A density-matrix model of photosynthetic electron transfer with microscopically estimated vibrational relaxation times

Inverted region in the reaction of the quinone reduction in the A1-site of photosystem I from cyanobacteria

Photosystem I from the menB strain of Synechocystis sp. PCC 6803 containing foreign quinones in the A1 sites was used for studying the primary steps of electron transfer by pump-probe femtosecond laser spectroscopy. The free energy gap (- ΔG) of electron transfer between the reduced primary acceptor A0 and the quinones bound in the A1 site varied from 0.12 eV for the low-potential 1,2-diamino-anthraquinone to 0.88 eV for the high-potential 2,3-dichloro-1,4-naphthoquinone, compared to 0.5 eV for the native phylloquinone. It was shown that the kinetics of charge separation between the special pair chlorophyll P700 and the primary acceptor A0 was not affected by quinone substitutions, whereas the rate of A0 → A1 electron transfer was sensitive to the redox-potential of quinones: the decrease of - ΔG by 400 meV compared to the native phylloquinone resulted in a ~ fivefold slowing of the reaction The presence of the asymmetric inverted region in the ΔG dependence of the reaction rate indicates that the electron transfer in photosystem I is controlled by nuclear tunneling and should be treated in terms of quantum electron-phonon interactions. A three-mode implementation of the multiphonon model, which includes modes around 240 cm-1 (large-scale protein vibrations), 930 cm-1 (out-of-plane bending of macrocycles and protein backbone vibrations), and 1600 cm-1 (double bonds vibrations) was applied to rationalize the observed dependence. The modes with a frequency of at least 1600 cm-1 make the predominant contribution to the reorganization energy, while the contribution of the "classical" low-frequency modes is only 4%.

Calculated solvent reorganization entropies, free energies, and fluctuations of the energy gaps for intramolecular electron transfer and excitation of the solvatochromic dye B30

Intramolecular electron transfer between two biphenyl groups linked by an androstane spacer and excitation of the pyridinium-N-phenolate betaine dye B30 to the first excited singlet state are studied by quantum/classical molecular-dynamics simulations at temperatures between 150 and 300 K in solvents with a range of polarities. Temperature dependences of the solvent reorganization energies, free energies, entropies, and the inhomogeneous broadening of B30's absorption band are examined. The variances of fluctuations of the energy gap between the reactant and product states do not have the direct proportionality to temperature that often is assumed to hold. An explanation for the observations is suggested.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Reorganization Energies, Entropies, and Free Energy Surfaces for Electron Transfer

Reorganization energies for an intramolecular self-exchange electron-transfer reaction are calculated by quantum-classical molecular dynamics simulations in four solvents with varying polarity and at temperatures ranging from 250 to 350 K. The reorganization free energies for polar solvents decrease systematically with increasing temperature, indicating that they include substantial contributions from entropy changes. The variances of the energy gap between the reactant and product states have a major component that is relatively insensitive to temperature. Explanations are suggested for these observations, which appear to necessitate rethinking the free energy functions of a distributed coordinate that frequently are used in discussions of reaction dynamics.

Control of electron transfer by protein dynamics in photosynthetic reaction centers

Trehalose and glycerol are low molecular mass sugars/polyols that have found widespread use in the protection of native protein states, in both short- and long-term storage of biological materials, and as a means of understanding protein dynamics. These myriad uses are often attributed to their ability to form an amorphous glassy matrix. In glycerol, the glass is formed only at cryogenic temperatures, while in trehalose, the glass is formed at room temperature, but only upon dehydration of the sample. While much work has been carried out to elucidate a mechanistic view of how each of these matrices interact with proteins to provide stability, rarely have the effects of these two independent systems been directly compared to each other. This review aims to compile decades of research on how different glassy matrices affect two types of photosynthetic proteins: (i) the Type II bacterial reaction center from Rhodobacter sphaeroides and (ii) the Type I Photosystem I reaction center from cyanobacteria. By comparing aggregate data on electron transfer, protein structure, and protein dynamics, it appears that the effects of these two distinct matrices are remarkably similar. Both seem to cause a "tightening" of the solvation shell when in a glassy state, resulting in severely restricted conformational mobility of the protein and associated water molecules. Thus, trehalose appears to be able to mimic, at room temperature, nearly all of the effects on protein dynamics observed in low temperature glycerol glasses.

