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Timpmann K, Rätsep M, Kangur L, Lehtmets A, Wang-Otomo ZY, Freiberg A. Exciton Origin of Color-Tuning in Ca 2+-Binding Photosynthetic Bacteria. Int J Mol Sci 2021; 22:ijms22147338. [PMID: 34298960 PMCID: PMC8303132 DOI: 10.3390/ijms22147338] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2021] [Revised: 07/02/2021] [Accepted: 07/06/2021] [Indexed: 11/16/2022] Open
Abstract
Flexible color adaptation to available ecological niches is vital for the photosynthetic organisms to thrive. Hence, most purple bacteria living in the shade of green plants and algae apply bacteriochlorophyll a pigments to harvest near infra-red light around 850–875 nm. Exceptions are some Ca2+-containing species fit to utilize much redder quanta. The physical basis of such anomalous absorbance shift equivalent to ~5.5 kT at ambient temperature remains unsettled so far. Here, by applying several sophisticated spectroscopic techniques, we show that the Ca2+ ions bound to the structure of LH1 core light-harvesting pigment–protein complex significantly increase the couplings between the bacteriochlorophyll pigments. We thus establish the Ca-facilitated enhancement of exciton couplings as the main mechanism of the record spectral red-shift. The changes in specific interactions such as pigment–protein hydrogen bonding, although present, turned out to be secondary in this regard. Apart from solving the two-decade-old conundrum, these results complement the list of physical principles applicable for efficient spectral tuning of photo-sensitive molecular nano-systems, native or synthetic.
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Affiliation(s)
- Kõu Timpmann
- Institute of Physics, University of Tartu, W. Ostwald Str. 1, 50411 Tartu, Estonia; (K.T.); (M.R.); (L.K.); (A.L.)
| | - Margus Rätsep
- Institute of Physics, University of Tartu, W. Ostwald Str. 1, 50411 Tartu, Estonia; (K.T.); (M.R.); (L.K.); (A.L.)
| | - Liina Kangur
- Institute of Physics, University of Tartu, W. Ostwald Str. 1, 50411 Tartu, Estonia; (K.T.); (M.R.); (L.K.); (A.L.)
| | - Alexandra Lehtmets
- Institute of Physics, University of Tartu, W. Ostwald Str. 1, 50411 Tartu, Estonia; (K.T.); (M.R.); (L.K.); (A.L.)
| | | | - Arvi Freiberg
- Institute of Physics, University of Tartu, W. Ostwald Str. 1, 50411 Tartu, Estonia; (K.T.); (M.R.); (L.K.); (A.L.)
- Correspondence:
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Reppert M. Delocalization Effects in Chlorophyll Fluorescence: Nonperturbative Line Shape Analysis of a Vibronically Coupled Dimer. J Phys Chem B 2020; 124:10024-10033. [PMID: 33138372 DOI: 10.1021/acs.jpcb.0c05789] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Non-adiabatic vibrational/electronic (vibronic) interactions in photosynthetic pigment/protein complexes (PPCs) have recently attracted considerable interest as a potential source for long-lived dynamic coherence and optimized light harvesting. The analysis of such effects is limited, however, by the complexity of the vibrational spectrum of biological pigments such as chlorophyll (Chl) molecules, which often makes numerical calculations prohibitively expensive and complicates the interpretation of experimental spectroscopic data. This work contributes to both challenges by using numerically exact computational methods to systematically examine vibronic mixing effects in the low-temperature fluorescence spectra of a Chl dimer possessing a full complement of local vibrations, using parameters extracted from experimental data. The results highlight the varying roles local vibrations can play in energy-transfer dynamics, both enhancing delocalization through vibronic resonance and, conversely, inducing dynamic localization by acting as a "self-bath" for local electronic transitions. In the specific context of line-narrowed fluorescence, the results indicate that, while low-frequency features are strongly suppressed by delocalization, high-frequency modes are likely to be dynamically localized in the parameter regime relevant to most photosynthetic complexes.
