First, I tried a famous example for abnormal pKa value: the bovine chymotrypsin, which was one of the first proteases whose catalytic mechanism was unveiled. All textbooks on biochemistry describe this: we have a 'catalytic triad', which are Asp102, His57, and Ser195. Asp102 forms a Hydrogen bond with His57, making its other aromatic nitrogen a strong bases, which deprotonates Ser195. Thus the Serine becomes a nucleophile and attacks the carbon in the peptide bond.
So I expected from the pKa predictors that they find out that the Histidine becomes a strong base, and that the Serine is deprotonated.
First, I tried the PROPKA server, giving 1ab9 (BOVINE GAMMA-CHYMOTRYPSIN)
pKa pKmodel
ASP 102B 0.40 3.80
HIS 57B 6.19 6.50
This is not what I expected. The Histidine is actually getting a bit acidic; while the Aspartate is very acidic. Trying on H++:
HIS57: 11.3
ASP102 -5.1
I am satisfied with the prediction on the Histidine: it became a strong base; but -5.1 for the Asp is a bit off the mark...
Next, I tried Caspase 3, a cysteine protease, with PDB structure 1rhk. H++ did not accept it, complaining about missing residues. The catalytic residue is Cys165A, for which propka gives pKa = 11.14, instead of the standard 9.0. So the cysteine indeed became a strong base and nucleophile.

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