Towards understanding the crystallization of photosystem II: influence of poly(ethylene glycol) of various molecular sizes on the micelle formation of alkyl maltosides.

The influence of poly(ethylene glycol) (PEG) polymers H-(O-CH2-CH2)p-OH with different average molecular sizes p on the micelle formation of n-alkyl-ß-D-maltoside detergents with the number of carbon atoms in the alkyl chain ranging from 10 to 12 is investigated with the aim to learn more about the detergent behavior under conditions suitable for the crystallization of the photosynthetic pigment-protein complex photosystem II. PEG is shown to increase the critical micelle concentration (CMC) of all three detergents in the crystallization buffer in a way that the free energy of micelle formation increases linearly with the concentration of oxyethylene units (O-CH2-CH2) irrespective of the actual molecular weight of the polymer. The CMC shift is modeled by assuming for simplicity that it is dominated by the interaction between PEG and detergent monomers and is interpreted in terms of an increase of the transfer free energy of a methylene group of the alkyl chain by 0.2 kJ mol-1 per 1 mol L-1 increase of the concentration of oxyethylene units at 298 K. Implications of this effect for the solubilization and crystallization of protein-detergent complexes as well as detergent extraction from crystals are discussed.

Short-Range Effects in the Special Pair of Photosystem II Reaction Centers: The Nonconservative Nature of Circular Dichroism.

Photosystem II reaction centers extract electrons from water, providing the basis of oxygenic life on earth. Among the light-sensitive pigments of the reaction center, a central chlorophyll a dimer, known as the special pair, so far has escaped a complete theoretical characterization of its excited state properties. The close proximity of the special pair pigments gives rise to short-range effects that comprise a coupling between local and charge transfer (CT) excited states as well as other intermolecular quantum effects. Using a multiscale simulation and a diabatization technique, we show that the coupling to CT states is responsible for 45% of the excitonic coupling in the special pair. The other short-range effects cause a nonconservative nature of the circular dichroism spectrum of the reaction center by effectively rotating the electric transition dipole moments of the special pair pigments inverting and strongly enhancing their intrinsic rotational strength.

Living on the edge: light-harvesting efficiency and photoprotection in the core of green sulfur bacteria.

Photosynthetic green sulfur bacteria are able to survive under extreme low light conditions. Nevertheless, the light-harvesting efficiencies reported so far, in particular for Fenna-Matthews-Olson (FMO) protein-reaction center complex (RCC) supercomplexes, are much lower than for photosystems of other species. Here, we approach this problem with a structure-based theory. Compelling evidence for a light-harvesting efficiency around 95% is presented for native (anaerobic) conditions that can drop down to 47% when the FMO protein is switched into a photoprotective mode in the presence of molecular oxygen. Light-harvesting bottlenecks are found between the FMO protein and the RCC, and the antenna of the RCC and its reaction center (RC) with forward energy transfer time constants of 39 ps and 23 ps, respectively. The latter time constant removes an ambiguity in the interpretation of time-resolved spectra of RCC probing primary charge transfer and provides strong evidence for a transfer-to-the trap limited kinetics of excited states. Different factors influencing the light-harvesting efficiency are investigated. A fast primary electron transfer in the RC is found to be more important for a high efficiency than the site energy funnel in the FMO protein, quantum effects of nuclear motion, or variations in the mutual orientation between the FMO protein and the RCC.

Refined definition of the critical micelle concentration and application to alkyl maltosides used in membrane protein research.