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Affiliation(s)
- Mike Reppert
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907-2050, United States
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Leiger K, Linnanto JM, Freiberg A. Establishment of the Qy Absorption Spectrum of Chlorophyll a Extending to Near-Infrared. Molecules 2020; 25:molecules25173796. [PMID: 32825445 PMCID: PMC7503670 DOI: 10.3390/molecules25173796] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2020] [Revised: 08/17/2020] [Accepted: 08/19/2020] [Indexed: 02/06/2023] Open
Abstract
A weak absorption tail related to the Qy singlet electronic transition of solvated chlorophyll a is discovered using sensitive anti-Stokes fluorescence excitation spectroscopy. The quasi-exponentially decreasing tail was, at ambient temperature, readily observable as far as -2400 cm-1 from the absorption peak and at relative intensity of 10-7. The tail also weakened rapidly upon cooling the sample, implying its basic thermally activated nature. The shape of the spectrum as well as its temperature dependence were qualitatively well reproduced by quantum chemical calculations involving the pigment intramolecular vibrational modes, their overtones, and pairwise combination modes, but no intermolecular/solvent modes. A similar tail was observed earlier in the case of bacteriochlorophyll a, suggesting generality of this phenomenon. Long vibronic red tails are, thus, expected to exist in all pigments of light-harvesting relevance at physiological temperatures.
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Affiliation(s)
- Kristjan Leiger
- Institute of Physics, University of Tartu, W. Ostwaldi 1, 51011 Tartu, Estonia; (K.L.); (J.M.L.)
| | - Juha Matti Linnanto
- Institute of Physics, University of Tartu, W. Ostwaldi 1, 51011 Tartu, Estonia; (K.L.); (J.M.L.)
| | - Arvi Freiberg
- Institute of Physics, University of Tartu, W. Ostwaldi 1, 51011 Tartu, Estonia; (K.L.); (J.M.L.)
- Institute of Molecular and Cell Biology, University of Tartu, Riia 23, 51014 Tartu, Estonia
- Estonian Academy of Sciences, Kohtu 6, 10130 Tallinn, Estonia
- Correspondence:
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Cupellini L, Bondanza M, Nottoli M, Mennucci B. Successes & challenges in the atomistic modeling of light-harvesting and its photoregulation. BIOCHIMICA ET BIOPHYSICA ACTA-BIOENERGETICS 2019; 1861:148049. [PMID: 31386831 DOI: 10.1016/j.bbabio.2019.07.004] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2019] [Revised: 07/10/2019] [Accepted: 07/15/2019] [Indexed: 12/21/2022]
Abstract
Light-harvesting is a crucial step of photosynthesis. Its mechanisms and related energetics have been revealed by a combination of experimental investigations and theoretical modeling. The success of theoretical modeling is largely due to the application of atomistic descriptions combining quantum chemistry, classical models and molecular dynamics techniques. Besides the important achievements obtained so far, a complete and quantitative understanding of how the many different light-harvesting complexes exploit their structural specificity is still missing. Moreover, many questions remain unanswered regarding the mechanisms through which light-harvesting is regulated in response to variable light conditions. Here we show that, in both fields, a major role will be played once more by atomistic descriptions, possibly generalized to tackle the numerous time and space scales on which the regulation takes place: going from the ultrafast electronic excitation of the multichromophoric aggregate, through the subsequent conformational changes in the embedding protein, up to the interaction between proteins.
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Affiliation(s)
- Lorenzo Cupellini
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, Pisa 56124, Italy
| | - Mattia Bondanza
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, Pisa 56124, Italy
| | - Michele Nottoli
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, Pisa 56124, Italy
| | - Benedetta Mennucci
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, Pisa 56124, Italy.
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Leiger K, Linnanto JM, Rätsep M, Timpmann K, Ashikhmin AA, Moskalenko AA, Fufina TY, Gabdulkhakov AG, Freiberg A. Controlling Photosynthetic Excitons by Selective Pigment Photooxidation. J Phys Chem B 2018; 123:29-38. [DOI: 10.1021/acs.jpcb.8b08083] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Kristjan Leiger
- Institute of Physics, University of Tartu, W. Ostwaldi 1, Tartu 50411, Estonia
| | - Juha Matti Linnanto
- Institute of Physics, University of Tartu, W. Ostwaldi 1, Tartu 50411, Estonia
| | - Margus Rätsep
- Institute of Physics, University of Tartu, W. Ostwaldi 1, Tartu 50411, Estonia
| | - Kõu Timpmann
- Institute of Physics, University of Tartu, W. Ostwaldi 1, Tartu 50411, Estonia
| | | | | | | | | | - Arvi Freiberg
- Institute of Physics, University of Tartu, W. Ostwaldi 1, Tartu 50411, Estonia
- Institute of Molecular and Cell Biology, University of Tartu, Riia 23, Tartu 51014, Estonia
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Cupellini L, Caprasecca S, Guido CA, Müh F, Renger T, Mennucci B. Coupling to Charge Transfer States is the Key to Modulate the Optical Bands for Efficient Light Harvesting in Purple Bacteria. J Phys Chem Lett 2018; 9:6892-6899. [PMID: 30449098 DOI: 10.1021/acs.jpclett.8b03233] [Citation(s) in RCA: 47] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
The photosynthetic apparatus of purple bacteria uses exciton delocalization and static disorder to modulate the position and broadening of its absorption bands, leading to efficient light harvesting. Its main antenna complex, LH2, contains two rings of identical bacteriochlorophyll pigments, B800 and B850, absorbing at 800 and 850 nm, respectively. It has been an unsolved problem why static disorder of the strongly coupled B850 ring is several times larger than that of the B800 ring. Here we show that mixing between excitons and charge transfer states in the B850 ring is responsible for the effect. The linear absorption spectrum of the LH2 system is simulated by using a multiscale approach with an exciton Hamiltonian generalized to include the charge transfer states that involve adjacent pigment pairs, with static disorder modeled microscopically by molecular dynamics simulations. Our results show that sufficient inhomogeneous broadening of the B850 band, needed for efficient light harvesting, is only obtained by utilizing static disorder in the coupling between local excited and interpigment charge transfer states.