Dynamics of the Excited State in Photosynthetic Bacterial Reaction Centers

In the initial charge-separation reaction of photosynthetic bacterial reaction centers, a dimer of strongly interacting bacteriochlorophylls (P) transfers an electron to a third bacteriochlorophyll (B_L). It has been suggested that light first generates an exciton state of the dimer and that an electron then moves from one bacteriochlorophyll to the other within P to form a charge-transfer state (P_L⁺P_M^-), which passes an electron to B_L. This scheme, however, is at odds with the most economical analysis of the spectroscopic properties of the reaction center and particularly with the unusual temperature dependence of the long-wavelength absorption band. The present paper explores this conflict with the aid of a simple model in which exciton and charge-transfer states are coupled to three vibrational modes. It then uses a similar model to show that the main experimental evidence suggesting the formation of P_L⁺P_M^- as an intermediate could reflect pure dephasing of vibrational modes that modulate stimulated emission.

Effects of Free Energy and Solvent on Rates of Intramolecular Electron Transfer in Organic Radical Anions

Rates of intramolecular electron transfer from a 1,1'-biphenylyl radical anion to six different acceptors on an androstane scaffold are examined with the aid of a theory that was developed recently to include effects of vibrational relaxations and dephasing. The electronic-interaction matrix element and other parameters needed for the theory are obtained by quantum-mechanical/molecular-mechanical simulations of the reactions in five solvents ranging from iso-octane to methyltetrahydrofuran. Intramolecular vibrational modes that are coupled to electron transfer are resolved in simulations in iso-octane and cyclohexane. The energies and coupling factors for these modes allow extension of the theory to incorporate transitions to and from excited vibrational levels. The calculated rates of electron transfer agree well with experimental measurements from the literature, except for reactions in which excited electronic states of the products become important.

Theoretical study of vibrational energy transfer of free OH groups at the water-air interface

Recent experimental studies have shown that the vibrational dynamics of free OH groups at the water-air interface is significantly different from that in bulk water. In this work, by performing molecular dynamics simulations and mixed quantum/classical calculations, we investigate different vibrational energy transfer pathways of free OH groups at the water-air interface. The calculated intramolecular vibrational energy transfer rate constant and the free OH bond reorientation time scale agree well with the experiment. It is also found that, due to the small intermolecular vibrational couplings, the intermolecular vibrational energy transfer pathway that is very important in bulk water plays a much less significant role in the vibrational energy relaxation of the free OH groups at the water-air interface.

Elastic Vibrations in the Photosynthetic Bacterial Reaction Center Coupled to the Primary Charge Separation: Implications from Molecular Dynamics Simulations and Stochastic Langevin Approach

Primary electron transfer reactions in the bacterial reaction center are difficult for theoretical explication: the reaction kinetics, almost unalterable over a wide range of temperature and free energy changes, revealed oscillatory features observed initially by Shuvalov and coauthors (1997, 2002). Here the reaction mechanism was studied by molecular dynamics and analyzed within a phenomenological Langevin approach. The spectral function of polarization around the bacteriochlorophyll special pair PLPM and the dielectric response upon the formation of PL(+)PM(-) dipole within the special pair were calculated. The system response was approximated by Langevin oscillators; the respective frequencies, friction, and energy coupling coefficients were determined. The protein dynamics around PL and PM were distinctly asymmetric. The polarization around PL included slow modes with the frequency 30-80 cm(-1) and the total amplitude of 130 mV. Two main low-frequency modes of protein response around PM had frequencies of 95 and 155 cm(-1) and the total amplitude of 30 mV. In addition, a slowly damping mode with the frequency of 118 cm(-1) and the damping time >1.1 ps was coupled to the formation of PL(+)PM(-) dipole. It was attributed to elastic vibrations of α-helices in the vicinity of PLPM. The proposed trapping of P excitation energy in the form of the elastic vibrations can rationalize the observed properties of the primary electron transfer reactions, namely, the unusual temperature and ΔG dependences, the oscillating phenomena in kinetics, and the asymmetry of the charge separation reactions.

