Resonant vibrations produce quantum bridge over high-energy states in heterogeneous antenna.

Photosynthetic light-harvesting complexes usually contain several pools of molecules with a big difference in transition energies, for example, chlorophylls a and b in plant antennas. Some pathways of the excitation energy transfer may include pigments from the low-energy pool separated by a site occupied by a high-energy molecule. We demonstrate that such pathways may be functional if high-frequency intramolecular vibrations fall in resonance with the energy gap between the neighboring molecules belonging to different pools. In this case, a vibration-assisted mixing of the excited states can produce delocalized vibronic states playing a role of 'quantum bridge' that facilitates a passage over high-energy barrier. We perform calculations of the excitation dynamics in the model three-state system with the parameters emerging from our previous studies of real antennas. Simulation of the dynamics in an explicit electron-vibrational basis demonstrates that the rate of transfer between the two chlorophylls a through the chlorophyll b intermediate is increased by a factor of 1.7-2 in the presence of resonant vibration. A possible influence of energetic disorder and other (non-resonant) vibrations on this effect is discussed.

The location of the low-energy states in Lhca1 favors excitation energy transfer to the core in the plant PSI-LHCI supercomplex.

Lhca1 is one of the four pigment-protein complexes composing the outer antenna of plant Photosystem I-light-havesting I supercomplex (PSI-LHCI). It forms a functional dimer with Lhca4 but, differently from this complex, it does not contain 'red-forms,' i.e., pigments absorbing above 700 nm. Interestingly, the recent PSI-LHCI structures suggest that Lhca1 is the main point of delivering the energy harvested by the antenna to the core. To identify the excitation energy pathways in Lhca1, we developed a structure-based exciton model based on the simultaneous fit of the low-temperature absorption, linear dichroism, and fluorescence spectra of wild-type Lhca1 and two mutants, lacking chlorophylls contributing to the long-wavelength region of the absorption. The model enables us to define the locations of the lowest energy pigments in Lhca1 and estimate pathways and timescales of energy transfer within the complex and to the PSI core. We found that Lhca1 has a particular energy landscape with an unusual (compared to Lhca4, LHCII, and CP29) configuration of the low-energy states. Remarkably, these states are located near the core, facilitating direct energy transfer to it. Moreover, the low-energy states of Lhca1 are also coupled to the red-most state (red forms) of the neighboring Lhca4 antenna, providing a pathway for effective excitation energy transfer from Lhca4 to the core.

Excitation dynamics in photosynthetic light-harvesting complex B850: exact solution versus Redfield and Förster limits.

We model the excitation dynamics in bacterial B850 antenna using the standard Redfield, modified Redfield, and Förster approaches and comparing them with the exact solution obtained with hierarchical equation of motion (HEOM). We have found that the modified Redfield is capable of reproducing the dynamics associated with downhill relaxation from higher exciton levels, but fails to explain the migration of quasi-equilibrated excitation over the B850 ring (and its spectral signatures like transient anisotropy decay). Neglecting the population-to-coherence transfers leads to a quick decoherence between the exciton states resulting in unrealistically fast delocalization looking like instantaneous transfer around the ring. The standard (non-secular) Redfield gives a more satisfactory picture of this kind of migration, but in some cases the results can be corrupted by artifacts emerging from the one-phonon character of this theory.

Excitation energy equilibration in a trimeric LHCII complex involves unusual pathways.

We explore the energy equilibration within the LHCII trimer using various approaches, including the Redfield-Förster method (with different compartmentalization schemes) and the exact hierarchical equation of motion (HEOM). We demonstrate that the inter-monomeric migration in the trimeric LHCII complex is not limited to direct transfers between quasi-equilibrated chlorophylls (Chls) a, but also involves additional pathways with uphill transfers from Chls a to the stromal-side Chls b (connecting the Chls a clusters from different monomeric subunits). Although these uphill transfers are slow they still can increase the total rate of inter-monomeric transfers by a factor of 1.5. The same stromal-side Chls b also promote a depopulation of the Chl a604 long-lived state (blue-shifted and mixed with the lumenal-side Chls b). Due to the connection between the stromal- and lumenal-side Chls b clusters the intra- and inter-monomeric transfers from a604 to the main Chls a become faster by a factor of 1.6 and 1.75, respectively.

Synchronization of opening and closing of two gramicidin A channels pulled together by a linker: possible relevance to channel clustering.