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Affiliation(s)
- Lorenzo Cupellini
- Dipartimento di Chimica e Chimica Industriale , University of Pisa , via G. Moruzzi 13 , 56124 Pisa , Italy
| | - Stefano Caprasecca
- Dipartimento di Chimica e Chimica Industriale , University of Pisa , via G. Moruzzi 13 , 56124 Pisa , Italy
| | - Ciro A Guido
- Dipartimento di Chimica e Chimica Industriale , University of Pisa , via G. Moruzzi 13 , 56124 Pisa , Italy
| | - Frank Müh
- Institute of Theoretical Physics, Department of Theoretical Biophysics , Johannes Kepler University Linz , Altenberger Strasse 69 , 4040 Linz , Austria
| | - Thomas Renger
- Institute of Theoretical Physics, Department of Theoretical Biophysics , Johannes Kepler University Linz , Altenberger Strasse 69 , 4040 Linz , Austria
| | - Benedetta Mennucci
- Dipartimento di Chimica e Chimica Industriale , University of Pisa , via G. Moruzzi 13 , 56124 Pisa , Italy
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Pieper J, Artene P, Rätsep M, Pajusalu M, Freiberg A. Evaluation of Electron–Phonon Coupling and Spectral Densities of Pigment–Protein Complexes by Line-Narrowed Optical Spectroscopy. J Phys Chem B 2018; 122:9289-9301. [DOI: 10.1021/acs.jpcb.8b05220] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
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Rätsep M, Muru R, Freiberg A. High temperature limit of photosynthetic excitons. Nat Commun 2018; 9:99. [PMID: 29311621 PMCID: PMC5758513 DOI: 10.1038/s41467-017-02544-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2017] [Accepted: 12/06/2017] [Indexed: 11/24/2022] Open
Abstract
Excitons in light-harvesting complexes are known to significantly improve solar-energy harnessing. Here we demonstrate photosynthetic excitons at super-physiological temperatures reaching 60–80 °C in different species of mesophilic photosynthetic bacteria. It is shown that the survival of light-harvesting excitons in the peripheral LH2 antennae is restricted by thermal decomposition of the pigment–protein complex rather than by any intrinsic property of excitons. The regular spatial organization of the bacteriochlorophyll a pigments supporting excitons in this complex is lost upon the temperature-induced breakdown of its tertiary structure. Secondary structures of the complexes survive even higher temperatures. The discovered pivotal role of the protein scaffold in the stabilization of excitons comprises an important aspect of structure–function relationship in biology. These results also intimately entangle the fundamental issues of quantum mechanical concepts in biology and in the folding of proteins. Excitons in light-harvesting complexes are known to significantly improve solar energy harnessing. Here, the authors investigate and explain extreme robustness against temperature of excitons in purple photosynthetic bacteria.
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Affiliation(s)
- Margus Rätsep
- Institute of Physics, University of Tartu, W. Ostwald Str. 1, 50411, Tartu, Estonia
| | - Renata Muru
- Institute of Physics, University of Tartu, W. Ostwald Str. 1, 50411, Tartu, Estonia
| | - Arvi Freiberg
- Institute of Physics, University of Tartu, W. Ostwald Str. 1, 50411, Tartu, Estonia. .,Institute of Molecular and Cell Biology, University of Tartu, Riia 23, 51010, Tartu, Estonia.