Spectral exhibition of electron-vibrational relaxation in P* state of Rhodobacter sphaeroides reaction centers

Electron-vibrational relaxation in the excited state of the primary electron donor, bacteriochlorophyll dimer P, in the reaction centers (RCs) of purple photosynthetic bacteria Rhodobacter sphaeroides is modeled. A multimode model of three states (i.e., the ground state Pg, initially excited P1*, and relaxed excited P2*) is used to calculate the incoherent dynamics of the difference (ΔA) spectra on a femtosecond timescale for the YM210 W mutant RCs. The relaxation processes are described by the step-ladder model. The model shows that the electron-vibrational relaxation in the excited state of P is visualized by the transient red shift of the stimulated emission from P*. The dynamics of this shift is observed as a change in the ΔA spectrum shape in its red-most part, within a few hundreds of femtoseconds after excitation. As a result, an initial rise in the red-side ΔA kinetics is delayed with respect to the blue-side kinetics. The time constant of the P1* → P2* electronic relaxation (54 fs) and the Pg, P1*, and P2* vibrational relaxations (120 fs), used in the model, provided the best fit of the experimental time-resolved ΔA spectra and kinetics at 90 and 293 K. The possible nature of the P1* → P2* electronic relaxation is discussed.

Constructing polyatomic potential energy surfaces by interpolating diabatic Hamiltonian matrices with demonstration on green fluorescent protein chromophore

Simulating molecular dynamics directly on quantum chemically obtained potential energy surfaces is generally time consuming. The cost becomes overwhelming especially when excited state dynamics is aimed with multiple electronic states. The interpolated potential has been suggested as a remedy for the cost issue in various simulation settings ranging from fast gas phase reactions of small molecules to relatively slow condensed phase dynamics with complex surrounding. Here, we present a scheme for interpolating multiple electronic surfaces of a relatively large molecule, with an intention of applying it to studying nonadiabatic behaviors. The scheme starts with adiabatic potential information and its diabatic transformation, both of which can be readily obtained, in principle, with quantum chemical calculations. The adiabatic energies and their derivatives on each interpolation center are combined with the derivative coupling vectors to generate the corresponding diabatic Hamiltonian and its derivatives, and they are subsequently adopted in producing a globally defined diabatic Hamiltonian function. As a demonstration, we employ the scheme to build an interpolated Hamiltonian of a relatively large chromophore, para-hydroxybenzylidene imidazolinone, in reference to its all-atom analytical surface model. We show that the interpolation is indeed reliable enough to reproduce important features of the reference surface model, such as its adiabatic energies and derivative couplings. In addition, nonadiabatic surface hopping simulations with interpolation yield population transfer dynamics that is well in accord with the result generated with the reference analytic surface. With these, we conclude by suggesting that the interpolation of diabatic Hamiltonians will be applicable for studying nonadiabatic behaviors of sizeable molecules.

Quantum Coherence in Photosynthesis for Efficient Solar Energy Conversion

The crucial step in the conversion of solar to chemical energy in Photosynthesis takes place in the reaction center where the absorbed excitation energy is converted into a stable charge separated state by ultrafast electron transfer events. However, the fundamental mechanism responsible for the near unity quantum efficiency of this process is unknown. Here we elucidate the role of coherence in determining the efficiency of charge separation in the plant photosystem II reaction centre (PSII RC) by comprehensively combining experiment (two-dimensional electronic spectroscopy) and theory (Redfield theory). We reveal the presence of electronic coherence between excitons as well as between exciton and charge transfer states which we argue to be maintained by vibrational modes. Furthermore, we present evidence for the strong correlation between the degree of electronic coherence and efficient and ultrafast charge separation. We propose that this coherent mechanism will inspire the development of new energy technologies.

