Concentration Quenching of Fluorescence Decay Kinetics of Molecular Systems.

Fluorescence concentration quenching occurs when increasing molecular concentration of fluorophores results in a decreasing fluorescence quantum yield. Even though this phenomenon has been studied for decades, its mechanisms and signatures are not yet fully understood. The complexity of the problem arises due to energy migration and trapping in huge networks of molecules. Most of the available theoretical work focuses on integral quantities like fluorescence quantum yield and mean excitation lifetime. In this work, we present a numerical study of the fluorescence decay kinetics of three-dimensional and two-dimensional molecular systems. We investigate the differences arising from the variations in models of trap formations. We also analyze the influence of the molecular orientations to the fluorescence decay kinetics. We compare our results to the well-known analytical models and discuss their ranges of validity. Our findings suggest that the analytical models can provide inspiration for different ways of approximating the fluorescence kinetics, yet more detailed analysis of the experimental data should be done by comparison with numerical simulations.

Fluorescence quenching in aggregates of fucoxanthin-chlorophyll protein complexes: Interplay of fluorescing and dark states.

Diatoms, a major group of algae, account for about a quarter of the global primary production on Earth. These photosynthetic organisms face significant challenges due to light intensity variations in their underwater habitat. To avoid photodamage, they have developed very efficient non-photochemical quenching (NPQ) mechanisms. These mechanisms originate in their light-harvesting antenna - the fucoxanthin-chlorophyll protein (FCP) complexes. Spectroscopic studies of NPQ in vivo are often hindered by strongly overlapping signals from the photosystems and their antennae. Fortunately, in vitro FCP aggregates constitute a useful model system to study fluorescence (FL) quenching in diatoms. In this work, we present streak-camera FL measurements on FCPa and FCPb complexes, isolated from a centric diatom Cyclotella meneghiniana, and their aggregates. We find that spectra of non-aggregated FCP are dominated by a single fluorescing species, but the FL spectra of FCP aggregates additionally contain contributions from a redshifted emissive state. We relate this red state to a charge transfer state between chlorophyll c and chlorophyll a molecules. The FL quenching, on the other hand, is due to an additional dark state that involves incoherent energy transfer to the fucoxanthin carotenoids. Overall, the global picture of energy transfer and quenching in FCP aggregates is very similar to that of major light-harvesting complexes in higher plants (LHCII), but microscopic details between FCPs and LHCIIs differ significantly.

Two phases of trans-stilbene in a polystyrene matrix.

Variability in the spectral properties of solid conformations of stilbene under various external conditions still remains obscure. The photophysical properties of trans-stilbene solution in solid polystyrene glass have been studied by absorption and time-resolved fluorescence. Concentration-induced quenching has been observed for small concentrations of stilbene. At large concentrations, the spectroscopic characteristics become split between the two phases of the sample: single-molecule properties are responsible for absorption, while the micro-crystalline phase dominates in fluorescence. Ab initio and molecular dynamics analyses suggest permanent twisting of the stilbene molecular structure upon crystallization, which supports spectroscopic phase separation.

Structure-based model of fucoxanthin-chlorophyll protein complex: Calculations of chlorophyll electronic couplings.

Diatoms are a group of marine algae that are responsible for a significant part of global oxygen production. Adapted to life in an aqueous environment dominated by the blue-green light, their major light-harvesting antennae-fucoxanthin-chlorophyll protein complexes (FCPs)-exhibit different pigment compositions than of plants. Despite extensive experimental studies, until recently the theoretical description of excitation energy dynamics in these complexes was limited by the lack of high-resolution structural data. In this work, we use the recently resolved crystallographic information of the FCP complex from Phaeodactylum tricornutum diatom [Wang et al., Science 363, 6427 (2019)] and quantum chemistry-based calculations to evaluate the chlorophyll transition dipole moments, atomic transition charges from electrostatic potential, and the inter-chlorophyll couplings in this complex. The obtained structure-based excitonic couplings form the foundation for any modeling of stationary or time-resolved spectroscopic data. We also calculate the inter-pigment Förster energy transfer rates and identify two quickly equilibrating chlorophyll clusters.