The critical micelle concentration (CMC) of nonionic detergents is defined as the breaking point in the monomer concentration as a function of the total detergent concentration, identified by setting the third derivate of this function to zero. Combined with a mass action model for micelle formation, this definition yields analytic formulae for the concentration ratio of monomers to total detergent at the CMC and the relationship between the CMC and the free energy of micellization g mic. The theoretical breaking point is shown to coincide with the breaking point of the experimental titration curve, if the fluorescence enhancement of 8-anilino-1-naphthalene-sulfonic acid (ANS) or a similar probe dye is used to monitor micelle formation. Application to a series of n-alkyl-ß-d-maltosides with the number of carbon atoms in the alkyl chain ranging from 8 to 12 demonstrates the good performance of a molecular thermodynamic model, in which the free energy of micellization is given by g mic = σΦ + g pack + g st. In this model, σ is a fit parameter with the dimension of surface tension, Φ represents the change in area of hydrophobic molecular surfaces in contact with the aqueous phase, and g pack and g st are contributions, respectively, from alkyl chain packing in the micelle interior and steric repulsion of detergent head groups. The analysis of experimental data from different sources shows that varying experimental conditions such as co-solutes in the aqueous phase can be accounted for by adapting only σ, if the co-solutes do not bind to the detergent to an appreciable extent. The model is considered a good compromise between theory and practicability to be applied in the context of in vitro investigations of membrane proteins.

A unified framework for the numerical evaluation of the Q-subtractive Kramers-Kronig relations and application to the reconstruction of optical constants of quartz.

The direct usage of the Kramers-Kronig (KK) relations is complicated by two factors: limited frequency range of the available spectra and experimental errors. Here, we reconsider the application of the KK relations to experimental data for the construction of a self-consistent set of optical constants over a wide spectral range: the real part of the complex optical constant, F1, is reconstructed using the imaginary part F2, obtained from an experiment. The focus is on multiply (Q-)subtractive KK relations, which in contrast to the standard KK transformation, exploit information about F1 at a certain number Q of anchor frequencies. We develop a general mathematical framework of the Q-subtractive KK relations and analyze all sources of errors contributing to the inaccuracy of the reconstructed F1. We show that for the reconstruction of F1 only a single evaluation of the standard KK relation is needed together with a correction term given by an approximate evaluation of the error in the standard KK. It is demonstrated that in the classical form of the Q-subtractive KK relations, this correction term coincides with the Lagrange interpolation polynomial of the error with nodes at the anchor frequencies. Another correction term can also be constructed as a lower degree polynomial through a least squares fit, a particular realization of which is taking the average of Q singly subtractive KK relations. As a result, recommendations for the application of Q-subtractive KK relations are given. The accuracy of the considered approaches is illustrated on synthetic examples and experimental data of fused SiO2.

Structural determinants of a permeation barrier of the SecYEG translocon in the active state.

The SecYEG translocon is a channel in bacteria, which provides a passage for secretory proteins across as well as integration of membrane proteins into the plasma membrane. The molecular mechanism, by which SecYEG manages protein transport while preventing water and ion leakage through the membrane, is still controversial. We employed molecular dynamics simulations to assess the contribution of the major structural elements - the plug and the pore ring (PR) - to the sealing of SecYEG in the active state, i.e., with a signal sequence helix occupying the lateral gate. We found, that the PR alone can provide a very tight seal for the wild-type translocon in the active state for both water and ions. Simulations of the mutant I403N, in which one of the PR-defining isoleucine residues is replaced with asparagine, suggest that hydrophobic interactions within the PR and between the PR and the plug are important for maintaining a tight conformation of the wild-type channel around the PR. Disruption of these interactions results in strong fluctuations of helix TM7 and water leakage of the translocon.

Normal mode analysis of spectral density of FMO trimers: Intra- and intermonomer energy transfer.

The intermolecular contribution to the spectral density of the exciton-vibrational coupling of the homotrimeric Fenna-Matthews-Olson (FMO) light-harvesting protein of green sulfur bacteria P. aestuarii is analyzed by combining a normal mode analysis of the protein with the charge density coupling method for the calculation of local transition energies of the pigments. Correlations in site energy fluctuations across the whole FMO trimer are found at low vibrational frequencies. Including, additionally, the high-frequency intrapigment part of the spectral density, extracted from line-narrowing spectra, we study intra- and intermonomer exciton transfer. Whereas the intrapigment part of the spectral density is important for fast intramonomer exciton relaxation, the intermolecular contributions (due to pigment-environment coupling) determine the intermonomer exciton transfer. Neither the variations of the local Huang-Rhys factors nor the correlations in site energy fluctuations have a critical influence on energy transfer. At room temperature, the intermonomer transfer in the FMO protein occurs on a 10 ps time scale, whereas intramonomer exciton equilibration is roughly two orders of magnitude faster. At cryogenic temperatures, intermonomer transfer limits the lifetimes of the lowest exciton band. The lifetimes are found to increase between 20 ps in the center of this band up to 100 ps toward lower energies, which is in very good agreement with the estimates from hole burning data. Interestingly, exciton delocalization in the FMO monomers is found to slow down intermonomer energy transfer, at both physiological and cryogenic temperatures.