Modeling of reversible charge separation in reaction centers of photosynthesis: an incoherent approach

Primary charge separation in reaction centers (RCs) of bacterial photosynthesis is modeled in this work. An incoherent population dynamics of RCs states is formulated by kinetic equations. It is assumed that charge separation is accompanied by regular motion of the system along additional coordinates. This motion modulates an energetics of the reactions, and this modulation causes femtosecond oscillations in the population of the states. The best qualitative and quantitative accordance with experimental data on native, modified and mutant RCs of Rba. sphaeroides is achieved in the five states model that includes two excited states P(*)905BAHA and P(*)940BAHA and three charge separated states I, P(+)BA(-)HA and P(+)BAHA(-) (P is a primary electron donor, bacteriochlorophyll dimer, BA and HA are electron acceptors, monomeric bacteriochlorophyll and bacteriopheophytin in active A-branch respectively). The excited states emit at 905 and 940 nm and have approximately the same energy and high interaction rate. The intermediate state I is populated earlier than the P(+)BA(-)HA state and has energy close to the energy of the excited states, a high rate of population and depopulation and spectral identity to the BA(-). A sum of the I and P(+)BA(-)HA populations fits the experimental kinetics of the BA(-) absorption band at 1020 nm. The model explains an oscillatory phenomenon in the kinetics of the P(*) stimulated emission and of the BA(-) absorption. In the schemes without the I state, accordance with the experiment is achieved at unreal parameter values or is not achieved at all. A qualitative agreement of the model with the experiment can be achieved at a wide range of parameter values. The nature of the states I and P(*)940BAHA is discussed in terms of partial charge separation between P and BA and inside P respectively.

Franck–Condon factors—Computational approaches and recent developments

Algorithms and methodologies for the calculation of Franck–Condon integrals are reviewed. Starting from the standard approach based on the Cartesian representation of the normal modes and the use of Duschinsky's transformation and recursion formulas, methods for treating large displacements of the equilibrium positions and anharmonic and non-Condon effects are considered. Finally, focusing attention on problems arising from the use of recurrence relations, some of the proposed solutions are critically reviewed along with new alternative approaches.

Photoinduced Charge Transfer from Titania to Surface Doping Site

We evaluate a theoretical model in which Ru is substituting for Ti at the (100) surface of anatase TiO2. Charge transfer from the photo-excited TiO2 substrate to the catalytic site triggers the photo-catalytic event (such as water oxidation or reduction half-reaction). We perform ab-initio computational modeling of the charge transfer dynamics on the interface of TiO2 nanorod and catalytic site. A slab of TiO2 represents a fragment of TiO2 nanorod in the anatase phase. Titanium to ruthenium replacement is performed in a way to match the symmetry of TiO2 substrate. One molecular layer of adsorbed water is taken into consideration to mimic the experimental conditions. It is found that these adsorbed water molecules saturate dangling surface bonds and drastically affect the electronic properties of systems investigated. The modeling is performed by reduced density matrix method in the basis of Kohn-Sham orbitals. A nano-catalyst modeled through replacement defect contributes energy levels near the bottom of the conduction band of TiO2 nano-structure. An exciton in the nano-rod is dissipating due to interaction with lattice vibrations, treated through non-adiabatic coupling. The electron relaxes to conduction band edge and then to the Ru cite with faster rate than hole relaxes to the Ru cite. These results are of the importance for an optimal design of nano-materials for photo-catalytic water splitting and solar energy harvesting.

