Theory of Coupled Electron and Proton Transfer Reactions

Coupled electron and proton transfer reactions play a key role in the mechanisms of biological energy transduction.1–3 Such reactions are also fundamental for artificial energy-related systems such as fuel cells, chemical sensors, and other electrochemical devices. Biological examples include, among others, cytochrome c oxidase,4,5 bc1 complex,6,7 and photosynthetic reaction centers.8,9 In such systems, electrons tunnel between redox cofactors of an enzyme, while the coupled protons are transferred either across a single hydrogen bond or between protonatable groups along special proton-conducting channels. In this paper general theories and models of coupled electron transfer/proton transfer (ET/PT) reactions are discussed. Pure electron transfer reactions in proteins have been thoroughly studied in the past, both experimentally10–17 and theoretically.18–25 The coupled reactions are relatively new and currently are gaining attention in the field.6,8,26–43 Two types of coupled reactions can be distinguished. In concerted electron and proton transfer reactions (denoted PCET in Refs. 29,30,43–45, although this term is also used more generally), both the ET and PT transitions occur in one step. Such concerted processes occur in reactions in which proton transfer is typically limited to one hydrogen bond; however, examples with multiple hydrogen bond rearrangements are also known.46 In sequential reactions, the transitions occur in two steps: ET/PT or PT/ET. Typically each individual step is uphill in energy, while the coupled reaction is downhill. A sequential reaction can proceed along two parallel channels: ET then PT (EP) or PT then ET (PE). In each channel the reaction involves two sequential steps: uphill activation, and then downhill reaction to the final product state. The lifetime of the activated complex is limited by the back reaction. The general formula for the rate of such reactions can be easily developed. In the context of bioenergetics issues, however, it is interesting to analyze all of the possible cases separately because each corresponds to a different mechanism: for example, an electron can go first and pull out a proton; alternatively, a proton can go first and pull out an electron; or an electron can jump back and forth between donor and acceptor and gradually pull out a proton. In enzymes involving coupled proton and electron transport, the exact mechanism of the reaction is of prime interest. First we will consider a simple four-state model of reactions where the proton moves across a single hydrogen bond; both concerted and sequential reactions will be treated. Then we will consider models for long-distance proton transfer, also denoted proton transport or proton translocation. Typically, electron transfer coupled to proton translocation in proteins involves an electron tunneling over a long distance between two redox cofactors, coupled to a proton moving along a proton conducting channel in a classical, diffusion-like random walk fashion. Again, separately the electron and proton transfer reactions are typically uphill, while the coupled reaction is downhill in energy. The schematics of this process is shown in Fig. 1. The kinetics of such reactions can be much different from those involving proton transfer across a single hydrogen bond. In this paper, we will discuss the specifics of such long-distance proton-coupled reactions. Fig. 1 Schematics of the electron transfer reaction coupled to proton translocation. In the reaction, an electron is tunneling over a long distance between two redox cofactors, O and R, and a coupled proton is transferred over a proton conducting channel. The ... Following the review of theoretical concepts, a few applications will be discussed. First the phenoxyl/phenol and benzyl/toluene self-exchange reactions will be examined. The phenoxyl/phenol reaction involves electronically nonadiabatic proton transfer and corresponds to a proton-coupled electron transfer (PCET) mechanism, whereas the benzyl/toluene reaction involves electronically adiabatic proton transfer and corresponds to a hydrogen atom transfer (HAT) mechanism. Comparison of these two systems provides insight into fundamental aspects of electron-proton interactions in these types of systems. Next a series of theoretical calculations on experimentally studied PCET reactions in solution and enzymes will be summarized, along with general predictions concerning the dependence of rates and kinetic isotope effects (the ratio of the rate constants for hydrogen and deuterium transfer) on system properties such as temperature and driving force. The final application that will be discussed is cytochrome c oxidase (CcO). CcO is the terminal component of the electron transport chain of the respiratory system in mitochondria and is one of the key enzymes responsible for energy generation in cells. The intricate correlation between the electron and proton transport via electrostatic interactions, as well as the kinetics of the coupled transitions, appear to be the basis of the pumping mechanism in this enzyme.