The form is similar to the partition function of the single-site case; however, here we include a new (un)cooperativity term which follows from the fact that: 1) the cycle is closed (i.e., K 1 + K 3 = K 2 + K 4 ), and 2) there is an "interaction free energy", w, associated with the second (de)protonation event given the first. When this interaction is zero, we have a standard two-site binding equilibrium: the proton can bind to either site, and this is governed only by the proton concentration and binding constants; however, when this interaction is positive or negative, the initial binding to one site will disfavor or favor the binding of a second proton to the other site. This interaction notation, as defined by T. L. Hill,