Excitation quenching in chlorophyll-carotenoid antenna systems: 'coherent' or 'incoherent'

Role of Quantum Information in HEOM Trajectories

Open quantum systems often operate in the non-Markovian regime where a finite history of a trajectory is intrinsic to its evolution. The degree of non-Markovianity for a trajectory may be measured in terms of the amount of information flowing from the bath back into the system. In this study, we consider how information flows through the auxiliary density operators (ADOs) in the hierarchical equations of motion. We consider three cases for a range of baths, underdamped, intermediate, and overdamped. By understanding how information flows, we are able to determine the relative importance of different ADOs within the hierarchy. We show that ADOs sharing a common Matsubara axis behave similarly, while ADOs on different Matsubara axes behave differently. Using this knowledge, we are able to truncate hierarchies significantly, thus reducing the computation time, while obtaining qualitatively similar results. This is illustrated by comparing 2D electronic spectra for a molecule with an underdamped vibration subsumed into the bath spectral density.

Unravelling the fluorescence kinetics of light-harvesting proteins with simulated measurements

The plant light-harvesting pigment-protein complex LHCII is the major antenna sub-unit of PSII and is generally (though not universally) accepted to play a role in photoprotective energy dissipation under high light conditions, a process known Non-Photochemical Quenching (NPQ). The underlying mechanisms of energy trapping and dissipation within LHCII are still debated. Various models have been proposed for the underlying molecular detail of NPQ, but they are often based on different interpretations of very similar transient absorption measurements of isolated complexes. Here we present a simulated measurement of the fluorescence decay kinetics of quenched LHCII aggregates to determine whether this relatively simple measurement can discriminate between different potential NPQ mechanisms. We simulate not just the underlying physics (excitation, energy migration, quenching and singlet-singlet annihilation) but also the signal detection and typical experimental data analysis. Comparing this to a selection of published fluorescence decay kinetics we find that: (1) Different proposed quenching mechanisms produce noticeably different fluorescence kinetics even at low (annihilation free) excitation density, though the degree of difference is dependent on pulse width. (2) Measured decay kinetics are consistent with most LHCII trimers becoming relatively slow excitation quenchers. A small sub-population of very fast quenchers produces kinetics which do not resemble any observed measurement. (3) It is necessary to consider at least two distinct quenching mechanisms in order to accurately reproduce experimental kinetics, supporting the idea that NPQ is not a simple binary switch.

Impact of Structure, Coupling Scheme, and State of Interest on the Energy Transfer in CP29

The Qy and Bx excitation energy transfer (EET) in the minor light-harvesting complex CP29 (LHCII B4.1) antenna complex of Pisum sativum was characterized using a computational approach. We applied Förster resonance energy transfer (FRET) and the transition density cube (TDC) method to estimate the Coulombic coupling, based on a combination of classical molecular dynamics and quantum mechanics/molecular mechanics calculations. Employing TDC instead of FRET mostly affects the EET between chlorophylls (Chls) and carotenoids (Crts), as expected due to the Crts being spatially more challenging for FRET. Only between Chls, effects are found to be small (about only 0.1 EET efficiency change when introducing TDC instead of FRET). Effects of structural sampling were found to be small, illustrated by a small average standard deviation for the Qy state coupling elements (FRET/TDC: 0.97/0.94 cm-1). Due to the higher flexibility of the Bx state, the corresponding deviations are larger (FRET/TDC between Chl-Chl pairs: 17.58/22.67 cm-1, between Crt-Chl pairs: 62.58/31.63 cm-1). In summary, it was found for the Q band that the coupling between Chls varies only slightly depending on FRET or TDC, resulting in a minute effect on EET acceptor preference. In contrast, the coupling in the B band spectral region is found to be more affected. Here, the S2 (1Bu) states of the spatially challenging Crts may act as acceptors in addition to the B states of the Chls. Depending on FRET or TDC, several Chls show different Chl-to-Crt couplings. Interestingly, the EET between Chls or Crts in the B band is found to often outcompete the corresponding decay processes. The individual efficiencies for B band EET to Crts vary however strongly with the chosen coupling scheme (e.g., up to 0.29/0.99 FRET/TDC efficiency for the Chl a604/neoxanthin pair). Thus, the choice of the coupling scheme must involve a consideration of the state of interest.

