To model the chemically coupled sites in the histidine side chain, Khandogin and Brooks introduced two λ-coordinates: one that interpolates between the double and single protonated forms and a second coordinate switching between protonation at the N δ and the N atoms. Donnini et al. introduced separate λ-coordinates for N δ and N . In both solutions, the coupling between the coordinates is achieved with a two-dimensional correction potential.