Electronic and Vibrational Properties of Allene Carotenoids.

Carotenoids are conjugated linear molecules built from the repetition of terpene units, which display a large structural diversity in nature. They may, in particular, contain several types of side or end groups, which tune their functional properties, such as absorption position and photochemistry. We report here a detailed experimental study of the absorption and vibrational properties of allene-containing carotenoids, together with an extensive modeling of these experimental data. Our calculations can satisfactorily explain the electronic properties of vaucheriaxanthin, where the allene group introduces the equivalent of one C═C double bond into the conjugated C═C chain. The position of the electronic absorption of fucoxanthin and butanoyloxyfucoxanthin requires long-range corrections to be found correctly on the red side of that of vaucheriaxanthin; however, these corrections tend to overestimate the effect of the conjugated and nonconjugated C═O groups in these molecules. We show that the resonance Raman spectra of these carotenoids are largely perturbed by the presence of the allene group, with the two major Raman contributions split into two components. These perturbations are satisfactorily explained by modeling, through a gain in the Raman intensity of the C═C antisymmetric stretching mode, induced by the presence of the allene group in the carotenoid C═C chain.

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.

Aggregation-related quenching of LHCII fluorescence in liposomes revealed by single-molecule spectroscopy.

Incorporation of membrane proteins into reconstituted lipid membranes is a common approach for studying their structure and function relationship in a native-like environment. In this work, we investigated fluorescence properties of liposome-reconstituted major light-harvesting complexes of plants (LHCII). By utilizing liposome labelling with the fluorescent dye molecules and single-molecule microscopy techniques, we were able to study truly liposome-reconstituted LHCII and compare them with bulk measurements and liposome-free LHCII aggregates bound to the surface. Our results showed that fluorescence lifetime obtained in bulk and in single liposome measurements were correlated. The fluorescence lifetimes of LHCII were shorter for liposome-free LHCII than for reconstituted LHCII. In the case of liposome-reconstituted LHCII, fluorescence lifetime showed dependence on the protein density reminiscent to concentration quenching. The dependence of fluorescence lifetime of LHCII on the liposome size was not significant. Our results demonstrated that fluorescence quenching can be induced by LHCII - LHCII interactions in reconstituted membranes, most likely occurring via the same mechanism as photoprotective non-photochemical quenching in vivo.

Confronting FCP structure with ultrafast spectroscopy data: evidence for structural variations.

Diatoms are a major group of algae, responsible for a quarter of the global primary production on our planet. Their adaptation to marine environments is ensured by their light-harvesting antenna - the fucoxanthin-chlorophyll protein (FCP) complex, which absorbs strongly in the blue-green spectral region. Although these essential proteins have been the subject of many studies, for a long time their comprehensive description was not possible in the absence of structural data. Last year, the 3D structures of several FCP complexes were revealed. The structure of an FCP dimer was resolved by crystallography for the pennate diatom Phaeodactylum tricornutum [W. Wang et al., Science, 2019, 363, 6427] and the structure of the PSII supercomplex from the centric diatom Chaetoceros gracilis, containing several FCPs, was obtained by electron microscopy [X. Pi et al., Science, 2019, 365, 6452; R. Nagao et al., Nat. Plants, 2019, 5, 890]. In this Perspective article, we evaluate how precisely these structures may account for previously published ultrafast spectroscopy results, describing the excitation energy transfer in the FCP from another centric diatom Cyclotella meneghiniana. Surprisingly, we find that the published FCP structures cannot explain several observations obtained from ultrafast spectroscopy. Using the available structures, and results from electron microscopy, we construct a trimer-based FCP model for Cyclotella meneghiniana, consistent with ultrafast experimental data. As a whole, our observations suggest that the structures from the proteins belonging to the FCP family display larger variations than the equivalent LHC proteins in plants, which may reflect species-specific adaptations or original strategies for adapting to rapidly changing marine environments.

