Each of the calculations described above was performed using vacuum boundary conditions. As an alternative, we introduce low-dielectric boundary conditions using a polarizable continuum model (PCM). For protein electrostatics calculations based on the Poisson-Boltzmann equation, it is common to use a dielectric constant in the range ε = 2-4 to represent the hydrophobic interior of the protein, although larger values have occassionally been suggested. The precise value of ε may matter for pK a calculations, but reaction barrier heights converge quickly as a function of ε and results for ε = 2 are often indistinguishable from much larger values, although different from gas-phase (ε = 1) values.