Static Disorder in Excitation Energies of the Fenna-Matthews-Olson Protein: Structure-Based Theory Meets Experiment.

Inhomogeneous broadening of optical lines of the Fenna-Matthews-Olson (FMO) light-harvesting protein is investigated by combining a Monte Carlo sampling of low-energy conformational substates of the protein with a quantum chemical/electrostatic calculation of local transition energies (site energies) of the pigments. The good agreement between the optical spectra calculated for the inhomogeneous ensemble and the experimental data demonstrates that electrostatics is the dominant contributor to static disorder in site energies. Rotamers of polar amino acid side chains are found to cause bimodal distribution functions of site energy shifts, which can be probed by hole burning and single-molecule spectroscopy. When summing over the large number of contributions, the resulting distribution functions of the site energies become Gaussians, and the correlations in site energy fluctuations at different sites practically average to zero. These results demonstrate that static disorder in the FMO protein is in the realm of the central limit theorem of statistics.

Structural basis of light-harvesting in the photosystem II core complex.

Photosystem II (PSII) is a membrane-spanning, multi-subunit pigment-protein complex responsible for the oxidation of water and the reduction of plastoquinone in oxygenic photosynthesis. In the present review, the recent explosive increase in available structural information about the PSII core complex based on X-ray crystallography and cryo-electron microscopy is described at a level of detail that is suitable for a future structure-based analysis of light-harvesting processes. This description includes a proposal for a consistent numbering scheme of protein-bound pigment cofactors across species. The structural survey is complemented by an overview of the state of affairs in structure-based modeling of excitation energy transfer in the PSII core complex with emphasis on electrostatic computations, optical properties of the reaction center, the assignment of long-wavelength chlorophylls, and energy trapping mechanisms.

Coupling to Charge Transfer States is the Key to Modulate the Optical Bands for Efficient Light Harvesting in Purple Bacteria.

The photosynthetic apparatus of purple bacteria uses exciton delocalization and static disorder to modulate the position and broadening of its absorption bands, leading to efficient light harvesting. Its main antenna complex, LH2, contains two rings of identical bacteriochlorophyll pigments, B800 and B850, absorbing at 800 and 850 nm, respectively. It has been an unsolved problem why static disorder of the strongly coupled B850 ring is several times larger than that of the B800 ring. Here we show that mixing between excitons and charge transfer states in the B850 ring is responsible for the effect. The linear absorption spectrum of the LH2 system is simulated by using a multiscale approach with an exciton Hamiltonian generalized to include the charge transfer states that involve adjacent pigment pairs, with static disorder modeled microscopically by molecular dynamics simulations. Our results show that sufficient inhomogeneous broadening of the B850 band, needed for efficient light harvesting, is only obtained by utilizing static disorder in the coupling between local excited and interpigment charge transfer states.

Structure-Based Theory of Fluctuation-Induced Energy Transfer in a Molecular Dyad.

We present a microscopic theory for the description of fluctuation-induced excitation energy transfer in chromophore dimers to explain experimental data on a perylene biscarboximide dyad with orthogonal transition dipole moments. Our non-Condon extension of Förster theory takes into account the fluctuations of excitonic couplings linear and quadratic in the normal coordinates, treated microscopically by quantum chemical/electrostatic calculations. The modulation of the optical transition energies of the chromophores is inferred from optical spectra of the isolated chromophores. The application of the theory to the considered dyad reveals a two to three order of magnitude increase in the rate constant by non-Condon effects. These effects are found to be dominated by fluctuations linear in the normal coordinates and provide a structure-based qualitative interpretation of the experimental time constant for energy transfer as well as its dependence on temperature.

Optimizing Crystal Size of Photosystem II by Macroseeding: Toward Neutron Protein Crystallography.