Fluorescence of tryptophan in designed hairpin and Trp-cage miniproteins: measurements of fluorescence yields and calculations by quantum mechanical molecular dynamics simulations

The quantum yield of tryptophan (Trp) fluorescence was measured in 30 designed miniproteins (17 β-hairpins and 13 Trp-cage peptides), each containing a single Trp residue. Measurements were made in D(2)O and H(2)O to distinguish between fluorescence quenching mechanisms involving electron and proton transfer in the hairpin peptides, and at two temperatures to check for effects of partial unfolding of the Trp-cage peptides. The extent of folding of all the peptides also was measured by NMR. The fluorescence yields ranged from 0.01 in some of the Trp-cage peptides to 0.27 in some hairpins. Fluorescence quenching was found to occur by electron transfer from the excited indole ring of the Trp to a backbone amide group or the protonated side chain of a nearby histidine, glutamate, aspartate, tyrosine, or cysteine residue. Ionized tyrosine side chains quenched strongly by resonance energy transfer or electron transfer to the excited indole ring. Hybrid classical/quantum mechanical molecular dynamics simulations were performed by a method that optimized induced electric dipoles separately for the ground and excited states in multiple π-π* and charge-transfer (CT) excitations. Twenty 0.5 ns trajectories in the tryptophan's lowest excited singlet π-π* state were run for each peptide, beginning by projections from trajectories in the ground state. Fluorescence quenching was correlated with the availability of a CT or exciton state that was strongly coupled to the π-π* state and that matched or fell below the π-π* state in energy. The fluorescence yields predicted by summing the calculated rates of charge and energy transfer are in good accord with the measured yields.

At the dawn of the 21st century: Is dynamics the missing link for understanding enzyme catalysis?

Enzymes play a key role in almost all biological processes, accelerating a variety of metabolic reactions as well as controlling energy transduction, the transcription, and translation of genetic information, and signaling. They possess the remarkable capacity to accelerate reactions by many orders of magnitude compared to their uncatalyzed counterparts, making feasible crucial processes that would otherwise not occur on biologically relevant timescales. Thus, there is broad interest in understanding the catalytic power of enzymes on a molecular level. Several proposals have been put forward to try to explain this phenomenon, and one that has rapidly gained momentum in recent years is the idea that enzyme dynamics somehow contributes to catalysis. This review examines the dynamical proposal in a critical way, considering basically all reasonable definitions, including (but not limited to) such proposed effects as "coupling between conformational and chemical motions," "landscape searches" and "entropy funnels." It is shown that none of these proposed effects have been experimentally demonstrated to contribute to catalysis, nor are they supported by consistent theoretical studies. On the other hand, it is clarified that careful simulation studies have excluded most (if not all) dynamical proposals. This review places significant emphasis on clarifying the role of logical definitions of different catalytic proposals, and on the need for a clear formulation in terms of the assumed potential surface and reaction coordinate. Finally, it is pointed out that electrostatic preorganization actually accounts for the observed catalytic effects of enzymes, through the corresponding changes in the activation free energies.

Electronic pathway in reaction centers from Rhodobacter sphaeroides and Chloroflexus aurantiacus

The reaction centers (RC) of Chloroflexus aurantiacus and Rhodobacter sphaeroidesH(M182)L mutant were investigated. Prediction for electron transfer (ET) at very low temperatures was also performed. To describe the kinetics of the C. aurantiacus RCs, the incoherent model of electron transfer was used. It was shown that the asymmetry in electronic coupling parameters must be included to explain the experiments. For the description of R. sphaeroidesH(M182)L mutant RCs, the coherent and incoherent models of electron transfer were used. These two models are discussed with regard to the observed electron transfer kinetics. It seems likely that the electron transfer asymmetry in R. sphaeroides RCs is caused mainly by the asymmetry in the free energy levels of L- and M-side cofactors. In the case of C. aurantiacus RCs, the unidirectionality of the charge separation can be caused mainly by the difference in the electronic coupling parameters in two branches.

