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. Vertical spans in the lower row indicate experimental pK a values and uncertainties (note that D83 has a pK a < 2.2). Error bands were bootstrapped. a-c correspond to the SNase + ∆PHS system, while d corresponds to the DJ-1 system.