Improving the accuracy of protein pKa calculations: conformational averaging versus the average structure

Several methods for including the conformational flexibility of proteins in the calculation of titration curves are compared. The methods use the linearized Poisson-Boltzmann equation to calculate the electrostatic free energies of solvation and are applied to bovine pancreatic trypsin inhibitor (BPTI) and hen egg-white lysozyme (HEWL). An ensemble of conformations is generated by a molecular dynamics simulation of the proteins with explicit solvent. The average titration curve of the ensemble is calculated in three different ways: an average structure is used for the pKa calculation; the electrostatic interaction free energies are averaged and used for the pKa calculation; and the titration curve for each structure is calculated and the curves are averaged. The three averaging methods give very similar results and improve the pKa values to approximately the same degree. This suggests, in contrast to implications from other work, that the observed improvement of pKa values in the present studies is due not to averaging over an ensemble of structures, but rather to the generation of a single properly averaged structure for the pKa calculation.