Why is the osmotic second virial coefficient related to protein crystallization?

A molecular basis is presented for characterizing the osmotic second virial coefficient, B₂₂, of dilute protein solutions, which provides a measure of the nature of protein-protein interactions and has been shown to be correlated with crystallization behavior. Experimental measurements of the second virial coefficient of lysozyme and bovine α-chymotrypsinogen A were performed by static light scattering, as a function of pH and electrolyte concentration. Although some of the trends can be explained qualitatively by simple colloidal models of protein interactions, a more realistic interpretation based on protein crystallographic structures suggests a different explanation of experimental trends. The interactions accounted for are solute-solute excluded volume (steric), electrostatic and short-range (mainly van der Waals) interactions. The interactions depend strongly on orientation, and this profoundly affects calculated second virial coefficients. We find that molecular configurations in which complementary surfaces are apposed contribute disproportionately to the second virial coefficient, mainly through short-range interactions; electrostatic interactions play a secondary role in many of these configurations. Thus molecular recognition events can play a role in determining the solution thermodynamic properties of proteins, and this provides a plausible basis for explaining the observed relationship with crystallization behavior.