Because we resolve the pK a at a single pH, these curves are sigmoidal. Observe that with no coupling (left column), the pK a values are constant; however, when coupling is introduced, this is no longer the case. Columns a-d correspond to four different coupling scenarios. dependence, the large difference in reference values means that the pH effects dominate; both inflection points of the free energy curves and the inflection point of the pH-dependent pK a values occur far from one another. As a result, the titration curves computed from the microscopic pK a values suggest that there is no coupling between residues. The singly protonated microstates for each residue occur with a dramatically different probability, that is, residue B 2 is never protonated while C 1 deprotonates.