The coupling of protonation and reduction in proteins with multiple redox centers: Theory, computational method, and application to cytochrome c(3)

The coupling of protonation and reduction is crucial in many biological cha rge transfer reactions and is known as redox Bohr effect. It is caused by e lectrostatic interactions between protonatable and redox-active groups. In this study, I describe a method to calculate protonation and oxidation prob abilities depending on the solution pH and redox potential. The energetic c alculations are based on the linearized Poisson-Boltzmann equation. The act ual calculation of the oxidation and protonation probabilities is done with a hybrid statistical mechanics/Tanford-Roxby approach. The method is appli ed to cytochrome c(3), a small protein that binds four hemes. The protein i s known for coupling a protonation to the reduction reactions. The propiona te D of heme I shows the strongest redox potential dependence of its proton ation probability and is thus most likely responsible for the redox Bohr ef fect. The computational results agree well with experimental data. Because of the interactions between the many titratable groups in proteins, titrati on curves often deviate significantly from the sigmoidal shape of Henderson -Hasselbalch or Nernst titration curves. This deviation requires the defini tion of pK(a) and E-o values that depend on the pH and solution redox poten tial. The definitions of pK(a) and E-o values provided in this study are ap propriate for discussing the energetics of protonation and redox reactions throughout the whole investigated pH and solution redox potential range.