Unusual temperature dependence of the fluorescence decay in heterostructured stilbene.

Fluorescence spectra as well as the fluorescence decay kinetics of hot-pressed and sublimated films of stilbene have been studied in a wide temperature range, from 15 K up to room temperature. The fluorescence decay kinetics demonstrate unusual elongation of the excitation lifetime with a temperature increase. This is in contrast to the corresponding data of stilbene solutions in chloroform and in a polystyrene (PS) matrix. It is well known that the excitation dynamics of stilbene in solution and in a PS matrix is controlled by the molecular isomerization/twisting process of separate molecules. The data analysis and quantum chemistry calculations of stilbene aggregates suggest that the temperature dependence of the fluorescence kinetics of bulk stilbene solids can be explained by fast exciton diffusion, which yields a thermalized exciton distribution in a relatively small number of fluorescence centres. The temperature dependence of the distribution can thus explain the observed fluorescence decay lifetimes.

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.

Characterization of thymine microcrystals by CARS and SHG microscopy.

Identification of chemically homologous microcrystals in a polycrystal sample is a big challenge and requires developing specific highly sensitive tools. Second harmonic (SHG) and coherent anti-Stokes Raman scattering (CARS) spectroscopy can be used to reveal arrangement of thymine molecules, one of the DNA bases, in microcrystalline sample. Strong dependence of CARS and SHG intensity on the orientation of the linear polarization of the excitation light allows to obtain high resolution images of thymine microcrystals by additionally utilizing the scanning microscopy technique. Experimental findings and theoretical interpretation of the results are compared. Presented experimental data together with quantum chemistry-based theoretical interpretation allowed us to determine the most probable organization of the thymine molecules.

Light-harvesting complexes access analogue emissive states in different environments.

The light-harvesting complexes (LHCs) of plants can regulate the level of excitation in the photosynthetic membrane under fluctuating light by switching between different functional states with distinct fluorescence properties. One of the most fascinating yet obscure aspects of this regulation is how the vast conformational landscape of LHCs is modulated in different environments. Indeed, while in isolated antennae the highly fluorescent light-harvesting conformation dominates, LHC aggregates display strong fluorescence quenching, representing therefore a model system for the process of energy dissipation developed by plants to avoid photodamage in high light. This marked difference between the isolated and oligomeric conditions has led to the widespread belief that aggregation is the trigger for the photoprotective state of LHCs. Here, a detailed analysis of time-resolved fluorescence experiments performed on aggregates of CP29 - a minor LHC of plants - provides new insights into the heterogeneity of emissive states of this antenna. A comparison with the data on isolated CP29 reveals that, though aggregation can stabilize short-lived conformations to a certain extent, the massive quenching upon protein clustering is mainly achieved by energetic connectivity between complexes that maintain the same long-lived and dissipative states accessed in the isolated form. Our results also explain the typical far-red enhancement in the emission of antenna oligomers in terms of a sub-population of long-lived redshifted complexes competing with quenched complexes in the energy trapping. Finally, the role of selected chlorophylls in shaping the conformational landscape of the antenna is also addressed by studying mutants lacking specific pigments.

Benchmarking the forward-backward trajectory solution of the quantum-classical Liouville equation.

