Protonation free energy levels in complex molecular systems

All proteins, nucleic acids, and other biomolecules contain residues capable of exchanging protons with their environment. These proton transfer phenomena lead to pH sensitivity of many molecular processes underlying biological phenomena. In the course of biological evolution, Nature has invented some mechanisms to use pH gradients to regulate biomolecular processes inside cells or in interstitial fluids. Therefore, an ability to model protonation equilibria in molecular systems accurately would be of enormous value for our understanding of biological processes and for possible rational influence on them, like in developing pH dependent drugs to treat particular diseases. This work presents a derivation, by thermodynamic and statistical mechanical methods, of an expression for the free energy of a complex molecular system at arbitrary ionization state of its titratable residues. This constitutes one of the elements of modeling protonation equilibria. Starting from a consideration of a simple acid-base equilibrium of a model compound with a single tritratable group, we arrive at an expression which is of general validity for complex systems. The only approximation used in this derivation is the postulating that the interaction energy between any pair of titratable sites does not depend on the protonation states of all the remaining ionizable groups.