Simultaneous Quantification and Visualization of Photosynthetic Pigments in Lycopersicon esculentum Mill. under Different Levels of Nitrogen Application with Visible-Near Infrared Hyperspectral Imaging Technology

Leaf photosynthetic pigments play a crucial role in evaluating nutritional elements and physiological states. In facility agriculture, it is vital to rapidly and accurately obtain the pigment content and distribution of leaves to ensure precise water and fertilizer management. In our research, we utilized chlorophyll a (Chla), chlorophyll b (Chlb), total chlorophylls (Chls) and total carotenoids (Cars) as indicators to study the variations in the leaf positions of Lycopersicon esculentum Mill. Under 10 nitrogen concentration applications, a total of 2610 leaves (435 samples) were collected using visible-near infrared hyperspectral imaging (VNIR-HSI). In this study, a "coarse-fine" screening strategy was proposed using competitive adaptive reweighted sampling (CARS) and the iteratively retained informative variable (IRIV) algorithm to extract the characteristic wavelengths. Finally, simultaneous and quantitative models were established using partial least squares regression (PLSR). The CARS-IRIV-PLSR was used to create models to achieve a better prediction effect. The coefficient determination (R2), root mean square error (RMSE) and ratio performance deviation (RPD) were predicted to be 0.8240, 1.43 and 2.38 for Chla; 0.8391, 0.53 and 2.49 for Chlb; 0.7899, 2.24 and 2.18 for Chls; and 0.7577, 0.27 and 2.03 for Cars, respectively. The combination of these models with the pseudo-color image allowed for a visual inversion of the content and distribution of the pigment. These findings have important implications for guiding pigment distribution, nutrient diagnosis and fertilization decisions in plant growth management.

Combined contributions of carotenoids and chlorophylls in two-photon spectra of photosynthetic pigment-protein complexes-A new way to quantify carotenoid dark state to chlorophyll energy transfer?

Transitions into the first excited state of carotenoids, Car S₁, are optically forbidden in conventional one-photon excitation (OPE) but are possible via two-photon excitation (TPE). This can be used to quantify the amount of Car S₁ to Chlorophyll (Chl) energy transfer in pigment-protein complexes and plants by observing the chlorophyll fluorescence intensity after TPE in comparison to the intensity observed after direct chlorophyll OPE. A parameter, Φ_Coupling ^{Car S1-Chl}, can be derived that directly reflects relative differences or changes in the Car S₁ → Chl energy transfer of different pigment-protein complexes and even living plants. However, very careful calibrations are necessary to ensure similar OPE and TPE excitation probabilities and transition energies. In plants, the exact same sample spot must be observed at the same time. All this is experimentally quite demanding. Φ_Coupling ^{Car S1-Chl} also corrects intrinsically for direct chlorophyll TPE caused by larger chlorophyll excesses in the complexes, but recently it turned out that in certain TPE wavelengths ranges, its contribution can be quite large. Fortunately, this finding opens also the possibility of determining Φ_Coupling ^{Car S1-Chl} in a much easier way by directly comparing values in TPE spectra observed at wavelengths that are either more dominated by Cars or Chls. This avoids tedious comparisons of OPE and TPE experiments and potentially allows measurement at even only two TPE wavelengths. Here, we explored this new approach to determine Φ_Coupling ^{Car S1-Chl} directly from single TPE spectra and present first examples using known experimental spectra from Cars, Chl a, Chl b, LHC II, and PS 1.

