An accurate density functional theory based estimation of pK(a) values of polar residues combined with experimental data: from amino acids to minimal proteins.

We report a scheme for estimating the acid dissociation constant (pK(a)) based on quantum-chemical calculations combined with a polarizable continuum model, where a parameter is determined for small reference molecules. We calculated the pK(a) values of variously sized molecules ranging from an amino acid to a protein consisting of 300 atoms. This scheme enabled us to derive a semiquantitative pK(a) value of specific chemical groups and discuss the influence of the surroundings on the pK(a) values. As applications, we have derived the pK(a) value of the side chain of an amino acid and almost reproduced the experimental value. By using our computing schemes, we showed the influence of hydrogen bonds on the pK(a) values in the case of tripeptides, which decreases the pK(a) value by 3.0 units for serine in comparison with those of the corresponding monopeptides. Finally, with some assumptions, we derived the pK(a) values of tyrosines and serines in chignolin and a tryptophan cage. We obtained quite different pK(a) values of adjacent serines in the tryptophan cage; the pK(a) value of the OH group of Ser13 exposed to bulk water is 14.69, whereas that of Ser14 not exposed to bulk water is 20.80 because of the internal hydrogen bonds.