Ulrich Kleinekathöfer

Excitons in a photosynthetic light-harvesting system: A combined molecular dynamics, quantum chemistry, and polaron model study

The dynamics of pigment-pigment and pigment-protein interactions in light-harvesting complexes is studied with an approach that combines molecular dynamics simulations with quantum chemistry calculations and a polaron model analysis. The molecular dynamics simulation of light-harvesting (LH) complexes was performed on an 87 055 atom system comprised of a LH-II complex of Rhodospirillum molischianum embedded in a lipid bilayer and surrounded with appropriate water layers. For each of the 16 B850 bacteriochlorophylls (BChls), we performed 400 ab initio quantum chemistry calculations on geometries that emerged from the molecular dynamical simulations, determining the fluctuations of pigment excitation energies as a function of time. From the results of these calculations we construct a time-dependent Hamiltonian of the B850 exciton system from which we determine within linear response theory the absorption spectrum. Finally, a polaron model is introduced to describe both the excitonic and coupled phonon degrees of freedom by quantum mechanics. The exciton-phonon coupling that enters into the polaron model, and the corresponding phonon spectral function, are derived from the molecular dynamics and quantum chemistry simulations. The model predicts that excitons in the B850 BChl ring are delocalized over five pigments at room temperature. Also, the polaron model permits the calculation of the absorption and circular dichroism spectra of the B850 excitons from the sole knowledge of the autocorrelation function of the excitation energies of individual BChls, which is readily available from the combined molecular dynamics and quantum chemistry simulations. The obtained results are found to be in good agreement with the experimentally measured absorption and circular dichroism spectra.

From atomistic modeling to excitation transfer and two-dimensional spectra of the FMO light-harvesting complex

The experimental observation of long-lived quantum coherences in the Fenna-Matthews-Olson (FMO) light-harvesting complex at low temperatures has challenged general intuition in the field of complex molecular systems and provoked considerable theoretical effort in search of explanations. Here we report on room-temperature calculations of the excited-state dynamics in FMO using a combination of molecular dynamics simulations and electronic structure calculations. Thus we obtain trajectories for the Hamiltonian of this system which contains time-dependent vertical excitation energies of the individual bacteriochlorophyll molecules and their mutual electronic couplings. The distribution of energies and couplings is analyzed together with possible spatial correlations. It is found that in contrast to frequent assumptions the site energy distribution is non-Gaussian. In a subsequent step, averaged wave packet dynamics is used to determine the exciton dynamics in the system. Finally, with the time-dependent Hamiltonian, linear and two-dimensional spectra are determined. The thus-obtained linear absorption line shape agrees well with experimental observation and is largely determined by the non-Gaussian site energy distribution. The two-dimensional spectra are in line with what one would expect by extrapolation of the experimental observations at lower temperatures and indicate almost total loss of long-lived coherences.

Time-dependent atomistic view on the electronic relaxation in light-harvesting system II.

Aiming at a better understanding of the molecular details in light absorption during photosynthesis, spatial and temporal correlation functions as well as spectral densities have been determined. At the focus of the present study are the light-harvesting II complexes of the purple bacterium Rhodospirillum molischianum. The calculations are based on a time-dependent combination of molecular dynamics simulations and quantum chemistry methods. Using a 12 ps long trajectory, different quantum chemical methods have been compared to each other. Furthermore, several approaches to determine the couplings between the individual chromophores have been tested. Correlations between energy gap fluctuations of different individual pigments are analyzed but found to be negligible. From the energy gap fluctuations, spectral densities are extracted which serve as input for calculations of optical properties and exciton dynamics. To this end, the spectral densities are tested by determining the linear absorption of the complete two-ring system. One important difference from earlier studies is given by the severely extended length of the trajectory along which the quantum chemical calculations have been performed. Due to this extension, more accurate and reliable data have been obtained in the low frequency regime which is important in the dynamics of electronic relaxation.

Quest for spatially correlated fluctuations in the FMO light-harvesting complex.

The light absorption in light-harvesting complexes is performed by molecules such as chlorophyll, carotenoid, or bilin. Recent experimental findings in some of these complexes suggest the existence of long-lived coherences between the individual pigments at low temperatures. In this context, the question arises if the bath-induced fluctuations at different chromophores are spatially correlated or not. Here we investigate this question for the Fenna-Matthews-Olson (FMO) complex of Chlorobaculum tepidum by a combination of atomistic theories, i.e., classical molecular dynamics simulations and semiempirical quantum chemistry calculations. In these investigations at ambient temperatures, only weak correlations between the movements of the chromophores can be detected at the atomic level and none at the more coarse-grained level of site energies. The often-employed uncorrelated bath approximations indeed seem to be valid. Nevertheless, correlations between fluctuations in the electronic couplings between the pigments can be found. Depending on the level of theory employed, also correlations between the fluctuations of site energies and the fluctuations in electronic couplings are discernible.

