Consider the system given in Figure . In this example, unlike in the first, the interaction energy is non-zero. The free energies suggest that the first deprotonation event results in a less favorable second deprotonation. This is to be expected for nearby coupled residues, where the electrostatic repulsion associated with the introduction of a second negative charge would result in a less favorable free energy change. Instead of reporting a linear dependence, the ∆G protein (pH) curves each have an inflection point and two asymptotic values, corresponding to the protonation free energy of one residue, while the other residues remain in the same protonation state (Figure as evidenced by the flattening in the ∆G curve and an increase in the apparent pK a of A 1 : the formation of B - 2 makes the formation of A - 1 less favorable. Because the reference pK • a values of A 1 and B 2 are similar, this flattening occurs almost simultaneously with that of B 2 . In this regime, the ∆G protein for both residues changes slower and, in this example, remains relatively close to zero. We can think of this as the pH range over which the groups buffer each other, altering the favourability of protonation. As the pH continues to increase, a linear dependence is restored. Construction of the titration curves computed from the microscopic pK a values reveals the coupling between residues (Figure , bottom). The non-sigmoidal form of the curves follows from the fact that the singly protonated microstates for both residues occur with a similar probability.