We investigate the quantum dynamics of energy and charge transfer in a wheel-shaped artificial photosynthetic antenna-reaction center complex.This complex consists of six light-harvesting chromophores and an electron-acceptor fullerene. To describe q
uantum effects on a femtosecond time scale, we derive the set of exact non-Markovian equations for the Heisenberg operators of this photosynthetic complex in contact with a Gaussian heat bath. With these equations we can analyze the regime of strong system-bath interactions, where reorganization energies are of the order of the intersite exciton couplings. We show that the energy of the initially-excited antenna chromophores is efficiently funneled to the porphyrin-fullerene reaction center, where a charge-separated state is set up in a few picoseconds, with a quantum yield of the order of 95%. In the single-exciton regime, with one antenna chromophore being initially excited, we observe quantum beatings of energy between two resonant antenna chromophores with a decoherence time of $sim$ 100 fs. We also analyze the double-exciton regime, when two porphyrin molecules involved in the reaction center are initially excited. In this regime we obtain pronounced quantum oscillations of the charge on the fullerene molecule with a decoherence time of about 20 fs (at liquid nitrogen temperatures). These results show a way to directly detect quantum effects in artificial photosynthetic systems.
The Q-cycle mechanism plays an important role in the conversion of the redox energy into the energy of the proton electrochemical gradient across the biomembrane. The bifurcated electron transfer reaction, which is built into this mechanism, recycles
one electron, thus, allowing to translocate two protons per one electron moving to the high-potential redox chain. We study a kinetic model of the Q-cycle mechanism in an artificial system which mimics the bf complex of plants and cyanobacteria in the regime of ferredoxin-dependent cyclic electron flow. Using methods of condensed matter physics, we derive a set of master equations and describe a time sequence of electron and proton transfer reactions in the complex. We find energetic conditions when the bifurcation of the electron pathways at the positive side of the membrane occurs naturally, without any additional gates. For reasonable parameter values, we show that this system is able to translocate more than 1.8 protons, on average, per one electron, with a thermodynamic efficiency of the order of 32% or higher.
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 comple
x 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 analyze a theoretical model for energy and electron transfer in an artificial photosynthetic system. The photosystem consists of a molecular triad (i.e., with a donor, a photosensitive unit, and an acceptor) coupled to four accessory light-harvest
ing antennas pigments. The excitation energy transfer from the antennas to the artificial reaction center (the molecular triad) is here described by the F{o}rster mechanism. We consider two different kinds of arrangements of the accessory light-harvesting pigments around the reaction center. The first arrangement allows direct excitation transfer to the reaction center from all the surrounding pigments. The second configuration transmits energy via a cascade mechanism along a chain of light-harvesting chromophores, where only one chromophore is connected to the reaction center. At first sight, it would appear that the star-shaped configuration, with all the antennas directly coupled to the photosensitive center, would be more efficient. However, we show that the artificial photosynthetic system using the cascade energy transfer absorbs photons in a broader wavelength range and converts their energy into electricity with a higher efficiency than the system based on direct couplings between all the antenna chromophores and the reaction center.
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.
Respiration in bacteria involves a sequence of energetically-coupled electron and proton transfers creating an electrochemical gradient of protons (a proton-motive force) across the inner bacterial membrane. With a simple kinetic model we analyze a r
edox loop mechanism of proton-motive force generation mediated by a molecular shuttle diffusing inside the membrane. This model, which includes six electron-binding and two proton-binding sites, reflects the main features of nitrate respiration in E. coli bacteria. We describe the time evolution of the proton translocation process. We find that the electron-proton electrostatic coupling on the shuttle plays a significant role in the process of energy conversion between electron and proton components. We determine the conditions where the redox loop mechanism is able to translocate protons against the transmembrane voltage gradient above 200 mV with a thermodynamic efficiency of about 37%, in the physiologically important range of temperatures from 250 to 350 K.
We study a model of a light-induced proton pump in artificial reaction centers. The model contains a molecular triad with four electron states (i.e., one donor state, two photosensitive group states, and one acceptor state) as well as a molecular shu
ttle having one electron and one proton-binding sites. The shuttle diffuses between the sides of the membrane and translocates protons energetically uphill: from the negative side to the positive side of the membrane, harnessing for this purpose the energy of the electron-charge-separation produced by light. Using methods of quantum transport theory we calculate the range of light intensity and transmembrane potentials that maximize both the light-induced proton current and the energy transduction efficiency. We also study the effect of temperature on proton pumping. The light-induced proton pump in our model gives a quantum yield of proton translocation of about 55 %. Thus, our results explain previous experiments on these artificial photosynthetic reaction centers.
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) e
mbedded 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.
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.