Photosystem II (PSII) catalyzes the photo-oxidation of water to molecular oxygen and protons. The water splitting reaction occurs inside the oxygen-evolving complex (OEC) via a Mn4CaO5 cluster. To elucidate the reaction mechanism, detailed structural information for each intermediate state of the OEC is required. Despite the current high-resolution crystal structure of PSII at 1.85 Å and other efforts to follow the structural changes of the Mn4CaO5 cluster using X-ray free electron laser (XFEL) crystallography in addition to spectroscopic methods, many details about the reaction mechanism and conformational changes in the catalytic site during water oxidation still remain elusive. In this study, we present a rarely found successful application of the conventional macroseeding method to a large membrane protein like the dimeric PSII core complex (dPSIIcc). Combining microseeding with macroseeding crystallization techniques allowed us to reproducibly grow large dPSIIcc crystals with a size of ~3 mm. These large crystals will help improve the data collected from spectroscopic methods like polarized extended X-ray absorption fine structure (EXAFS) and single crystal electron paramagnetic resonance (EPR) techniques and are a prerequisite for determining a three-dimensional structure using neutron diffraction.

Red/Green Color Tuning of Visual Rhodopsins: Electrostatic Theory Provides a Quantitative Explanation.

We present a structure-based theory of the long-wavelength (red/green) color tuning in visual rhodopsins and its application to the analysis of site-directed mutagenesis experiments. Using a combination of electrostatic and molecular-mechanics methods, we explain the measured mutant-minus-wild-type absorption shifts and conclude that the dominant mechanism of the color tuning in these systems is electrostatic pigment-protein coupling. An important element of our analysis is the independent determination of protonation states of titratable residues in the wild type and the mutant protein as well as the self-consistent reoptimization of hydrogen atom positions, which includes the relaxation of the hydrogen bonding network and the reorientation of water molecules. On the basis of this analysis, we propose a "dipole-orientation rule" according to which both the position and the orientation of a polar group introduced in the protein environment determine the direction of the transition energy shift of the retinal chromophore.

Insights into the binding behavior of native and non-native cytochromes to photosystem I from Thermosynechococcus elongatus.

The binding of photosystem I (PS I) from Thermosynechococcus elongatus to the native cytochrome (cyt) c6 and cyt c from horse heart (cyt cHH) was analyzed by oxygen consumption measurements, isothermal titration calorimetry (ITC), and rigid body docking combined with electrostatic computations of binding energies. Although PS I has a higher affinity for cyt cHH than for cyt c6, the influence of ionic strength and pH on binding is different in the two cases. ITC and theoretical computations revealed the existence of unspecific binding sites for cyt cHH besides one specific binding site close to P700 Binding to PS I was found to be the same for reduced and oxidized cyt cHH Based on this information, suitable conditions for cocrystallization of cyt cHH with PS I were found, resulting in crystals with a PS I:cyt cHH ratio of 1:1. A crystal structure at 3.4-Å resolution was obtained, but cyt cHH cannot be identified in the electron density map because of unspecific binding sites and/or high flexibility at the specific binding site. Modeling the binding of cyt c6 to PS I revealed a specific binding site where the distance and orientation of cyt c6 relative to P700 are comparable with cyt c2 from purple bacteria relative to P870 This work provides new insights into the binding modes of different cytochromes to PS I, thus facilitating steps toward solving the PS I-cyt c costructure and a more detailed understanding of natural electron transport processes.

Role of missing carotenoid in reducing the fluorescence of single monomeric photosystem II core complexes.

The fluorescence of monomeric photosystem II core complexes (mPSIIcc) of the cyanobacterium Thermosynechococcus elongatus, originating from redissolved crystals, is investigated by using single-molecule spectroscopy (SMS) at 1.6 K. The emission spectra of individual mPSIIcc are dominated by sharp zero-phonon lines, showing the existence of different emitters compatible with the F685, F689, and F695 bands reported formerly. The intensity of F695 is reduced in single mPSIIcc as compared to single PSIIcc-dimers (dPSIIcc). Crystal structures show that one of the ß-carotene (ß-Car) cofactors located at the monomer-monomer interface in dPSIIcc is missing in mPSIIcc. This ß-Car in dPSIIcc is in van der Waals distance to chlorophyll (Chl) 17 in the CP47 subunit. We suggest that this Chl contributes to the F695 emitter. A loss of ß-Car cofactors in mPSIIcc preparations will lead to an increased lifetime of the triplet state of Chl 17, which can explain the reduced singlet emission of F695 as observed in SMS.