The influence of a Hamiltonian vibration vs a bath vibration on the 2D electronic spectra of a homodimer

We elucidate the influence of the system–bath boundary placement within an open quantum system, with emphasis on the two-dimensional electronic spectra, through the application of the hierarchical equations of motion formalism for an exciton system. We apply two different models, the Hamiltonian vibration model (HVM) and bath vibration model (BVM), to a monomer and a homodimer. In the HVM, we specifically include the vibronic states in the Hamiltonian capturing vibronic quenching, whereas in the BVM, all vibrational details are contained within the bath and described by an underdamped spectral density. The resultant spectra are analyzed in terms of energetic peak position and thermodynamic broadening precision in order to evaluate the efficacy of the two models. The HVM produces 2D spectra with accurate peak positional information, while the BVM is well suited to modeling dynamic peak broadening. For the monomer, both models produce equivalent spectra in the limit where additional damping associated with the underdamped vibration in the BVM approaches zero. This is supported by analytical results. However, for the homodimer, the BVM spectra are redshifted with respect to the HVM due to an absence of vibronic quenching in the BVM. The computational efficiency of the two models is also discussed in order to inform us of the most appropriate use of each method.

Stark absorption and Stark fluorescence spectroscopies: Theory and simulations

Stark spectroscopy experiments are widely used to study the properties of molecular systems, particularly those containing charge-transfer (CT) states. However, due to the small transition dipole moments and large static dipole moments of the CT states, the standard interpretation of the Stark absorption and Stark fluorescence spectra in terms of the Liptay model may be inadequate. In this work, we provide a theoretical framework for calculations of Stark absorption and Stark fluorescence spectra and propose new methods of simulations that are based on the quantum-classical theory. In particular, we use the forward-backward trajectory solution and a variant of the Poisson bracket mapping equation, which have been recently adapted for the calculation of conventional (field-free) absorption and fluorescence spectra. For comparison, we also apply the recently proposed complex time-dependent Redfield theory, while exact results are obtained using the hierarchical equations of motion approach. We show that the quantum-classical methods produce accurate results for a wide range of systems, including those containing CT states. The CT states contribute significantly to the Stark spectra, and the standard Liptay formalism is shown to be inapplicable for the analysis of spectroscopic data in those cases. We demonstrate that states with large static dipole moments may cause a pronounced change in the total fluorescence yield of the system in the presence of an external electric field. This effect is correctly captured by the quantum-classical methods, which should therefore prove useful for further studies of Stark spectra of real molecular systems. As an example, we calculate the Stark spectra for the Fenna-Matthews-Olson complex of green sulfur bacteria.

Quantum-Classical Approach for Calculations of Absorption and Fluorescence: Principles and Applications

Absorption and fluorescence spectroscopy techniques provide a wealth of information on molecular systems. The simulations of such experiments remain challenging, however, despite the efforts put into developing the underlying theory. An attractive method of simulating the behavior of molecular systems is provided by the quantum-classical theory─it enables one to keep track of the state of the bath explicitly, which is needed for accurate calculations of fluorescence spectra. Unfortunately, until now there have been relatively few works that apply quantum-classical methods for modeling spectroscopic data. In this work, we seek to provide a framework for the calculations of absorption and fluorescence lineshapes of molecular systems using the methods based on the quantum-classical Liouville equation, namely, the forward-backward trajectory solution (FBTS) and the non-Hamiltonian variant of the Poisson bracket mapping equation (PBME-nH). We perform calculations on a molecular dimer and the photosynthetic Fenna-Matthews-Olson complex. We find that in the case of absorption, the FBTS outperforms PBME-nH, consistently yielding highly accurate results. We next demonstrate that for fluorescence calculations, the method of choice is a hybrid approach, which we call PBME-nH-Jeff, that utilizes the effective coupling theory [Gelzinis, A.; J. Chem. Phys. 2020, 152, 051103] to estimate the excited state equilibrium density operator. Thus, we find that FBTS and PBME-nH-Jeff are excellent candidates for simulating, respectively, absorption and fluorescence spectra of real molecular systems.