Functional Rotation of the Transporter AcrB: Insights into Drug Extrusion from Simulations

The tripartite complex AcrAB-TolC is the major efflux system in Escherichia coli. It extrudes a wide spectrum of noxious compounds out of the bacterium, including many antibiotics. Its active part, the homotrimeric transporter AcrB, is responsible for the selective binding of substrates and energy transduction. Based on available crystal structures and biochemical data, the transport of substrates by AcrB has been proposed to take place via a functional rotation, in which each monomer assumes a particular conformation. However, there is no molecular-level description of the conformational changes associated with the rotation and their connection to drug extrusion. To obtain insights thereon, we have performed extensive targeted molecular dynamics simulations mimicking the functional rotation of AcrB containing doxorubicin, one of the two substrates that were co-crystallized so far. The simulations, including almost half a million atoms, have been used to test several hypotheses concerning the structure-dynamics-function relationship of this transporter. Our results indicate that, upon induction of conformational changes, the substrate detaches from the binding pocket and approaches the gate to the central funnel. Furthermore, we provide strong evidence for the proposed peristaltic transport involving a zipper-like closure of the binding pocket, responsible for the displacement of the drug. A concerted opening of the channel between the binding pocket and the gate further favors the displacement of the drug. This microscopically well-funded information allows one to identify the role of specific amino acids during the transitions and to shed light on the functioning of AcrB.

Calculation of absorption spectra for light-harvesting systems using non-Markovian approaches as well as modified Redfield theory

For an ensemble of B850 rings of the light-harvesting system LH2 of purple bacteria the linear absorption spectrum is calculated. Using different Markovian and non-Markovian, time-dependent and time-independent methods based on second-order perturbation theory in the coupling between the excitonic system and its surrounding environment as well as the modified Redfield theory, the influence of the shape of the spectral density on the linear absorption spectrum is demonstrated for single samples and in the ensemble average. For long bath correlation times non-Markovian effects clearly show up in the static absorption line shapes. Among the different spectral densities studied is one of the purple bacterium Rhodospirillum molischianum obtained by a molecular-dynamics simulation earlier. The effect of static disorder on its line shapes in the ensemble average is analyzed and the results of the present calculations are compared to experimental data.

The influence of ultrafast laser pulses on electron transfer in molecular wires studied by a non-Markovian density-matrix approach

New features of molecular wires can be observed when they are irradiated by laser fields. These effects can be achieved by periodically oscillating fields but also by short laser pulses. The theoretical foundation used for these investigations is a density-matrix formalism where the full system is partitioned into a relevant part and a thermal fermionic bath. The derivation of a quantum master equation, either based on a time-convolutionless or time-convolution projection-operator approach, incorporates the interaction with time-dependent laser fields nonperturbatively and is valid at low temperatures for weak system-bath coupling. From the population dynamics the electrical current through the molecular wire is determined. This theory including further extensions is used for the determination of electron transport through molecular wires. As examples, we show computations of coherent destruction of tunneling in asymmetric periodically driven quantum systems, alternating currents and the suppression of the directed current by using a short laser pulse.

Understanding Ion Conductance on a Molecular Level: An All-Atom Modeling of the Bacterial Porin OmpF

All-atom molecular dynamics simulations of the ion current through OmpF, the major porin in the outer membrane of Escherichia coli, were performed. Starting from the crystal structure, the all-atom modeling allows us to calculate a parameter-free ion conductance in semiquantitative agreement with experiment. Discrepancies between modeling and experiment occur, e.g., at salt concentrations above 1 M KCl or at high temperatures. At lower salt concentrations, the ions have separate pathways along the channel surface. The constriction zone in the channel contains, on one side, a series of positively charges (R42, R82, R132), and on the opposite side, two negatively charged residues (D113, E117). Mutations generated in the constriction zone by removing cationic residues enhance the otherwise small cation selectivity, whereas removing the anionic residues reverses the selectivity. Reduction of the negatively charged residues decreases the conductance by half, whereas cationic residues enhance the conductance. Experiments on mutants confirm the results of the molecular-level simulations.

Non-Markovian theories based on a decomposition of the spectral density

For the description of dynamical effects in quantum mechanical systems on ultrashort time scales, memory effects play an important role. Meier and Tannor [J. Chem. Phys. 111, 3365 (1999)] developed an approach which is based on a time-nonlocal scheme employing a numerical decomposition of the spectral density. Here we propose two different approaches which are based on a partial time-ordering prescription, i.e., a time-local formalism and also on a numerical decomposition of the spectral density. In special cases such as the Debye spectral density the present scheme can be employed even without the numerical decomposition of the spectral density. One of the proposed schemes is valid for time-independent Hamiltonians and can be given in a compact quantum master equation. In the case of time-dependent Hamiltonians one has to introduce auxiliary operators which have to be propagated in time along with the density matrix. For the example of a damped harmonic oscillator these non-Markovian theories are compared among each other, to the Markovian limit neglecting memory effects and time dependencies, and to exact path integral calculations. Good agreement between the exact calculations and the non-Markovian results is obtained. Some of the non-Markovian theories mentioned above treat the time dependence in the system Hamiltonians nonperturbatively. Therefore these methods can be used for the simulation of experiments with arbitrary large laser fields.

Potentials for some rare gas and alkali-helium systems calculated from the surface integral method

Abstract The van der Waals potential curves of H2(3Σ), He2, Ne2, HeNe, HHe, LiHe, NaHe, KHe, RbHe and CsHe have been calculated using a recently derived simple analytical formula. The repulsive potential is based on exchange energies calculated from the durface integral method applied to multielectron systems. With the exception of the long-range dispersion coefficients, all the input parameters are atomic properties of the free constituent atoms. The calculated curves agree well with both experimental and ab initio theoretical data.