Simulation of Electron-Proton Coupling with a Monte Carlo Method: Application to Cytochrome c3 Using Continuum Electrostatics

Abstract

A new method is presented for simulating the simultaneous binding equilibrium of electrons and protons on protein molecules, which makes it possible to study the full equilibrium thermodynamics of redox and protonation processes, including electron-proton coupling. The simulations using this method reflect directly the pH and electrostatic potential of the environment, thus providing a much closer and realistic connection with experimental parameters than do usual methods. By ignoring the full binding equilibrium, calculations usually overlook the twofold effect that binding fluctuations have on the behavior of redox proteins: first, they affect the energy of the system by creating partially occupied sites; second, they affect its entropy by introducing an additional empty/occupied site disorder (here named occupational entropy). The proposed method is applied to cytochrome c3 of Desulfovibrio vulgaris Hildenborough to study its redox properties and electron-proton coupling (redox-Bohr effect), using a continuum electrostatic method based on the linear Poisson-Boltzmann equation. Unlike previous studies using other methods, the full reduction order of the four hemes at physiological pH is successfully predicted. The sites more strongly involved in the redox-Bohr effect are identified by analysis of their titration curves/surfaces and the shifts of their midpoint redox potentials and pKa values. Site-site couplings are analyzed using statistical correlations, a method much more realistic than the usual analysis based on direct interactions. The site found to be more strongly involved in the redox-Bohr effect is propionate D of heme I, in agreement with previous studies; other likely candidates are His67, the N-terminus, and propionate D of heme IV. Even though the present study is limited to equilibrium conditions, the possible role of binding fluctuations in the concerted transfer of protons and electrons under nonequilibrium conditions is also discussed. The occupational entropy contributions to midpoint redox potentials and pKa values are computed and shown to be significant.

Tuning Heme Redox Potentials in the Cytochrome c Subunit of Photosynthetic Reaction Centers

“…Additionally, fluctuations in protonation and reduction/oxidation are accounted for by using an MC titration. The influence of such fluctuations was thoroughly investigated and termed "occupational entropy" by Baptista et al (32) in their study on cyt c 3 from Desulfovibrio vulgaris. In the equivalent treatment used here, a faithful representation of the system is achieved.…”

Redox-Bohr and Other Cooperativity Effects in the Nine-heme Cytochrome c from Desulfovibrio desulfuricans ATCC 27774

“…However, this is an approximation, because the pH and electrostatic potential have specific values in solution, whereas the protein redox and protonation states are fluctuating. Besides these fluctuations, the binding of electrons and protons mutually influence each other, and the correct way to simulate this is to consider a single, joint-binding equilibrium in which electrons and protons are treated simultaneously (42,45).…”

“…Studies were performed in several cases to estimate and understand redox potentials in proteins, using microscopic (34 -37) or continuum electrostatics (CE) (38 -45) methods. Because of their computational efficiency, the CE methods were used for the more extensive simulations of the actual binding equilibrium of electrons and protons (10,42,44,45). The most correct way to model coupling between reduction and protonation in proteins is to use methods introduced by us (42) that model the joint binding equilibrium of electrons and protons in proteins, using Monte Carlo techniques.…”

“…Because of their computational efficiency, the CE methods were used for the more extensive simulations of the actual binding equilibrium of electrons and protons (10,42,44,45). The most correct way to model coupling between reduction and protonation in proteins is to use methods introduced by us (42) that model the joint binding equilibrium of electrons and protons in proteins, using Monte Carlo techniques. Other similar approaches were later reported in the literature (43,44), aiming to model the same type of effects.…”

“…Other similar approaches were later reported in the literature (43,44), aiming to model the same type of effects. Multiheme cytochromes c 3 were extensively characterized using these theoretical methodologies aiming to understand coupling phenomena (10,12,42,43,45), with significant success. However, one limitation of the majority of these studies is the fact that only one conformation (x-ray structure) is used to characterize all possible states of the system, which is a significant simplification that leaves out the possibility that specific reorganization effects of reduction and protonation may occur.…”