Three-state mathematical model for the assessment of DCMU-treated photosystem II heterogeneity.

Photosystem II (PSII) is one of the main pigment-protein complexes of photosynthesis which is highly sensitive to unfavorable environmental factors. The heterogeneity of PSII properties is essential for the resistance of autotrophic organisms to stress factors. Assessment of the PSII heterogeneity may be used in environmental monitoring for on-line detection of contamination of the environment. We propose an approach to assess PSII oxygen-evolving complex and light-harvesting antenna heterogeneity that is based on mathematical modeling of the shape of chlorophyll a fluorescence rise of 3-(3,4-dichlorophenyl)-1,1-dimethylurea-treated samples. The hierarchy of characteristic times of the processes considered in the model makes it possible to reduce the model to a system of three ordinary differential equations. The analytic solution of the reduced three-state model is expressed as a sum of two exponential functions, and it exactly reproduces the solution of the complete system within the time range from microseconds to hundreds of milliseconds. The combination of several such models for reaction centers with different properties made it possible to use it as an instrument to study PSII heterogeneity. PSII heterogeneity was studied for Chlamydomonas at different intensities of actinic light, for Scenedesmus under short-term heating, and for Chlorella grown in nitrate-enriched and nitrate-depleted media.

Single-photon absorption and emission from a natural photosynthetic complex.

Photosynthesis is generally assumed to be initiated by a single photon1-3 from the Sun, which, as a weak light source, delivers at most a few tens of photons per nanometre squared per second within a chlorophyll absorption band1. Yet much experimental and theoretical work over the past 40 years has explored the events during photosynthesis subsequent to absorption of light from intense, ultrashort laser pulses2-15. Here, we use single photons to excite under ambient conditions the light-harvesting 2 (LH2) complex of the purple bacterium Rhodobacter sphaeroides, comprising B800 and B850 rings that contain 9 and 18 bacteriochlorophyll molecules, respectively. Excitation of the B800 ring leads to electronic energy transfer to the B850 ring in approximately 0.7 ps, followed by rapid B850-to-B850 energy transfer on an approximately 100-fs timescale and light emission at 850-875 nm (refs. 16-19). Using a heralded single-photon source20,21 along with coincidence counting, we establish time correlation functions for B800 excitation and B850 fluorescence emission and demonstrate that both events involve single photons. We also find that the probability distribution of the number of heralds per detected fluorescence photon supports the view that a single photon can upon absorption drive the subsequent energy transfer and fluorescence emission and hence, by extension, the primary charge separation of photosynthesis. An analytical stochastic model and a Monte Carlo numerical model capture the data, further confirming that absorption of single photons is correlated with emission of single photons in a natural light-harvesting complex.

Dynamic modelling of limitations on improving leaf CO2 assimilation under fluctuating irradiance.

A dynamic model of leaf CO2 assimilation was developed as an extension of the canonical steady-state model, by adding the effects of energy-dependent non-photochemical quenching (qE), chloroplast movement, photoinhibition, regulation of enzyme activity in the Calvin cycle, metabolite concentrations, and dynamic CO2 diffusion. The model was calibrated and tested successfully using published measurements of gas exchange and chlorophyll fluorescence on Arabidopsis thaliana ecotype Col-0 and several photosynthetic mutants and transformants affecting the regulation of Rubisco activity (rca-2 and rwt43), non-photochemical quenching (npq4-1 and npq1-2), and sucrose synthesis (spsa1). The potential improvements on CO2 assimilation under fluctuating irradiance that can be achieved by removing the kinetic limitations on the regulation of enzyme activities, electron transport, and stomatal conductance were calculated in silico for different scenarios. The model predicted that the rates of activation of enzymes in the Calvin cycle and stomatal opening were the most limiting (up to 17% improvement) and that effects varied with the frequency of fluctuations. On the other hand, relaxation of qE and chloroplast movement had a strong effect on average low-irradiance CO2 assimilation (up to 10% improvement). Strong synergies among processes were found, such that removing all kinetic limitations simultaneously resulted in improvements of up to 32%.

Proposal for probing energy transfer pathway by single-molecule pump-dump experiment.

The structure of Fenna-Matthews-Olson (FMO) light-harvesting complex had long been recognized as containing seven bacteriochlorophyll (BChl) molecules. Recently, an additional BChl molecule was discovered in the crystal structure of the FMO complex, which may serve as a link between baseplate and the remaining seven molecules. Here, we investigate excitation energy transfer (EET) process by simulating single-molecule pump-dump experiment in the eight-molecules complex. We adopt the coherent modified Redfield theory and non-Markovian quantum jump method to simulate EET dynamics. This scheme provides a practical approach of detecting the realistic EET pathway in BChl complexes with currently available experimental technology. And it may assist optimizing design of artificial light-harvesting devices.

Unified analysis of ensemble and single-complex optical spectral data from light-harvesting complex-2 chromoproteins for gaining deeper insight into bacterial photosynthesis.

