Consider the system given in Figure . Note that the interaction energy between the states is zero, as evidenced by the equality of opposite paths; the protonation of A 1 has no effect on the free energy required to protonate B 2 and vice-versa. It follows that ∆G titr (pH) is zero for all pH and ∆G protein (pH) is constant, implying pK a = pK int (Figure ). Computing the pK a , we obtain values of approximately 3 and 2.6 for A 1 and B 2 , respectively, unchanged and decreased from their reference values according to Equation .