteins are more favorable for salting out or crystallization when the solution is represented by a negative second virial coefficient.