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Rätsep M, Timpmann K, Kawakami T, Wang-Otomo ZY, Freiberg A. Spectrally Selective Spectroscopy of Native Ca-Containing and Ba-Substituted LH1-RC Core Complexes from Thermochromatium tepidum. J Phys Chem B 2017; 121:10318-10326. [PMID: 29058423 DOI: 10.1021/acs.jpcb.7b07841] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The LH1-RC core complex from the thermophilic photosynthetic purple sulfur bacterium Thermochromatium tepidum has recently attracted interest of many researchers because of its several unique properties, such as increased robustness against environmental hardships and the much red-shifted near-infrared absorption spectrum of the LH1 antenna exciton polarons. The known near-atomic-resolution crystal structure of the complex well supported this attention. Yet several mechanistic aspects of the complex prominence remained to be understood. In this work, samples of the native, Ca2+-containing core complexes were investigated along with those destabilized by Ba2+ substitution, using various spectrally selective steady-state and picosecond time-resolved spectroscopic techniques at physiological and cryogenic temperatures. As a result, the current interpretation of exciton spectra of the complex was significantly clarified. Specifically, by evaluating the homogeneous and inhomogeneous compositions of the spectra, we showed that there is little to no effect of cation substitution on the dynamic or kinetic properties of antenna excitons. Reasons of the extra red shift of absorption/fluorescence spectra observed in the Ca-LH1-RC and not in the Ba-LH1-RC complex should thus be searched in subtle structural differences following the inclusion of different cations into the core complex scaffold.
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Affiliation(s)
- Margus Rätsep
- Institute of Physics, University of Tartu , W. Ostwald Str. 1, 50411 Tartu, Estonia
| | - Kõu Timpmann
- Institute of Physics, University of Tartu , W. Ostwald Str. 1, 50411 Tartu, Estonia
| | | | | | - Arvi Freiberg
- Institute of Physics, University of Tartu , W. Ostwald Str. 1, 50411 Tartu, Estonia.,Institute of Molecular and Cell Biology, University of Tartu , Riia 23, 51010 Tartu, Estonia
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Kell A, Jassas M, Acharya K, Hacking K, Cogdell RJ, Jankowiak R. Conformational Complexity in the LH2 Antenna of the Purple Sulfur Bacterium Allochromatium vinosum Revealed by Hole-Burning Spectroscopy. J Phys Chem A 2017; 121:4435-4446. [PMID: 28531352 DOI: 10.1021/acs.jpca.7b03188] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
This work discusses the protein conformational complexity of the B800-850 LH2 complexes from the purple sulfur bacterium Allochromatium vinosum, focusing on the spectral characteristics of the B850 chromophores. Low-temperature B850 absorption and the split B800 band shift blue and red, respectively, at elevated temperatures, revealing isosbestic points. The latter indicates the presence of two (unresolved) conformations of B850 bacteriochlorophylls (BChls), referred to as conformations 1 and 2, and two conformations of B800 BChls, denoted as B800R and B800B. The energy differences between average site energies of conformations 1 and 2, and B800R and B800B are similar (∼200 cm-1), suggesting weak and strong hydrogen bonds linking two major subpopulations of BChls and the protein scaffolding. Although conformations 1 and 2 of the B850 chromophores, and B800R and B800B, exist in the ground state, selective excitation leads to 1 → 2 and B800R → B800B phototransformations. Different static inhomogeneous broadening is revealed for the lowest energy exciton states of B850 (fwhm ∼195 cm-1) and B800R (fwhm ∼140 cm-1). To describe the 5 K absorption spectrum and the above-mentioned conformations, we employ an exciton model with dichotomous protein conformation disorder. We show that both experimental data and the modeling study support a two-site model with strongly and weakly hydrogen-bonded B850 and B800 BChls, which under illumination undergo conformational changes, most likely caused by proton dynamics.
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Affiliation(s)
| | | | | | - Kirsty Hacking
- Institute of Molecular Cell and Systems Biology, College of Medical, Veterinary and Life Sciences, University of Glasgow , Glasgow G12 8TA, Scotland
| | - Richard J Cogdell
- Institute of Molecular Cell and Systems Biology, College of Medical, Veterinary and Life Sciences, University of Glasgow , Glasgow G12 8TA, Scotland
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Challenges facing an understanding of the nature of low-energy excited states in photosynthesis. BIOCHIMICA ET BIOPHYSICA ACTA-BIOENERGETICS 2016; 1857:1627-1640. [PMID: 27372198 DOI: 10.1016/j.bbabio.2016.06.010] [Citation(s) in RCA: 63] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2016] [Revised: 06/27/2016] [Accepted: 06/28/2016] [Indexed: 01/09/2023]
Abstract
While the majority of the photochemical states and pathways related to the biological capture of solar energy are now well understood and provide paradigms for artificial device design, additional low-energy states have been discovered in many systems with obscure origins and significance. However, as low-energy states are naively expected to be critical to function, these observations pose important challenges. A review of known properties of low energy states covering eight photochemical systems, and options for their interpretation, are presented. A concerted experimental and theoretical research strategy is suggested and outlined, this being aimed at providing a fully comprehensive understanding.
