The coupling of protonation and reduction in proteins with multiple redox centers:: Theory, computational method, and application to cytochrome c3

The coupling of protonation and reduction is crucial in many biological charge transfer reactions and is known as redox Bohr effect. It is caused by electrostatic interactions between protonatable and redox-active groups. In this study, I describe a method to calculate protonation and oxidation probabilities depending on the solution pH and redox potential. The energetic calculations are based on the linearized Poisson-Boltzmann equation. The actual calculation of the oxidation and protonation probabilities is done with a hybrid statistical mechanics/Tanford-Roxby approach. The method is applied to cytochrome c(3), a small protein that binds four hemes. The protein is known for coupling a protonation to the reduction reactions. The propionate D of heme I shows the strongest redox potential dependence of its protonation probability and is thus most likely responsible for the redox Bohr effect. The computational results agree well with experimental data. Because of the interactions between the many titratable groups in proteins, titration curves often deviate significantly from the sigmoidal shape of Henderson-Hasselbalch or Nernst titration curves. This deviation requires the definition of pK(a) and E-o values that depend on the pH and solution redox potential. The definitions of pK(a) and E-o values provided in this study are appropriate for discussing the energetics of protonation and redox reactions throughout the whole investigated pH and solution redox potential range.