Alexey Onufriev, David A. Case, G. Matthias Ullmann

When individual titratable sites in a molecule interact with each other, their pH titration can be considerably more complex than that of an independent site described by the classical Henderson-Hasselbalch equation. We propose a novel framework that decomposes any complex titration behavior into simple standard components. The approach maps the set of N interacting sites in the molecule onto a set of N independent, noninteracting quasi-sites, each characterized by a pK'(a) value. The titration curve of an individual site in the molecule is a weighted sum of Henderson-Hasselbalch curves corresponding to the quasi-sites. The total protonation curve is the unweighted sum of these Henderson-Hasselbalch curves. We show that pK'(a) values correspond to deprotonation constants available from methods that can be used to assess total proton uptake or release, and establish their connection to protonation curves of individual residues obtained by NMR or infrared spectroscopy. The new framework is tested on a small molecule diethylenetriaminepentaacetate (DTPA) exhibiting nonmonotonic titration curves, where it gives an excellent fit to experimental data. We demonstrate that the titration curve of a site in a group of interacting sites can be accurately reconstructed, if titration curves of the other sites are known. The application of the new framework to the protein rubredoxin demonstrates its usefulness in calculating and interpreting complicated titration curves.