PKa predictions with a coupled finite difference Poisson–Boltzmann and Debye–Hückel method

Abstract

Modeling charge interactions is important for understanding many aspects of biological structure and function, and continuum methods such as Finite Difference Poisson-Boltzmann (FDPB) are commonly employed. Calculations of pH-dependence have identified separate populations; surface groups that can be modeled with a simple Debye-Hückel (DH) model, and buried groups, with stronger resultant interactions that are dependent on detailed conformation. This observation led to the development of a combined FDPB and DH method for pK(a) prediction (termed FD/DH). This study reports application of this method to ionizable groups, including engineered buried charges, in staphylococcal nuclease. The data had been made available to interested research groups before publication of mutant structures and/or pK(a) values. Overall, FD/DH calculations perform as intended with low ΔpK(a) values for surface groups (RMSD between predicted and experimental pK(a) values of 0.74), and much larger ΔpK(a) values for the engineered internal groups, with RMSD = 1.64, where mutant structures were known and RMSD = 1.80, where they were modeled. The weaker resultant interactions of the surface groups are determined mostly by charge-charge interactions. For the buried groups, R(2) for correlation between predicted and measured ΔpK(a) values is 0.74, despite the high RMSDs. Charge-charge interactions are much less important, with the R(2) value for buried group ΔpK(a) values increasing to 0.80 when the term describing charge desolvation alone is used. Engineered charge burial delivers a relatively uniform, nonspecific effect, in terms of pK(a) . How the protein environment adapts in atomic detail to deliver this resultant effect is still an open question.