Various quantum-classical approaches to the simulation of processes taking place in real molecular systems have been shown to provide quantitatively correct results in a number of scenarios. However, it is not immediately clear how strongly the approximations related to the classical treatment of the system's environment compromise the accuracy of these methods. In this work, we present the analysis of the accuracy of the forward-backward trajectory solution (FBTS) of the quantum-classical Liouville equation. To this end, we simulate the excitation dynamics in a molecular dimer using the FBTS and the exact hierarchical equations of motion approach. To facilitate the understanding of the possible benefits of the FBTS, the simulations are also performed using a closely related quantum-classical Poisson Bracket Mapping Equation (PBME) method, as well as the well-known Förster and Redfield theories. We conclude that the FBTS is considerably more accurate than the PBME and the perturbative approaches for most realistic parameter sets and is, therefore, more versatile. We investigate the impact each parameter has on the accuracy of the FBTS. Our results can be used to predict whether the FBTS may be expected to yield satisfactory results when calculating system dynamics for the given system parameters.

Modeling Dynamic Conformations of Organic Molecules: Alkyne Carotenoids in Solution.

Calculating the spectroscopic properties of complex conjugated organic molecules in their relaxed state is far from simple. An additional complexity arises for flexible molecules in solution, where the rotational energy barriers are low enough so that nonminimum conformations may become dynamically populated. These metastable conformations quickly relax during the minimization procedures preliminary to density functional theory calculations, and so accounting for their contribution to the experimentally observed properties is problematic. We describe a strategy for stabilizing these nonminimum conformations in silico, allowing their properties to be calculated. Diadinoxanthin and alloxanthin present atypical vibrational properties in solution, indicating the presence of several conformations. Performing energy calculations in vacuo and polarizable continuum model calculations in different solvents, we found three different conformations with values for the δ dihedral angle of the end ring ca. 0, 180, and 90° with respect to the plane of the conjugated chain. The latter conformation, a nonglobal minimum, is not stable during the minimization necessary for modeling its spectroscopic properties. To circumvent this classical problem, we used a Car-Parinello MD supermolecular approach, in which diadinoxanthin was solvated by water molecules so that metastable conformations were stabilized by hydrogen-bonding interactions. We progressively removed the number of solvating waters to find the minimum required for this stabilization. This strategy represents the first modeling of a carotenoid in a distorted conformation and provides an accurate interpretation of the experimental data.

Analytical derivation of equilibrium state for open quantum system.

Calculation of the equilibrium state of an open quantum system interacting with a bath remains a challenge to this day, mostly due to a huge number of bath degrees of freedom. Here, we present an analytical expression for the reduced density operator in terms of an effective Hamiltonian for a high temperature case. Comparing with numerically exact results, we show that our theory is accurate for slow baths and up to intermediate system-bath coupling strengths. Our results demonstrate that the equilibrium state does not depend on the shape of spectral density in the slow bath regime. The key quantity in our theory is the effective coupling between the states, which depends exponentially on the ratio of the reorganization energy to temperature and, thus, has opposite temperature dependence than could be expected from the small polaron transformation.

Aggregation-Related Nonphotochemical Quenching in the Photosynthetic Membrane.

The photosynthetic apparatus of plants is a robust self-adjustable molecular system, able to function efficiently under varying environmental conditions. Under strong sunlight, it switches into photoprotective mode to avoid overexcitation by safely dissipating the excess absorbed light energy via nonphotochemical quenching (NPQ). Unfortunately, heterogeneous organization and simultaneous occurrence of multiple processes within the thylakoid membrane impede the study of natural NPQ under in vivo conditions; thus, usually artificially prepared antennae have been studied instead. However, it has never been shown directly that the origin of fluorescence quenching observed in these artificial systems underlies natural NPQ. Here we report the time-resolved fluorescence measurements of the dark-adapted and preilluminated-to induce NPQ-intact chloroplasts, performed over a broad temperature range. We show that their spectral response matches that observed in the LHCII aggregates, thus demonstrating explicitly for the first time that the latter in vitro system preserves essential properties of natural photoprotection.

Single-molecule microscopy studies of LHCII enriched in Vio or Zea.