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Leiger K, Freiberg A. Up-converted fluorescence from photosynthetic light-harvesting complexes linearly dependent on excitation intensity. PHOTOSYNTHESIS RESEARCH 2016; 127:77-87. [PMID: 25764015 DOI: 10.1007/s11120-015-0117-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2014] [Accepted: 03/05/2015] [Indexed: 06/04/2023]
Abstract
Weak up-converted fluorescence related to bacteriochlorophyll a was recorded from various detergent-isolated and membrane-embedded light-harvesting pigment-protein complexes as well as from the functional membranes of photosynthetic purple bacteria under continuous-wave infrared laser excitation at 1064 nm, far outside the optically allowed singlet absorption bands of the chromophore. The fluorescence increases linearly with the excitation power, distinguishing it from the previously observed two-photon excited fluorescence upon femtosecond pulse excitation. Possible mechanisms of this excitation are discussed.
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Affiliation(s)
- Kristjan Leiger
- Institute of Physics, University of Tartu, Ravila 14c, 51011, Tartu, Estonia.
| | - Arvi Freiberg
- Institute of Physics, University of Tartu, Ravila 14c, 51011, Tartu, Estonia.
- Institute of Molecular and Cell Biology, University of Tartu, Riia 23, 51014, Tartu, Estonia.
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Pajusalu M, Kunz R, Rätsep M, Timpmann K, Köhler J, Freiberg A. Unified analysis of ensemble and single-complex optical spectral data from light-harvesting complex-2 chromoproteins for gaining deeper insight into bacterial photosynthesis. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052709. [PMID: 26651725 DOI: 10.1103/physreve.92.052709] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2015] [Indexed: 05/15/2023]
Abstract
Bacterial light-harvesting pigment-protein complexes are very efficient at converting photons into excitons and transferring them to reaction centers, where the energy is stored in a chemical form. Optical properties of the complexes are known to change significantly in time and also vary from one complex to another; therefore, a detailed understanding of the variations on the level of single complexes and how they accumulate into effects that can be seen on the macroscopic scale is required. While experimental and theoretical methods exist to study the spectral properties of light-harvesting complexes on both individual complex and bulk ensemble levels, they have been developed largely independently of each other. To fill this gap, we simultaneously analyze experimental low-temperature single-complex and bulk ensemble optical spectra of the light-harvesting complex-2 (LH2) chromoproteins from the photosynthetic bacterium Rhodopseudomonas acidophila in order to find a unique theoretical model consistent with both experimental situations. The model, which satisfies most of the observations, combines strong exciton-phonon coupling with significant disorder, characteristic of the proteins. We establish a detailed disorder model that, in addition to containing a C_{2}-symmetrical modulation of the site energies, distinguishes between static intercomplex and slow conformational intracomplex disorders. The model evaluations also verify that, despite best efforts, the single-LH2-complex measurements performed so far may be biased toward complexes with higher Huang-Rhys factors.
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Affiliation(s)
- Mihkel Pajusalu
- Institute of Physics, University of Tartu, Ravila 14c, 50411 Tartu, Estonia
| | - Ralf Kunz
- Experimental Physics IV and Bayreuth Institute for Macromolecular Research, University of Bayreuth, 95440 Bayreuth, Germany
| | - Margus Rätsep
- Institute of Physics, University of Tartu, Ravila 14c, 50411 Tartu, Estonia
| | - Kõu Timpmann
- Institute of Physics, University of Tartu, Ravila 14c, 50411 Tartu, Estonia
| | - Jürgen Köhler
- Experimental Physics IV and Bayreuth Institute for Macromolecular Research, University of Bayreuth, 95440 Bayreuth, Germany
| | - Arvi Freiberg
- Institute of Physics, University of Tartu, Ravila 14c, 50411 Tartu, Estonia
- Institute of Molecular and Cell Biology, University of Tartu, Riia 23, 51010 Tartu, Estonia
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