A mesoscopic model for protein-protein interactions in solution.

Protein self-association may be detrimental in biological systems, but can be utilized in a controlled fashion for protein crystallization. It is hence of considerable interest to understand how factors like solution conditions prevent or promote aggregation. Here we present a computational model describing interactions between protein molecules in solution. The calculations are based on a molecular description capturing the detailed structure of the protein molecule using x-ray or nuclear magnetic resonance structural data. Both electrostatic and van der Waals interactions are included and the salt particles are explicitly treated allowing investigations of systems containing mono-, di-, and trivalent ions. For three different proteins-lysozyme, alpha-chymotrypsinogen, and calbindin D(9k)-we have investigated under which conditions (salt concentration, ion valency, pH, and/or solvent) the proteins are expected to aggregate via evaluation of the second virial coefficient. Good agreement is found with experimental data where available. Calbindin is investigated in more detail, and it is demonstrated how changes in solvent and/or counterion valency lead to attractive ion-ion correlation effects. For high valency counterions we have found abnormal trends in the second virial coefficient. With trivalent counterions, attraction of two negatively charged protein molecules can be favored because the repulsive term is decreased for entropic reasons due to the low number of particles present.