Free energy of proton binding in proteins

In this article we use literature data on the titration of denatured ribonuclease to test the accuracy of proton-binding distributions obtained using our recent approach employing moments. We find that using only the local slope of the titration curve at a small number of points (five, for example) we can reproduce the detailed proton-binding distribution at all pH values. Our method gives the complete proton-binding polynomial for a given protein and each coefficient in this polynomial in turn yields the free energy for binding a given number of protons in all ways to the protein. Using these net free energies, we can then compute the average proton-binding free energy per proton as a function of the fraction of protons bound. We find that this function is remarkably similar for different proteins, even for proteins that exhibit quite different titration behavior. For the special case of binding to independent sites, we obtain simple relations for the first and last terms in the free energy per-proton function. For this special case we also can calculate the distribution functions giving the probability that a molecule has a given number of positive or negative charges and the joint distribution that a molecule simultaneously has a given number of positive and negative charge.