Plants have developed multiple self-regulatory mechanisms to efficiently function under varying sunlight conditions. At high light intensities, non-photochemical quenching (NPQ) is activated on a molecular level, safely dissipating an excess excitation as heat. The exact molecular mechanism for NPQ is still under debate, but it is widely agreed that the direct participation of the carotenoid pigments is involved, one of the proposed candidate being the zeaxanthin. In this work, we performed fluorescence measurements of violaxanthin- and zeaxanthin-enriched major light-harvesting complexes (LHCII), in ensemble and at the single pigment-protein complex level, where aggregation is prevented by immobilization of LHCIIs onto a surface. We show that a selective enrichment of LHCII with violaxanthin or zeaxanthin affects neither the ability of LHCII to switch into a dissipative conformation nor the maximal level of induced quenching. However, the kinetics of the fluorescence decrease due to aggregation on the timescale of seconds are different, prompting towards a modulatory effect of zeaxanthin in the dynamics of quenching.

Two-dimensional spectroscopy for non-specialists.

Detailed studies of the excitation dynamics in photosynthetic pigment-proteins require an application of a wide range of spectroscopic methods. From the later part of the previous century, pump-probe and time-resolved fluorescence spectroscopy provided an impressive amount of information. Being simple to grasp, these methods are well-understood and widely used by the photosynthesis research community. In the last fifteen years, two-dimensional (2D) spectroscopy was developed. It has significant advantages over other methods, in particular higher temporal resolution available and higher signal-to-noise ratio. Even though it provides considerable opportunities in research, both its experimental realization and theoretical description are rather complicated, making it somewhat difficult to understand and apply. This makes an unfortunate gap in the community, with spectroscopy experts being able to use the technique, but sometimes lacking the relevant biological knowledge, while biologists having that knowledge are dubious about 2D spectroscopy due to the complexity of the approach. This publication is an attempt to fill this gap by providing an accessible introduction to the concepts, principles and possible applications of the 2D spectroscopy, aimed at the biologically trained members of the photosynthesis research community.

Fluorescence Microscopy of Single Liposomes with Incorporated Pigment-Proteins.

Reconstitution of transmembrane proteins into liposomes is a widely used method to study their behavior under conditions closely resembling the natural ones. However, this approach does not allow precise control of the liposome size, reconstitution efficiency, and the actual protein-to-lipid ratio in the formed proteoliposomes, which might be critical for some applications and/or interpretation of data acquired during the spectroscopic measurements. Here, we present a novel strategy employing methods of proteoliposome preparation, fluorescent labeling, purification, and surface immobilization that allow us to quantify these properties using fluorescence microscopy at the single-liposome level and for the first time apply it to study photosynthetic pigment-protein complexes LHCII. We show that LHCII proteoliposome samples, even after purification with a density gradient, always contain a fraction of nonreconstituted protein and are extremely heterogeneous in both protein density and liposome sizes. This strategy enables quantitative analysis of the reconstitution efficiency of different protocols and precise fluorescence spectroscopic study of various transmembrane proteins in a controlled nativelike environment.

Tracing feed-back driven exciton dynamics in molecular aggregates.

Perturbative treatment of excitation dynamics in molecular systems with respect to external interactions with a dissipative environment is extensively used for the description of excitation energy transfer and relaxation. However the simulated dynamics becomes sensitive to a specific representation basis set, which makes the conclusions obscure and questionable. We revisit questions of excitation creation patterns, coherent dynamics, relaxation and detection from a theoretical viewpoint, and demonstrate that a mixture of specific requirements should be met to observe coherent phenomena and incoherent decay processes. We discuss how intermixing of coherent components in relaxation phenomena is related to a non-perturbative regime of dynamics leading to nonlinear feed-back effects where bath relaxation also affects excitation wavepackets. We also discuss how bath equilibration causes local heating effects which is often neglected in numerical simulations. The parameters reflecting the complexity of the processes are related to excitation delocalization patterns in various basis representations. While these seem to be auxiliary nonobservable features, their evaluation allows better investigation of the physical behavior of quantum relaxation processes in molecular aggregate systems.