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Register a new userForster mechanism of electron-driven proton pump
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We examine a simple model of proton pumping through the inner membrane of mitochondria in the living cell. We demonstrate that the pumping process can be described using approaches of condensed matter physics. In the framework of this model, we show that the resonant Forster-type energy exchange due to electron-proton Coulomb interaction can provide an unidirectional flow of protons against an electrochemical proton gradient, thereby accomplishing proton pumping. The dependence of this effect on temperature as well as electron and proton voltage build-ups are obtained taking into account electrostatic forces and noise in the environment. We find that the proton pump works with maximum efficiency in the range of temperatures and transmembrane electrochemical potentials which correspond to the parameters of living cells.
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We present two models for electron-driven uphill proton transport across lipid membranes, with the electron energy converted to the proton gradient via the electrostatic interaction. In the first model, associated with the cytochrome c oxidase complex in the inner mitochondria membranes, the electrostatic coupling to the site occupied by an electron lowers the energy level of the proton-binding site, making the proton transfer possible. In the second model, roughly describing the redox loop in a nitrate respiration of E. coli bacteria, an electron displaces a proton from the negative side of the membrane to a shuttle, which subsequently diffuses across the membrane and unloads the proton to its positive side. We show that both models can be described by the same approach, which can be significantly simplified if the system is separated into several clusters, with strong Coulomb interaction inside each cluster and weak transfer couplings between them. We derive and solve the equations of motion for the electron and proton creation/annihilation operators, taking into account the appropriate Coulomb terms, tunnel couplings, and the interaction with the environment. For the second model, these equations of motion are solved jointly with a Langevin-type equation for the shuttle position. We obtain expressions for the electron and proton currents and determine their dependence on the electron and proton voltage build-ups, on-site charging energies, reorganization energies, temperature, and other system parameters. We show that the quantum yield in our models can be up to 100% and the power-conversion efficiency can reach 35%.
We propose a simple model of cytochrome c oxidase, including four redox centers and four protonable sites, to study the time evolution of electrostatically coupled electron and proton transfers initiated by the injection of a single electron into the enzyme. We derive a system of master equations for electron and proton state probabilities and show that an efficient pumping of protons across the membrane can be obtained for a reasonable set of parameters. All four experimentally observed kinetic phases appear naturally from our model. We also calculate the dependence of the pumping efficiency on the transmembrane voltage at different temperatures and discuss a possible mechanism of the redox-driven proton translocation.
We analyze the dynamics of rotary biomotors within a simple nano-electromechanical model, consisting of a stator part and a ring-shaped rotor having twelve proton-binding sites. This model is closely related to the membrane-embedded F$_0$ motor of adenosine triphosphate (ATP) synthase, which converts the energy of the transmembrane electrochemical gradient of protons into mechanical motion of the rotor. It is shown that the Coulomb coupling between the negative charge of the empty rotor site and the positive stator charge, located near the periplasmic proton-conducting channel (proton source), plays a dominant role in the torque-generating process. When approaching the source outlet, the rotor site has a proton energy level higher than the energy level of the site, located near the cytoplasmic channel (proton drain). In the first stage of this torque-generating process, the energy of the electrochemical potential is converted into potential energy of the proton-binding sites on the rotor. Afterwards, the tangential component of the Coulomb force produces a mechanical torque. We demonstrate that, at low temperatures, the loaded motor works in the shuttling regime where the energy of the electrochemical potential is consumed without producing any unidirectional rotation. The motor switches to the torque-generating regime at high temperatures, when the Brownian ratchet mechanism turns on. In the presence of a significant external torque, created by ATP hydrolysis, the system operates as a proton pump, which translocates protons against the transmembrane potential gradient. Here we focus on the F$_0$ motor, even though our analysis is applicable to the bacterial flagellar motor.
Shuttle-assisted charge transfer is pivotal for the efficient energy transduction from the food-stuff electrons to protons in the respiratory chain of animal cells and bacteria. The respiratory chain consists of four metalloprotein Complexes (I-IV) embedded in the inner membrane of a mitochondrion. Three of these complexes pump protons across the membrane, fuelled by the energy of food-stuff electrons. Despite extensive biochemical and biophysical studies, the physical mechanism of this proton pumping is still not well understood. Here we present a nanoelectromechanical model of the electron-driven proton pump related to the second loop of the respiratory chain, where a lipid-soluble ubiquinone molecule shuttles between the Complex I and Complex III, carrying two electrons and two protons. We show that the energy of electrons can be converted to the transmembrane proton potential gradient via the electrostatic interaction between electrons and protons on the shuttle. We find that the system can operate either as a proton pump, or, in the reverse regime, as an electron pump. For membranes with various viscosities, we demonstrate that the uphill proton current peaks near the body temperature $T approx 37 ^{circ}$C.
Single-electron pumps based on isolated impurity atoms have recently been experimentally demonstrated. In these devices the Coulomb potential of an atom creates a localised electron state with a large charging energy and considerable orbital level spacings, enabling robust charge capturing processes. In these single-atom pumps, the confinement potential is hardly affected by the periodic driving of the system. This is in contrast to the often used gate-defined quantum dot pumps, for which a strongly time-dependent potential leads to significantly different charge pumping processes. Here we describe the behaviour and the performance of an atomic, single parameter, electron pump. This is done by considering the loading, isolating and unloading of one electron at the time, on a phosphorous atom embedded in a silicon double gate transistor. The most important feature of the atom pump is its very isolated ground state, which can be populated through the fast loading of much higher lying excited states and a subsequent fast relaxation proces. This leads to a substantial increase in pumping accuracy, and is opposed to the adverse role of excited states as observed for quantum dot pumps due to non-adiabatic excitations. The pumping performances are investigated as a function of dopant position, revealing a pumping behaviour robust against the expected variability in atomic position.
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