The linear 15-mer peptide gramicidin A (gA) produced by Bacillus brevis is known to form the simplest natural ion channel in lipid membranes representing a head-to-head transmembrane dimer. Its incorporation into a planar lipid bilayer manifests itself in regular electrical current transitions. If two gA subunits are tightly connected by a water-soluble, flexible linker of a certain length, the current transitions become heterogeneous: in a part of them, the amplitude is almost twofold higher than that of a single channel, thereby demonstrating the synchronous opening of two single channels. The lifetime, i.e. the open-state duration, of this dual channel is by several orders of magnitude longer than that of the single channel. Here, we used the ideas of the theory of excitons to hypothesize about the mechanism of synchronous opening and closing of two adjacent channels. Two independent (uncoupled) single channels can be described by two independent conformational coordinates q1 and q2, while two closely located channels can exhibit collective behavior, if the coupling between them produces mixing of the individual states (q1,0) and (0,q2). We suppose that a similar phenomenon can occur not only with synthetic derivatives of gA, but also with such natural channel-forming peptide antibiotics and toxins as alamethicin and syringomycin. In particular, channel clustering observed with these peptides may be also associated with formation of collective conductance states, resulting from mixing of their monomeric states, which allows us to explain the fact that clusters of these channels transmit ions and nonelectrolytes of the same size as the original single channels.

Quantum design of photosynthesis for bio-inspired solar-energy conversion.

Photosynthesis is the natural process that converts solar photons into energy-rich products that are needed to drive the biochemistry of life. Two ultrafast processes form the basis of photosynthesis: excitation energy transfer and charge separation. Under optimal conditions, every photon that is absorbed is used by the photosynthetic organism. Fundamental quantum mechanics phenomena, including delocalization, underlie the speed, efficiency and directionality of the charge-separation process. At least four design principles are active in natural photosynthesis, and these can be applied practically to stimulate the development of bio-inspired, human-made energy conversion systems.

Excitonic interactions and Stark fluorescence spectra.

We develop the theory for the Stark fluorescence (SF) of molecular aggregates by taking into account the mixing of the excited states [including the states with charge-transfer (CT) characters]. We use the sum-over-state approach and modified rotating wave approximation to describe interactions of the static and optical fields with the permanent and transition dipoles of the excited states. The SF spectral profiles are calculated using the standard and modified Redfield theories for the emission lineshapes. The resulting expression allows an interpretation of the SF response based on the calculation of only one-exciton states (i.e., the calculation of two-exciton states is not needed). The shape and amplitude of the SF spectrum can exhibit dramatic changes in the presence of the CT states, especially when the CT state is mixed with the red-most emitting exciton levels. In this case, the SF responses are much more sensitive to the exciton-CT mixing as compared with the usual Stark absorption. The limitation of the proposed theory is related to the simplified nature of the Redfield picture, which neglects the dynamic localization within the mixed exciton-CT configuration.

Dynamics of diverse coherences in primary charge separation of bacterial reaction center at 77 K revealed by wavelet analysis.

To uncover the mechanism behind the high photo-electronic conversion efficiency in natural photosynthetic complexes it is essential to trace the dynamics of electronic and vibrational quantum coherences. Here we apply wavelet analysis to two-dimensional electronic spectroscopy data for three purple bacterial reaction centers with mutations that produce drastically different rates of primary charge separation. From the frequency distribution and dynamic evolution features of the quantum beating, electronic coherence with a dephasing lifetime of ~50 fs, vibronic coherence with a lifetime of ~150 fs and vibrational/vibronic coherences with a lifetime of 450 fs are distinguished. We find that they are responsible for, or couple to, different specific steps during the primary charge separation process, i.e., intradimer charge transfer inside the special bacteriochlorophyll pair followed by its relaxation and stabilization of the charge-transfer state. The results enlighten our understanding of how quantum coherences participate in, and contribute to, a biological electron transfer reaction.

Complete mapping of energy transfer pathways in the plant light-harvesting complex Lhca4.

The Lhca4 antenna complex of plant Photosystem I (PSI) is characterized by extremely red-shifted and broadened absorption and emission bands from its low-energy chlorophylls (Chls). The mixing of a charge-transfer (CT) state with the excited state manifold causing these so-called red forms results in highly complicated multi-component excited energy transfer (EET) kinetics within the complex. The two-dimensional electronic spectroscopy experiments presented here reveal that EET towards the CT state occurs on three timescales: fast from the red Chls (within 1 ps), slower (5-7 ps) from the stromal side Chls, and very slow (100-200 ps) from a newly discovered 690 nm luminal trap. The excellent agreement between the experimental data with the previously presented Redfield-Förster exciton model of Lhca4 strongly supports the equilibration scheme of the bulk excitations with the dynamically localized CT on the stromal side. Thus, a complete picture of the energy transfer pathways leading to the population of the CT final trap within the whole Lhca4 complex is presented. In view of the environmental sensitivity of the CT contribution to the Lhca4 energy landscape, we speculate that one role of the CT states is to regulate the EET from the peripheral antenna to the PSI core.