Excitation wavelength dependence of primary charge separation in reaction centers from Rhodobacter sphaeroides

The excitation wavelength dependence of the initial electron transfer rate in both wild type and mutant reaction centers from Rhodobacter sphaeroides has been studied between 840 and 920 nm as a function of temperature (10-295 K). The dynamics of primary charge separation show no resolvable excitation wavelength dependence at room temperature over this spectral range. A small variation in rate with excitation wavelength is observed at cryogenic temperatures. The low temperature results cannot be explained in terms either of a nonequilibrium model that assumes that the primary charge separation starts from a vibrationally hot state or a model that assumes a static inhomogeneous distribution of electron transfer driving forces. Instead these results are consistent with the concept that primary charge separation kinetics are controlled by the dynamics of protein conformational diffusion.

Free energies for biological electron transfer from QM/MM calculation: method, application and critical assessment

Computer simulations of biological electron transfer reactions are reviewed with a focus on the calculation of reaction free energy (driving force) and reorganization free energy. Then a mixed quantum mechanical/molecular mechanical (QM/MM) approach is described which is designed for computation of these quantities for pure electron transfer reactions with large donor-acceptor separation distances. The method is applied to intra-protein electron transfer in Ru(bpy)(2)(im)His33 cytochrome c and the results compared to experimental data. Several modeling aspects which are important for successful calculation of free energies with QM/MM are discussed in detail.

Energetics and kinetics of primary charge separation in bacterial photosynthesis

We report the results of molecular dynamics (MD) simulations and formal modeling of the free-energy surfaces and reaction rates of primary charge separation in the reaction center of Rhodobacter sphaeroides. Two simulation protocols were used to produce MD trajectories. Standard force-field potentials were employed in the first protocol. In the second protocol, the special pair was made polarizable to reproduce a high polarizability of its photoexcited state observed by Stark spectroscopy. The charge distribution between covalent and charge-transfer states of the special pair was dynamically adjusted during the simulation run. We found from both protocols that the breadth of electrostatic fluctuations of the protein/water environment far exceeds previous estimates, resulting in about 1.6 eV reorganization energy of electron transfer in the first protocol and 2.5 eV in the second protocol. Most of these electrostatic fluctuations become dynamically frozen on the time scale of primary charge separation, resulting in much smaller solvation contributions to the activation barrier. While water dominates solvation thermodynamics on long observation times, protein emerges as the major thermal bath coupled to electron transfer on the picosecond time of the reaction. Marcus parabolas were obtained for the free-energy surfaces of electron transfer by using the first protocol, while a highly asymmetric surface was obtained in the second protocol. A nonergodic formulation of the diffusion-reaction electron-transfer kinetics has allowed us to reproduce the experimental results for both the temperature dependence of the rate and the nonexponential decay of the population of the photoexcited special pair.

Underdamped vibrations control the primary electron transfer in photosynthesis at low temperatures

Measurements performed with the help of ultrafast laser spectroscopy have clearly shown that the primary electron transfer in photosynthesis lasts no longer than a few picoseconds. Equally fast are processes of vibrational relaxation which have to be taken into account in the correct description of the phenomenon. Here, we consider a simple theory combining the electron transfer process with diffusion in the energy space of a chosen underdamped vibrational mode of protein environment. Analytical formulas for effective transition rate constants are derived, and a transient kinetics is considered. The quality of analytical approximations is verified by numerical simulations for various physical conditions. Efficient parallel computations have been applied. The model can explain a peculiar temperature dependence of pump-probe spectra observed.

Theoretical description of femtosecond fluorescence depletion spectrum of molecules in solution

A theoretical model used for calculating the fluorescence depletion spectrum (FDS) of molecules in liquids induced by femtosecond pump-probe laser pulses is proposed based on the reduced density matrix theory. The FDS intensity is obtained by calculating the stimulated emission of the excited electronic state. As an application of the theoretical model, the FDS of oxazine 750 (OX-750) molecule in acetone solution is calculated. The simulated FDS agrees with the experimental result of Liu et al. [J. Y. Liu et al., J. Phys. Chem. A 107, 10857 (2003)]. The calculated vibrational relaxation rate is 2.5 ps(-1) for the OX-750 molecule. Vibrational population dynamics and wave packet evolution in the excited state are described in detail. The effect of the probe pulse parameter on the FDS is also discussed.

