In addition, potentials are introduced to bias sampling towards the physical states at λ = 0 and λ = 1. Protons are not transferred directly between the titratable residues and the solvent molecules, but rather exchanged with an external proton bath. Because the chemical potential of this bath is determined by the proton concentration (pH) of the aqueous solution, constant pH MD (CpHMD) simulations based on λ-dynamics are performed in a grand canonical ensemble for the proton degrees of freedom.