Dynamics of the mixed exciton and charge-transfer states in light-harvesting complex Lhca4: Hierarchical equation approach.

We model the energy transfer dynamics in the Lhca4 peripheral antenna of photosystem I from higher plants. Equilibration between the bulk exciton levels of the antenna and the red-shifted charge-transfer (CT) states is described using the numerically inexpensive Redfield-Förster approach and exact hierarchical equation (HEOM) method. We propose a compartmentalization scheme allowing a quantitatively correct description of the dynamics with the Redfield-Förster theory, including the exciton-type relaxation within strongly coupled compartments and hopping-type migration between them. The Redfield-Förster method gives the kinetics close to the HEOM solution when treating the CT state as dynamically localized. We also demonstrate that the excited states strongly coupled with the CT should be considered as localized as well.

Exciton-vibrational resonance and dynamics of charge separation in the photosystem II reaction center.

The dynamics of charge separation in the photosystem II reaction center (PSII-RC) in the presence of intramolecular vibrations with their frequency matching the energy gap between the exciton state acting as the primary electron donor and the first charge-transfer (CT) state are investigated. A reduced PSII-RC 4-state model explicitly including a CT state is analyzed within Redfield relaxation theory in the multidimensional exciton-vibrational (vibronic) basis. This model is used to study coherent energy/electron transfers and their spectral signatures obtained by two-dimensional electronic spectroscopy (2DES). Modeling of the time-resolved 2D frequency maps obtained by wavelet analysis reveals the origins of the coherences which produce the observed oscillating features in 2DES and allows comparing the lifetimes of the coherences. The results suggest faster excitonic decoherence as compared with longer-lived vibronic oscillations. The emerging picture of the dynamics unravels the role of resonant vibrations in sustaining the effective energy conversion in the PSII-RC. We demonstrate that the mixing of the exciton and CT states promoted by a resonant vibrational quantum allows faster penetration of excitation energy into the CT with subsequent dynamic localization at the bottom of the CT potential induced by the remaining non-resonant nuclear modes. The degree of vibration-assisted mixing and, correspondingly, the rate of primary charge separation, increases significantly in the case of electron-vibrational resonance. The observed features illustrate the principles of quantum design of the photosynthetic unit. These principles are connected with the phenomenon of coherent mixing within vibronic eigenstates, increasing the effectiveness of charge separation not only upon coherent and impulsive laser excitation utilized in the 2DES experiment, but also under natural conditions under non-coherent non-impulsive solar light illumination.

Evidence for coherent mixing of excited and charge-transfer states in the major plant light-harvesting antenna, LHCII.

LHCII, the major light harvesting antenna from plants, plays a dual role in photosynthesis. In low light it is a light-harvester, while in high light it is a quencher that protects the organism from photodamage. The switching mechanism between these two orthogonal conditions is mediated by protein dynamic disorder and photoprotective energy dissipation. The latter in particular is thought to occur in part via spectroscopically 'dark' states. We searched for such states in LHCII trimers from spinach, at both room temperature and at 77 K. Using 2D electronic spectroscopy, we explored coherent interactions between chlorophylls absorbing on the low-energy side of LHCII, which is the region that is responsible for both light-harvesting and photoprotection. 2D beating frequency maps allow us to identify four frequencies with strong excitonic character. In particular, our results show the presence of a low-lying state that is coupled to a low-energy excitonic state. We assign this to a mixed excitonic-charge transfer state involving the state with charge separation within the Chl a603-b609 heterodimer, borrowing some dipole strength from the Chl a602-a603 excited states. Such a state may play a role in photoprotection, in conjunction with specific and environmentally controlled realizations of protein dynamic disorder. Our identification and assignment of the coherences observed in the 2D frequency maps suggests that the structure of exciton states as well as a mixing of the excited and charge-transfer states is affected by coupling of these states to resonant vibrations in LHCII.

The Role of Resonant Vibrations in Electronic Energy Transfer.