Bacterial light-harvesting pigment-protein complexes are very efficient at converting photons into excitons and transferring them to reaction centers, where the energy is stored in a chemical form. Optical properties of the complexes are known to change significantly in time and also vary from one complex to another; therefore, a detailed understanding of the variations on the level of single complexes and how they accumulate into effects that can be seen on the macroscopic scale is required. While experimental and theoretical methods exist to study the spectral properties of light-harvesting complexes on both individual complex and bulk ensemble levels, they have been developed largely independently of each other. To fill this gap, we simultaneously analyze experimental low-temperature single-complex and bulk ensemble optical spectra of the light-harvesting complex-2 (LH2) chromoproteins from the photosynthetic bacterium Rhodopseudomonas acidophila in order to find a unique theoretical model consistent with both experimental situations. The model, which satisfies most of the observations, combines strong exciton-phonon coupling with significant disorder, characteristic of the proteins. We establish a detailed disorder model that, in addition to containing a C_{2}-symmetrical modulation of the site energies, distinguishes between static intercomplex and slow conformational intracomplex disorders. The model evaluations also verify that, despite best efforts, the single-LH2-complex measurements performed so far may be biased toward complexes with higher Huang-Rhys factors.

Excitation energy transfer and charge separation are affected in Arabidopsis thaliana mutants lacking light-harvesting chlorophyll a/b binding protein Lhcb3.

The composition of LHCII trimers as well as excitation energy transfer and charge separation in grana cores of Arabidopsis thaliana mutant lacking chlorophyll a/b binding protein Lhcb3 have been investigated and compared to those in wild-type plants. In grana cores of lhcb3 plants we observed increased amounts of Lhcb1 and Lhcb2 apoproteins per PSII core. The additional copies of Lhcb1 and Lhcb2 are expected to substitute for Lhcb3 in LHCII trimers M as well as in the LHCII "extra" pool, which was found to be modestly enlarged as a result of the absence of Lhcb3. Time-resolved fluorescence measurements reveal a deceleration of the fast phase of excitation dynamics in grana cores of the mutant by ~15 ps, whereas the average fluorescence lifetime is not significantly altered. Monte Carlo modeling predicts a slowing down of the mean hopping time and an increased stabilization of the primary charge separation in the mutant. Thus our data imply that absence of apoprotein Lhcb3 results in detectable differences in excitation energy transfer and charge separation.

Monte Carlo simulations of excitation and electron transfer in grana membranes.

Time-resolved fluorescence measurements on grana membranes with instrumental response function of 3 ps reveal faster excitation dynamics (120 ps) than those reported previously. A possible reason for the faster decay may be a relatively low amount of "extra" LHCII trimers per reaction center of Photosystem II. Monte Carlo modeling of excitation dynamics in C2S2M2 form of PSII-LHCII supercomplexes has been performed using a coarse grained model of this complex, constituting a large majority of proteins in grana membranes. The main factor responsible for the fast fluorescence decay reported in this work was the deep trap constituted by the primary charge separated state in the reaction center (950-1090 cm(-1)). This value is critical for a good fit, whereas typical hopping times between antenna polypeptides (from ~4.5 to ~10.5 ps) and reversible primary charge separation times (from ~4 to ~1.5 ps, respectively) are less critical. Consequently, respective mean migration times of excitation from anywhere in the PSII-LHCII supercomplexes to reaction center range from ~30 to ~80 ps. Thus 1/4-2/3 of the ~120-ps average excitation lifetime is necessary for the diffusion of excitation to reaction center, whereas the remaining time is due to the bottle-neck effect of the trap. Removal of 27% of the Lhcb6 apoprotein pool by mutagenesis of DEG5 gene caused the acceleration of the excitation decay from ~120 to ~100 ps. This effect may be due to the detachment of LHCII-M trimers from PSII-LHCII supercomplexes, accompanied by deepening of the reaction center trap.

Importance of excitation and trapping conditions in photosynthetic environment-assisted energy transport.

It has been argued that excitonic energy transport in photosynthetic complexes is efficient because of a balance between coherent evolution and decoherence, a phenomenon called environment-assisted quantum transport (ENAQT). Studies of ENAQT have usually assumed that the excitation is initially localized on a particular chromophore, and that it is transferred to a reaction center through a similarly localized trap. However, these assumptions are not physically accurate. We show that more realistic models of excitation and trapping can lead to very different predictions about the importance of ENAQT. In particular, although ENAQT is a robust effect if one assumes a localized trap, its effect can be negligible if the trapping is more accurately modeled as Förster transfer to a reaction center. Our results call into question the suggested role of ENAQT in the photosynthetic process of green sulfur bacteria and highlight the subtleties associated with drawing lessons for designing biomimetic light-harvesting complexes.

Coexistence of fluid and crystalline phases of proteins in photosynthetic membranes.

