where k 1 and x 0 define the steepness and kink position of the step function. In this form, illustrated in Figure , the pH dependent potential also aids in preventing the sampling of non-physical states, i. e., 0.1 < λ < 0.9. To compensate for the shortcomings of the force field and obtain a zero free energy difference between the two protonation states (A+B), we add the correction potential, V MM i (λ), shown in panel B. A biasing potential, V bias (λ), is introduced to avoid sampling of non-physical states (panel C). To model the proton chemical potential (pH), we add a pH dependent term, V pH (λ i ) (panel D). For a titratable residue at pH = pK a , the total λ-dependent potential, including the interpolated force field functions and the three additional terms, is illustrated in panel (A+B+C+D).