Nuclear vibrations play a prominent role in the spectroscopy and dynamics of electronic systems. As recent experimental and theoretical studies suggest, this may be even more so when vibrational frequencies are resonant with transitions between the electronic states. Herein, a vibronic multilevel Redfield model is reported for excitonically coupled electronic two-level systems with a few explicitly included vibrational modes and interacting with a phonon bath. With numerical simulations the effects of the quantized vibrations on the dynamics of energy transfer and coherence in a model dimer are illustrated. The resonance between the vibrational frequency and energy gap between the sites leads to a large delocalization of vibronic states, which then results in faster energy transfer and longer-lived mixed coherences.

Mixing of exciton and charge-transfer states in light-harvesting complex Lhca4.

Lhca4 is one of the peripheral antennae of higher plant photosystem I and it is characterized by the presence of chlorophyll a with absorption and emission bands around 30 nm red-shifted compared to those of the other chlorophylls associated with plant complexes. In this work we have investigated the origin of this red shift by using the recent structure of Lhca4 (Qin et al., Science, 2015, 348, 989) to build an exciton model that includes a charge-transfer (CT) state mixed with the excited-state manifold. A simultaneous quantitative fit of absorption, linear dichroism, fluorescence, and Stark absorption spectra of the wild-type Lhca4 and NH mutant (where the sites involved in CT are affected) enables us to determine the origin of the CT state and explore its spectral signatures. A huge borrowing of dipole strength by the CT, accompanied by anomalous broadening and red-shifting of the fluorescence as well as dramatic changes in the Stark spectrum, can be accounted for by a model implying an exciton-type mixing between excited states and CT states.

Conformational switching in a light-harvesting protein as followed by single-molecule spectroscopy.

Among the ultimate goals of protein physics, the complete, experimental description of the energy paths leading to protein conformational changes remains a challenge. Single protein fluorescence spectroscopy constitutes an approach of choice for addressing protein dynamics, and, among naturally fluorescing proteins, light-harvesting (LH) proteins from purple bacteria constitute an ideal object for such a study. LHs bind bacteriochlorophyll a molecules, which confer on them a high intrinsic fluorescence yield. Moreover, the electronic properties of these pigment-proteins result from the strong excitonic coupling between their bound bacteriochlorophyll a molecules in combination with the large energetic disorder due to slow fluctuations in their structure. As a result, the position and probability of their fluorescence transition delicately depends on the precise realization of the disorder of the set of bound pigments, which is governed by the LH protein dynamics. Analysis of these parameters using time-resolved single-molecule fluorescence spectroscopy thus yields direct access to the protein dynamics. Applying this technique to the LH2 protein from Rhodovulum (Rdv.) sulfidophilum, the structure-and consequently the fluorescence properties-of which depends on pH, allowed us to follow a single protein, pH-induced, reversible, conformational transition. Hence, for the first time, to our knowledge, a protein transition can be visualized through changes in the electronic structure of the intrinsic cofactors, at a level of a single LH protein, which opens a new, to our knowledge, route for understanding the changes in energy landscape that underlie protein function and adaptation to the needs of living organisms.

How exciton-vibrational coherences control charge separation in the photosystem II reaction center.

In photosynthesis absorbed sun light produces collective excitations (excitons) that form a coherent superposition of electronic and vibrational states of the individual pigments. Two-dimensional (2D) electronic spectroscopy allows a visualization of how these coherences are involved in the primary processes of energy and charge transfer. Based on quantitative modeling we identify the exciton-vibrational coherences observed in 2D photon echo of the photosystem II reaction center (PSII-RC). We find that the vibrations resonant with the exciton splittings can modify the delocalization of the exciton states and produce additional states, thus promoting directed energy transfer and allowing a switch between the two charge separation pathways. We conclude that the coincidence of the frequencies of the most intense vibrations with the splittings within the manifold of exciton and charge-transfer states in the PSII-RC is not occurring by chance, but reflects a fundamental principle of how energy conversion in photosynthesis was optimized.

The nature of coherences in the B820 bacteriochlorophyll dimer revealed by two-dimensional electronic spectroscopy.