Photoinduced Vibrational Coherence Transfer in Molecular Dimers

At short times that are faster than dephasing, photoinduced evolution of the vibrational subsystem in an electron-phonon molecular structure depends strongly on the electronic evolution. As the electronic population shifts between the donor and acceptor states, in the diabatic description the state with the largest population determines the equilibrium positions and frequencies of the vibrational modes, which oscillate continuously and without loss of coherence. The vibrational coherence transfer between the electronic states detected recently in a number of systems is described theoretically by application of the quantized Hamiltonian dynamics (QHD) formalism [J. Chem. Phys. 2000, 113, 6557] to the coupled electronic and vibrational degrees of freedom of a model heterodimer. The observed coherent modulation of the frequency of the probe signal is represented with simple analytic and numeric QHD models.

Theoretical Determination of the Standard Reduction Potentials of Pheophytin-ainN,N-Dimethyl Formamide and Membrane

Quantum mechanical/molecular mechanics (QM/MM) calculations were performed on the neutral, anionic, and dianionic forms of Pheophytin-a (Pheo-a) in N,N-dimethyl formamide (DMF) in order to calculate the absolute free energy of reduction of Pheo-a in solution. The geometry of the solvated species was optimized by restricted open-shell density functional treatment (ROB3LYP) using the 6-31G(d) basis set for the molecular species while the primary solvent shell consisting of 45 DMF molecules was treated by the MM method using the universal force field (UFF). Electronic energies of the neutral, anionic, and dianionic species were obtained by carrying out single point density functional theory (DFT) calculations using the 6-311+G(2d,2p) basis set on the respective ONIOM optimized geometries. The CHARMM27 force field was used to account for the dynamical nature of the primary solvation shell of 45 DMF molecules. In the calculations using solvent shells, the required atomic charges for each solvent molecule were obtained from ROB3LYP/6-31G(d) calculation on a single isolated DMF molecule. Randomly sampled configurations generated by the Monte Carlo (MC) technique were used to determine the contribution of the primary shell to the free energy of solvation of the three species. The dynamical nature of the primary shell significantly corrects the free energy of solvation. Frequency calculations at the ROB3LYP/6-31G(d) level were carried out on the optimized geometries of truncated 47-atom models of the neutral and ionic species in vacuum so as to determine the differences in thermal energy and molecular entropy. The Born energy of ion-dielectric interaction, the Onsager energy of dipole-dielectric interaction, and the Debye-Hückel energy of ion-ionic cloud interaction for the pheophytin-solvent aggregate were added as perturbative corrections. The Born interaction also makes a large contribution to the absolute free energy of reduction. An implicit solvation model (DPCM) was also employed for the calculation of standard reduction potentials in DMF. Both the models were successful in reproducing the standard reduction potentials. An explicit solvent treatment(QM/MM/MC + Born + Onsager + Debye corrections) yielded the one electron reduction potential of Pheo-a as -0.92 +/- 0.27 V and the two electron reduction potential as -1.34 +/- 0.25 V at 298.15 K, while the implicit solvent treatment yielded the corresponding values as -1.03 +/- 0.17 and -1.30 +/- 0.17 V, respectively. The calculated values more or less agree with the experimental midpoint potentials of -0.90 and -1.25 V, respectively. Moreover, a numerical finite difference Poisson-Boltzmann solver (FDPB) along with the DPCM methodology was employed to obtain the reduction potential of pheophytin in the thylakoid membrane. The calculated reduction potential value of -0.58 V is in excellent agreement with the reported value -0.61 V.