Ultrafast energy transfer between lipid-linked chromophores and plant light-harvesting complex II

Light-Harvesting Complex II (LHCII) is a membrane protein found in plant chloroplasts that has the crucial role of absorbing solar energy and subsequently performing excitation energy transfer to the reaction centre subunits of Photosystem II. LHCII provides strong absorption of blue and red light, however, it has minimal absorption in the green spectral region where solar irradiance is maximal. In a recent proof-of-principle study, we enhanced the absorption in this spectral range by developing a biohybrid system where LHCII proteins together with lipid-linked Texas Red (TR) chromophores were assembled into lipid membrane vesicles. The utility of these systems was limited by significant LHCII quenching due to protein-protein interactions and heterogeneous lipid structures. Here, we organise TR and LHCII into a lipid nanodisc, which provides a homogeneous, well-controlled platform to study the interactions between TR molecules and single LHCII complexes. Fluorescence spectroscopy determined that TR-to-LHCII energy transfer has an efficiency of at least 60%, resulting in a 262% enhancement of LHCII fluorescence in the 525-625 nm range, two-fold greater than in the previous system. Ultrafast transient absorption spectroscopy revealed two time constants of 3.7 and 128 ps for TR-to-LHCII energy transfer. Structural modelling and theoretical calculations indicate that these timescales correspond to TR-lipids that are loosely- or tightly-associated with the protein, respectively, with estimated TR-to-LHCII separations of ∼3.5 nm and ∼1 nm. Overall, we demonstrate that a nanodisc-based biohybrid system provides an idealised platform to explore the photophysical interactions between extrinsic chromophores and membrane proteins with potential applications in understanding more complex natural or artificial photosynthetic systems.

Trivial Excitation Energy Transfer to Carotenoids Is an Unlikely Mechanism for Non-photochemical Quenching in LHCII

Higher plants defend themselves from bursts of intense light via the mechanism of Non-Photochemical Quenching (NPQ). It involves the Photosystem II (PSII) antenna protein (LHCII) adopting a conformation that favors excitation quenching. In recent years several structural models have suggested that quenching proceeds via energy transfer to the optically forbidden and short-lived S ₁ states of a carotenoid. It was proposed that this pathway was controlled by subtle changes in the relative orientation of a small number of pigments. However, quantum chemical calculations of S ₁ properties are not trivial and therefore its energy, oscillator strength and lifetime are treated as rather loose parameters. Moreover, the models were based either on a single LHCII crystal structure or Molecular Dynamics (MD) trajectories about a single minimum. Here we try and address these limitations by parameterizing the vibronic structure and relaxation dynamics of lutein in terms of observable quantities, namely its linear absorption (LA), transient absorption (TA) and two-photon excitation (TPE) spectra. We also analyze a number of minima taken from an exhaustive meta-dynamical search of the LHCII free energy surface. We show that trivial, Coulomb-mediated energy transfer to S ₁ is an unlikely quenching mechanism, with pigment movements insufficiently pronounced to switch the system between quenched and unquenched states. Modulation of S ₁ energy level as a quenching switch is similarly unlikely. Moreover, the quenching predicted by previous models is possibly an artifact of quantum chemical over-estimation of S ₁ oscillator strength and the real mechanism likely involves short-range interaction and/or non-trivial inter-molecular states.

A Protein Environment-Modulated Energy Dissipation Channel in LHCII Antenna Complex

The major light-harvesting complex of photosystem II (LHCII) is the main contributor to sunlight energy harvesting in plants. The flexible design of LHCII underlies a photoprotective mechanism whereby this complex switches to a dissipative state in response to high light stress, allowing the rapid dissipation of excess excitation energy (non-photochemical quenching, NPQ). In this work, we locked single LHCII trimers in a quenched conformation after immobilization of the complexes in polyacrylamide gels to impede protein interactions. A comparison of their pigment excited-state dynamics with quenched LHCII aggregates in buffer revealed the presence of a new spectral band at 515 nm arising after chlorophyll excitation. This is suggested to be the signature of a carotenoid excited state, linked to the quenching of chlorophyll singlet excited states. Our data highlight the marked sensitivity of pigment excited-state dynamics in LHCII to structural changes induced by the environment.