Photosystem II (PSII) and its associated light-harvesting complex II (LHCII) are highly concentrated in the stacked grana regions of photosynthetic thylakoid membranes. PSII-LHCII supercomplexes can be arranged in disordered packings, ordered arrays, or mixtures thereof. The physical driving forces underlying array formation are unknown, complicating attempts to determine a possible functional role for arrays in regulating light harvesting or energy conversion efficiency. Here, we introduce a coarse-grained model of protein interactions in coupled photosynthetic membranes, focusing on just two particle types that feature simple shapes and potential energies motivated by structural studies. Reporting on computer simulations of the model's equilibrium fluctuations, we demonstrate its success in reproducing diverse structural features observed in experiments, including extended PSII-LHCII arrays. Free energy calculations reveal that the appearance of arrays marks a phase transition from the disordered fluid state to a system-spanning crystal. The predicted region of fluid-crystal coexistence is broad, encompassing much of the physiologically relevant parameter regime; we propose experiments that could test this prediction. Our results suggest that grana membranes lie at or near phase coexistence, conferring significant structural and functional flexibility to this densely packed membrane protein system.

Quantification of non-Markovian effects in the Fenna-Matthews-Olson complex.

The excitation energy transfer dynamics in the Fenna-Matthews-Olson complex is quantified in terms of a non-Markovianity measure based on the time evolution of the trace distance of two quantum states. We use a system description derived from experiments and different environmental fluctuation spectral functions, which are obtained either from experimental data or from molecular dynamics simulations. These exhibit, in all cases, a nontrivial structure with several peaks attributed to vibrational modes of the pigment-protein complex. Such a structured environmental spectrum can, in principle, give rise to strong non-Markovian effects. We present numerically exact real-time path-integral calculations for the transfer dynamics and find, in all cases, a monotonic decrease of the trace distance with increasing time which renders a Markovian description valid.

Efficient energy transfer in light-harvesting systems: quantum-classical comparison, flux network, and robustness analysis.

Following the calculation of optimal energy transfer in thermal environment in our first paper [J. L. Wu, F. Liu, Y. Shen, J. S. Cao, and R. J. Silbey, New J. Phys. 12, 105012 (2010)], full quantum dynamics and leading-order "classical" hopping kinetics are compared in the seven-site Fenna-Matthews-Olson (FMO) protein complex. The difference between these two dynamic descriptions is due to higher-order quantum corrections. Two thermal bath models, classical white noise (the Haken-Strobl-Reineker (HSR) model) and quantum Debye model, are considered. In the seven-site FMO model, we observe that higher-order corrections lead to negligible changes in the trapping time or in energy transfer efficiency around the optimal and physiological conditions (2% in the HSR model and 0.1% in the quantum Debye model for the initial site at BChl 1). However, using the concept of integrated flux, we can identify significant differences in branching probabilities of the energy transfer network between hopping kinetics and quantum dynamics (26% in the HSR model and 32% in the quantum Debye model for the initial site at BChl 1). This observation indicates that the quantum coherence can significantly change the distribution of energy transfer pathways in the flux network with the efficiency nearly the same. The quantum-classical comparison of the average trapping time with the removal of the bottleneck site, BChl 4, demonstrates the robustness of the efficient energy transfer by the mechanism of multi-site quantum coherence. To reconcile with the latest eight-site FMO model which is also investigated in the third paper [J. Moix, J. L. Wu, P. F. Huo, D. F. Coker, and J. S. Cao, J. Phys. Chem. Lett. 2, 3045 (2011)], the quantum-classical comparison with the flux network analysis is summarized in Appendix C. The eight-site FMO model yields similar trapping time and network structure as the seven-site FMO model but leads to a more disperse distribution of energy transfer pathways.

Classical master equation for excitonic transport under the influence of an environment.

In a previous paper [Phys. Rev. E 83, 051911 (2011)] we have shown that the results of a quantum-mechanical calculation of electronic energy transfer (EET) over aggregates of coupled monomers can be described also by a model of interacting classical electric dipoles in a weak-coupling approximation, which we referred to as the realistic coupling approximation (RCA). The method was illustrated by EET on a simple linear chain of molecules and also by energy transfer on an arrangement of monomers corresponding to that of the Fenna-Matthews-Olson (FMO) complex relevant for photosynthesis. The study was limited to electronic degrees of freedom, since this is the origin of coherent EET in the quantum case. Nevertheless, more realistic models of EET require the inclusion of the decohering effects of coupling to an environment, when the molecular aggregate becomes an open quantum system. Here we consider the quantum description of EET on a linear chain and on the FMO complex, incorporating environment coupling and constructing the classical version of the same systems in the density matrix formalism. The close agreement of the exact quantum and exact classical results in the RCA is demonstrated and justified analytically in the RCA. This lends further support to the conclusion that the coherence properties of EET in the FMO complex are evident at the classical level and should not be ascribed as solely due to quantum effects.

Quantum coherence and its interplay with protein environments in photosynthetic electronic energy transfer.

Recent experiments suggest that electronic energy transfer in photosynthetic pigment-protein complexes involves long-lived quantum coherence among electronic excitations of pigments. [Engel et al., Nature, 2007, 446, 782-786.] The observation has led to the suggestion that quantum coherence might play a significant role in achieving the remarkable efficiency of photosynthetic light harvesting. At the same time, the observation has raised questions regarding the role of the surrounding protein in protecting the quantum coherence. In this Perspective, we provide an overview of recent experimental and theoretical investigations of photosynthetic electronic energy transfer paying particular attention to the underlying mechanisms of long-lived quantum coherence and its non-Markovian interplay with the protein environment.