Light-harvesting in photosynthesis is determined by the excitonic interactions in disordered antennae and the coupling of collective electronic excitations to fast nuclear motions, producing efficient energy transfer with a complicated interplay between exciton and vibrational coherences. Two-dimensional electronic spectroscopy (2DES) is a powerful tool to study the presence of these coherences in photosynthetic complexes. However, the unambiguous assignment of the nature of the observed coherences is still under debate. In this paper we apply 2DES to an excitonically coupled bacteriochlorophyll dimer, the B820 subunit of the light harvesting complex 1 (LH1-RC) of R. rubrum G9. Fourier analysis of the measured kinetics and modeling of the spectral responses in a complete basis of electronic and vibrational states allow us to distinguish between pure vibrational, mixed exciton-vibrational (vibronic), and predominantly exciton coherences. The mixed coherences have been found in a wide range of oscillation frequencies, whereas exciton coherences give the biggest contributions for the frequencies in the 400-550 cm(-1) range, corresponding to the exciton splitting energy of the B820 dimer. Significant exciton coherences are also present at higher frequencies, i.e., up to 800 cm(-1), which are determined by realizations of the disorder with a large energy gap between the two pigments (which increases the apparent value of the exciton splitting). Although the B820 dimer is a model system, the approach presented here represents a basis for further analyses of more complicated systems, providing a tool for studying the interplay between electronic and vibrational coherences in disordered photosynthetic antennae and reaction centres.

Direct visualization of exciton reequilibration in the LH1 and LH2 complexes of Rhodobacter sphaeroides by multipulse spectroscopy.

The dynamics of the excited states of the light-harvesting complexes LH1 and LH2 of Rhodobacter sphaeroides are governed, mainly, by the excitonic nature of these ring-systems. In a pump-dump-probe experiment, the first pulse promotes LH1 or LH2 to its excited state and the second pulse dumps a portion of the excited state. By selective dumping, we can disentangle the dynamics normally hidden in the excited-state manifold. We find that by using this multiple-excitation technique we can visualize a 400-fs reequilibration reflecting relaxation between the two lowest exciton states that cannot be directly explored by conventional pump-probe. An oscillatory feature is observed within the exciton reequilibration, which is attributed to a coherent motion of a vibrational wavepacket with a period of ∼150 fs. Our disordered exciton model allows a quantitative interpretation of the observed reequilibration processes occurring in these antennas.

Multiple charge-separation pathways in photosystem II: modeling of transient absorption kinetics.

We explain the transient absorption kinetics (E. Romero, I. H. M. van Stokkum, V. I. Novoderezhkin, J. P. Dekker, R. van Grondelle, Biochemistry 2010, 49, 4300) measured for isolated reaction centers of photosystem II at 77 K upon excitation of the primary donor band (680 nm). The excited-state dynamics is modeled on the basis of the exciton states of 6 cofactors coupled to 4 charge-transfer (CT) states. One CT state (corresponding to charge separation within the special pair) is supposed to be strongly coupled with the excited states, whereas the other radical pairs are supposed to be localized. Relaxation within the strongly coupled manifold and transfer to localized CT's are described by the modified Redfield and generalized Förster theories, respectively. A simultaneous and quantitative fit of the 680, 545, and 460 nm kinetics (corresponding to respectively the Q(y) transitions of the red-most cofactors, Q(x) transition of pheophytin, and pheophytin anion absorption) enables us to define the pathways and time scales of primary electron transfer. A consistent modeling of the data is only possible with a Scheme where charge separation occurs from both the accessory chlorophyll and from the special pair, giving rise to fast and slow components of the pheophytin anion formation, respectively.

Dynamics of exciton relaxation in LH2 antenna probed by multipulse nonlinear spectroscopy.

We explain the relaxation dynamics in the LH2-B850 antenna as revealed by multipulse pump-dump-probe spectroscopy (Th. A. Cohen Stuart, M. Vengris, V. I. Novoderezhkin, R. J. Cogdell, C. N. Hunter, R. van Grondelle, submitted). The theory of pump-dump-probe response is evaluated using the doorway-window approach in combination with the modified Redfield theory. We demonstrate that a simultaneous fit of linear spectra, pump-probe, and pump-dump-probe kinetics can be obtained at a quantitative level using the disordered exciton model, which is essentially the same as used to model the spectral fluctuations in single LH2 complexes (Novoderezhkin, V.; Rutkauskas, D.; van Grondelle, R. Biophys. J. 2006, 90, 2890). The present studies suggest that the observed relaxation rates are strongly dependent on the realization of the disorder. A big spread of the rates (exceeding 3 orders of magnitude) is correlated with the disorder-induced changes in delocalization length and overlap of the exciton wave functions. We conclude that the bulk kinetics reflect a superposition of many pathways corresponding to different physical limits of energy transfer, varying from sub-20 fs relaxation between delocalized and highly spatially overlapping exciton states to >20 ps jumps between states localized at the opposite sides of the ring.