Integrated Kinetics for the Production of Glucose in Plant Cells and the Effect of Temperature

We prepare a temperature-dependent formulation of the integrated kinetics for the overall process of photosynthesis in eukaryotic cells. To avoid complexity, the C4 plants are chosen because their rate of photosynthesis is independent of the partial pressure of O2. A systematically simplified but comprehensive scheme for both light and dark reactions is considered. The reaction rate per reaction center in the thylakoid membrane is related to the rate of exciton transfer between chlorophyll neighbors. An expression is formulated for the light reaction rate (R1'). The NADPH formation rate is related to R1' and the survival probability of the membrane. Rates of different steps in the simplified scheme can be related to each other by applying a few steady state conditions. The saturation probability of CO2 in a bundle sheath is also considered. The photochemical efficiency (phi) appears in terms of these probabilities. We find the glucose production rate as R(glucose) = (8/3) upsilon L: [corrected] R1'phi g(T)([G3P]/[P(i)]2) exp(-deltaG(E)S/RT), where g(T) is the activation quotient of the involved enzymes, G3P and P(i) represent glyceraldehyde-3-phosphate and inorganic phosphates, and deltaG(E)S is the free energy for the apparent equilibrium between G3P and glucose. This is the first time that such a comprehensive expression for R(glucose) has been derived. The probabilities are generally given by sigmoid curves. The corresponding parameters can be easily determined. The quotient g(T) incorporates a Gaussian distribution for temperature dependence and a sigmoid function describing deactivation. The theoretical plots of photochemical efficiency and glucose production rate versus temperature are in excellent agreement with the experimental ones, thereby validating the formalism.

Vibrational coherence in bacterial reaction centers with genetically modified B-branch pigment composition

Femtosecond absorption difference spectroscopy was applied to study the time and spectral evolution of low-temperature (90 K) absorbance changes in isolated reaction centers (RCs) of the HM182L mutant of Rhodobacter (Rb.) sphaeroides. In this mutant, the composition of the B-branch RC cofactors is modified with respect to that of wild-type RCs by replacing the photochemically inactive BB accessory bacteriochlorophyll (BChl) by a photoreducible bacteriopheophytin molecule (referred to as PhiB). We have examined vibrational coherence within the first 400 fs after excitation of the primary electron donor P with 20-fs pulses at 870 nm by studying the kinetics of absorbance changes at 785 nm (PhiB absorption band), 940 nm (P*-stimulated emission), and 1020 nm (BA- absorption band). The results of the femtosecond measurements are compared with those recently reported for native Rb. sphaeroides R-26 RCs containing an intact BB BChl. At delay times longer than approximately 50 fs (maximum at 120 fs), the mutant RCs exhibit a pronounced BChl radical anion (BA-) absorption band at 1020 nm, which is similar to that observed for Rb. sphaeroides R-26 RCs and represents the formation of the intermediate charge-separated state P+ BA-. Femtosecond oscillations are revealed in the kinetics of the absorption development at 1020 nm and of decay of the P*-stimulated emission at 940 nm, with the oscillatory components of both kinetics displaying a generally synchronous behavior. These data are interpreted in terms of coupling of wave packet-like nuclear motions on the potential energy surface of the P* excited state to the primary electron-transfer reaction P*-->P+ BA- in the A-branch of the RC cofactors. At very early delay times (up to 80 fs), the mutant RCs exhibit a weak absorption decrease around 785 nm that is not observed for Rb. sphaeroides R-26 RCs and can be assigned to a transient bleaching of the Qy ground-state absorption band of the PhiB molecule. In the range of 740-795 nm, encompassing the Qy optical transitions of bacteriopheophytins HA, HB, and PhiB, the absorption difference spectra collected for mutant RCs at 30-50 fs resemble the difference spectrum of the P+ PhiB- charge-separated state previously detected for this mutant in the picosecond time domain (E. Katilius, Z. Katiliene, S. Lin, A.K.W. Taguchi, N.W. Woodbury, J. Phys. Chem., B 106 (2002) 1471-1475). The dynamics of bleaching at 785 nm has a non-monotonous character, showing a single peak with a maximum at 40 fs. Based on these observations, the 785-nm bleaching is speculated to reflect reduction of 1% of PhiB in the B-branch within about 40 fs, which is earlier by approximately 80 fs than the reduction process in the A-branch, both being possibly linked to nuclear wave packet motion in the P* state.