Accurate calculation of second osmotic virial coefficients of proteins using mixed Poisson–Boltzmann and extended DLVO theory†

The state of proteins in aqueous solution is determined by weak, nonspecific interactions affected by pH, solvent composition, and ionic strength. Protein–protein interactions play a crucial role in determining protein stability and solubility. The second osmotic coefficient (B₂₂) provides insight into effective interactions between proteins in solution. Models for calculating B₂₂ are valuable for estimating interactions, explaining measured phenomena, and reducing experimental time. However, existing models, like the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory, assume a simple spherical shape for proteins. Owing to the fact that proteins exhibit diverse shapes and charge distributions, influencing their electrostatic properties and overall interactions, DLVO accuracy is significantly reduced for nonspherical proteins. To address this limitation, we introduce the xDLVO-CGhybr model, which combines Poisson–Boltzmann (PB) and Debye–Hückel (DH) theories to account for electrostatic interactions between proteins. PB is used for short intermolecular distances (<2 nm) with an all-atom resolution, while DH is employed for longer distances on a coarse-grained level. Additionally, xDLVO-CGhybr incorporates an improved coarse-grained Lennard-Jones (LJ) potential derived directly from the all-atom potential to capture dispersion interactions. This model improves the calculated B₂₂ values compared to existing models and can be applied to proteins with arbitrary shape and charge under various solvent conditions (up to 1 M monovalent salt concentration). We demonstrate the application of xDLVO-CGhybr to bovine trypsin inhibitor, ribonuclease A, chymotrypsinogen, concanavalin A, bovine serum albumin, and human immunoglobulin type I proteins, validating the model against experimental data.