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.

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.

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.

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.

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.

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.

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.

Dynamic Stark Effect in Two-Dimensional Spectroscopy Revealing Modulation of Ultrafast Charge Separation in Bacterial Reaction Centers by an Inherent Electric Field.

Despite extensive study, mysteries remain regarding the highly efficient ultrafast charge separation processes in photosynthetic reaction centers (RCs). In this work, transient Stark signals were found to be present in ultrafast two-dimensional electronic spectra recorded for purple bacterial RCs at 77 K. These arose from the electric field that is inherent to the intradimer charge-transfer intermediate of the bacteriochlorophyll pair (P), PA+PB-. By comparing three mutated RCs, a correlation was found between the efficient formation of PA+PB- and a fast charge separation rate. Importantly, the energy level of P* was changed due to the Stark shift, influencing the driving force for P* → P+BA- electron transfer and hence its rate. Furthermore, the orientation and amplitude of the inherent electric field varied in different ways upon different mutation, leading to contrasting changes in the rates. This mechanism of modulation provides a solution to a long-lasting inconsistency between experimental observations and activation energy theory.

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.

Both electronic and vibrational coherences are involved in primary electron transfer in bacterial reaction center.

Understanding the mechanism behind the near-unity efficiency of primary electron transfer in reaction centers is essential for designing performance-enhanced artificial solar conversion systems to fulfill mankind's growing demands for energy. One of the most important challenges is distinguishing electronic and vibrational coherence and establishing their respective roles during charge separation. In this work we apply two-dimensional electronic spectroscopy to three structurally-modified reaction centers from the purple bacterium Rhodobacter sphaeroides with different primary electron transfer rates. By comparing dynamics and quantum beats, we reveal that an electronic coherence with dephasing lifetime of ~190 fs connects the initial excited state, P*, and the charge-transfer intermediate [Formula: see text]; this [Formula: see text] step is associated with a long-lived quasi-resonant vibrational coherence; and another vibrational coherence is associated with stabilizing the primary photoproduct, [Formula: see text]. The results show that both electronic and vibrational coherences are involved in primary electron transfer process and they correlate with the super-high efficiency.

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.

Vibronic Coherence in the Charge Separation Process of the Rhodobacter sphaeroides Reaction Center.

Two-dimensional electronic spectroscopy was applied to a variant of the reaction center (RC) of purple bacterium Rhodobacter sphaeroides lacking the primary acceptor ubiquinone in order to understand the ultrafast separation and transfer of charge between the bacteriochlorin cofactors. For the first time, characteristic 2D spectra were obtained for the participating excited and charge-transfer states, and the electron-transfer cascade (including two different channels, the P* and B* channels) was fully mapped. By analyzing quantum beats using 2D frequency maps, excited-state vibrational modes at 153 and 33 cm-1 were identified. We speculate that these modes couple to the charge separation (CS) process and collectively optimize the CS and are responsible for the superhigh efficiency.

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.

Quantum - coherent dynamics in photosynthetic charge separation revealed by wavelet analysis.

Experimental/theoretical evidence for sustained vibration-assisted electronic (vibronic) coherence in the Photosystem II Reaction Center (PSII RC) indicates that photosynthetic solar-energy conversion might be optimized through the interplay of electronic and vibrational quantum dynamics. This evidence has been obtained by investigating the primary charge separation process in the PSII RC by two-dimensional electronic spectroscopy (2DES) and Redfield modeling of the experimental data. However, while conventional Fourier transform analysis of the 2DES data allows oscillatory signatures of vibronic coherence to be identified in the frequency domain in the form of static 2D frequency maps, the real-time evolution of the coherences is lost. Here we apply for the first time wavelet analysis to the PSII RC 2DES data to obtain time-resolved 2D frequency maps. These maps allow us to demonstrate that (i) coherence between the excitons initiating the two different charge separation pathways is active for more than 500 fs, and (ii) coherence between exciton and charge-transfer states, the reactant and product of the charge separation reaction, respectively; is active for at least 1 ps. These findings imply that the PSII RC employs coherence (i) to sample competing electron transfer pathways, and ii) to perform directed, ultrafast and efficient electron transfer.

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.

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.

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.

Dark States in the Light-Harvesting complex 2 Revealed by Two-dimensional Electronic Spectroscopy.

Energy transfer and trapping in the light harvesting antennae of purple photosynthetic bacteria is an ultrafast process, which occurs with a quantum efficiency close to unity. However the mechanisms behind this process have not yet been fully understood. Recently it was proposed that low-lying energy dark states, such as charge transfer states and polaron pairs, play an important role in the dynamics and directionality of energy transfer. However, it is difficult to directly detect those states because of their small transition dipole moment and overlap with the B850/B870 exciton bands. Here we present a new experimental approach, which combines the selectivity of two-dimensional electronic spectroscopy with the availability of genetically modified light harvesting complexes, to reveal the presence of those dark states in both the genetically modified and the wild-type light harvesting 2 complexes of Rhodopseudomonas palustris. We suggest that Nature has used the unavoidable charge transfer processes that occur when LH pigments are concentrated to enhance and direct the flow of energy.

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.

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.