Origin of non-conservative circular dichroism of the CP29 antenna complex of photosystem II.

The origin of the non-conservative nature of the circular dichroism spectrum of the CP29 light-harvesting complex in the Qy spectral region is investigated. A structure-based Hamiltonian of coupled Qy transitions, determined previously [Müh et al., Phys. Chem. Chem. Phys., 2014, 16, 11848] is extended by including higher excited states of the chlorophylls and the S0 → S2 transition of carotenoids. Excitonic couplings are calculated with the Poisson-TrESP method, taking into account dipole strengths from experiments on isolated pigments. The coupling between Qy and higher excited states is found to be responsible for the major part of the non-conservativity of the CD spectrum. The remaining part is explained by the intrinsic CD of the chlorophylls that has been estimated from experiments on isolated pigments.

Electrostatic Asymmetry in the Reaction Center of Photosystem II.

The exciton Hamiltonian of the chlorophyll (Chl) and pheophytin (Pheo) pigments in the reaction center (RC) of photosystem II is computed based on recent crystal structures by using the Poisson-Boltzmann/quantum-chemical method. Computed site energies largely confirm a previous model inferred from fits of optical spectra, in which ChlD1 has the lowest site energy, while that of PheoD1 is higher than that of PheoD2. The latter assignment has been challenged recently under reference to mutagenesis experiments. We argue that these data are not in contradiction to our results. We conclude that ChlD1 is the primary electron donor in both isolated RCs and intact core complexes at least at cryogenic temperatures. The main source of asymmetry in site energies is the charge distribution in the protein. Because many small contributions from various structural elements have to be taken into account, it can be assumed that this asymmetry was established in evolution by global optimization of the RC protein.

Challenges facing an understanding of the nature of low-energy excited states in photosynthesis.

While the majority of the photochemical states and pathways related to the biological capture of solar energy are now well understood and provide paradigms for artificial device design, additional low-energy states have been discovered in many systems with obscure origins and significance. However, as low-energy states are naively expected to be critical to function, these observations pose important challenges. A review of known properties of low energy states covering eight photochemical systems, and options for their interpretation, are presented. A concerted experimental and theoretical research strategy is suggested and outlined, this being aimed at providing a fully comprehensive understanding.

The lowest-energy chlorophyll of photosystem II is adjacent to the peripheral antenna: Emitting states of CP47 assigned via circularly polarized luminescence.

The identification of low-energy chlorophyll pigments in photosystem II (PSII) is critical to our understanding of the kinetics and mechanism of this important enzyme. We report parallel circular dichroism (CD) and circularly polarized luminescence (CPL) measurements at liquid helium temperatures of the proximal antenna protein CP47. This assembly hosts the lowest-energy chlorophylls in PSII, responsible for the well-known "F695" fluorescence band of thylakoids and PSII core complexes. Our new spectra enable a clear identification of the lowest-energy exciton state of CP47. This state exhibits a small but measurable excitonic delocalization, as predicated by its CD and CPL. Using structure-based simulations incorporating the new spectra, we propose a revised set of site energies for the 16 chlorophylls of CP47. The significant difference from previous analyses is that the lowest-energy pigment is assigned as Chl 612 (alternately numbered Chl 11). The new assignment is readily reconciled with the large number of experimental observations in the literature, while the most common previous assignment for the lowest energy pigment, Chl 627(29), is shown to be inconsistent with CD and CPL results. Chl 612(11) is near the peripheral light-harvesting system in higher plants, in a lumen-exposed region of the thylakoid membrane. The low-energy pigment is also near a recently proposed binding site of the PsbS protein. This result consequently has significant implications for our understanding of the kinetics and regulation of energy transfer in PSII.