There is a very interesting paper
Using Unnatural Amino Acids to Probe the Energetics of Oxyanion Hole Hydrogen Bonds in the Ketosteroid Isomerase Active Site
Aditya Natarajan, Jason P. Schwans, and Daniel Herschlag
The key Tyrosine amino acid (Tyr16) is substituted with different fluorinated versions. These have different proton affinities (acidity or pKa) to the native amino acid. It is well established that the strength of a hydrogen bond is maximal when the hydrogen donor and acceptor have the same proton affinity [pKa matching]. This can be naturally understood in terms of a diabatic state model for H-bonding.
The aim of the experiment is to vary the strength of one of the key hydrogen bonds in the enzyme and see what effect it has on the activity of the enzyme. They vary the pKa from 8.35 to 9.95 and find negligible change in the activity of the enzyme. They conclude
The observed shallow dependence of activity on the pKa of the substituted Tyr residues suggests that the KSI oxyanion hole does not provide catalysis by forming an energetically exceptional pKa-matched hydrogen bond.I am puzzled because I have the opposite conclusion, i.e. the shallow dependence is what one expects for a strong short H-bond. For strong bonds you need to vary the pKa difference between the donor and acceptor by much more than 2. A pKa difference of 2 corresponds to “detuning” the two diabatic states by about 2.7 kcal/mol [11 kJ/mol]. Experimentally, you can also see this in the two figures below. The first [Figure 3(d) in this paper] shows the binding energy of a series of strong H-bonds as a function of the difference in proton affinity.
The second [Figure 2 in this paper] shows the softening of the O-H stretch as a function of the proton affinity difference [in kJ/mol].
Note that in both cases a pKa difference of 2 corresponds to a very small change in the strength of the H-bond.
This is also what one expects from the diabatic state model. For short bonds (donor acceptor distance R about 2.5 A) the diabatic coupling Delta(R) is of order 40 kcal/mol. Hence, detuning the two diabatic states by 3 kcal/mol will have negligible effect on the bond. Thus, I would not expect the pKa changes to have much effect on the enzyme activity.