The osmotic second virial coefficients B2 are directly related to the solubility of protein molecules in electrolyte solutions and can be useful to narrow down the search parameter space of protein crystallization conditions. Using a residue level model of protein-protein interaction in electrolyte solutions B2 of bovine pancreatic trypsin inhibitor and lysozyme in various solution conditions such as salt concentration, pH and temperature are calculated using an extended fast multipole method in combination with the boundary element formulation. Overall, the calculated B2 are well correlated with the experimental observations for various solution conditions. In combination with our previous work on the binding affinity calculations it is reasonable to expect that our residue level model can be used as a reliable model to describe protein-protein interaction in solutions. Disciplines Chemistry CommentsThis article is from Physical Review E 83 (2011) The osmotic second virial coefficients B 2 are directly related to the solubility of protein molecules in electrolyte solutions and can be useful to narrow down the search parameter space of protein crystallization conditions. Using a residue level model of protein-protein interaction in electrolyte solutions B 2 of bovine pancreatic trypsin inhibitor and lysozyme in various solution conditions such as salt concentration, pH and temperature are calculated using an extended fast multipole method in combination with the boundary element formulation. Overall, the calculated B 2 are well correlated with the experimental observations for various solution conditions. In combination with our previous work on the binding affinity calculations it is reasonable to expect that our residue level model can be used as a reliable model to describe protein-protein interaction in solutions.

In this paper, we used a coarse-grained model at the residue level to calculate the binding free energies of three protein-protein complexes. General formulations to calculate the electrostatic binding free energy and the van der Waals free energy are presented by solving linearized Poisson-Boltzmann equations using the boundary element method in combination with the fast multipole method. The residue level model with the fast multipole method allows us to efficiently investigate how the mutations on the active site of the proteinprotein interface affect the changes in binding affinities of protein complexes. Good correlations between the calculated results and the experimental ones indicate that our model can capture the dominant contributions to the protein-protein interactions. At the same time, additional effects on protein binding due to atomic details are also discussed in the context of the limitations of such a coarse-grained model.

I present a physical model to calculate protein-protein interactions. General formulations to calculate the electrostatic and the van der Waals free energies are brought by the boundary element method of solving linearized Poission-Boltzmann equation in an electrolyte solution, then further expanded to the application of the Fast Multipole Method(FMM). We built an efficient solver to investigate how the mutations on the active site of the protein-protein interface affect changes in binding affinities of protein complexes. Calculated results in addition to the structural analysis help us to understand the protein-protein interaction energy and provide a model to the important applications such as protein crystallization. The osmotic second virial coefficient B 2 is directly related to the solubility of protein molecule in electrolyte solution and determined by molecular interactions involving both solvent and solute molecules. Calculations of interaction energies account for the electrostatic and the van der Waals interactions with the structural anisotropic properties of protein molecules. The orientation dependence of interaction energies between two proteins is determined by the crystal space operations and small number of protein-protein pair configurations according to the anisotropic patch model are required to calculate B 2 . With the extended FMMs, double-tree and single-tree algorithms, the boundary element formulations of interaction energies can be applied with low computational cost to the proteins. B 2 Calculations of Bovine Pancreatic Trypsin Inhibitor are firstly performed to validate our model and the results of lysozyme protein under different salts, concentrations, pH and temperatures are correlated to the experimental B 2 . The reduced number of pair interaction energies between xiii two proteins are interpolated to predict all pair interaction energies in the patch model as a precursor of the protein phase diagram calculation.