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Effect of disorder and polarization sequences on two-dimensional spectra of light-harvesting complexes

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Two-dimensional electronic spectra (2DES) provide unique ways to track the energy transfer dynamics in light-harvesting complexes. The interpretation of the peaks and structures found in experimentally recorded 2DES is often not straightforward, since several processes are imaged simultaneously. The choice of specific pulse polarization sequences helps to disentangle the sometimes convoluted spectra, but brings along other disturbances. We show by detailed theoretical calculations how 2DES of the Fenna–Matthews–Olson complex are affected by rotational and conformational disorder of the chromophores.

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  1. Adolphs J, Renger T (2006) How proteins trigger excitation energy transfer in the FMO complex of green sulfur bacteria. Biophys J 91(8):2778–2797. https://doi.org/10.1529/biophysj.105.079483

  2. Adolphs J, Müh F, Madjet MEA, Renger T (2008) Calculation of pigment transition energies in the FMO protein. Photosynth Res 95(2–3):197–209. https://doi.org/10.1007/s11120-007-9248-z

  3. Aghtar M, Strümpfer J, Olbrich C, Schulten K, Kleinekathöfer U (2013) The FMO complex in a glycerol–water mixture. J Phys Chem B 117(24):7157–7163. https://doi.org/10.1021/jp311380k

  4. Avery J, Bay Z, Szent-Gyorgyi A (1961) On the energy transfer in biological systems. Proc Natl Acad Sci USA 47(11):1742–1744

  5. Bína D, Gardian Z, Vácha F, Litvín R (2016) Native FMO-reaction center supercomplex in green sulfur bacteria: an electron microscopy study. Photosynth Res 128(1):93–102. https://doi.org/10.1007/s11120-015-0205-y

  6. Blankenship RE (2014) Molecular mechanisms of photosynthesis, 2nd edn. Wiley, Oxford

  7. Brixner T, Stenger J, Vaswani HM, Cho M, Blankenship RE, Fleming GR (2005) Two-dimensional spectroscopy of electronic couplings in photosynthesis. Nature 434(7033):625–628. https://doi.org/10.1038/nature03429

  8. Chen L, Zheng R, Jing Y, Shi Q (2011) Simulation of the two-dimensional electronic spectra of the Fenna–Matthews–Olson complex using the hierarchical equations of motion method. J Chem Phys 134(19):194508–194508. https://doi.org/10.1063/1.3589982

  9. Cho M (2008) Coherent two-dimensional optical spectroscopy. Chem Rev 108(4):1331–1418. https://doi.org/10.1021/cr078377b

  10. Dostál J, Pšenčík J, Zigmantas D (2016) In situ mapping of the energy flow through the entire photosynthetic apparatus. Nat Chem 8(7):705–710. https://doi.org/10.1038/nchem.2525

  11. Engel GS, Calhoun TR, Read EL, Ahn TK, Mančal T, Cheng YC, Blankenship RE, Fleming GR (2007) Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446(7137):782–786. https://doi.org/10.1038/nature05678

  12. Fenna RE, Matthews BW (1975) Chlorophyll arrangement in a bacteriochlorophyll protein from Chlorobium limicola. Nature 258(5536):573–577. https://doi.org/10.1038/258573a0

  13. Gelin MF, Borrelli R, Domcke W (2017) Efficient orientational averaging of nonlinear optical signals in multi-chromophore systems. J Chem Phys 147(4):044114–044114. https://doi.org/10.1063/1.4996205

  14. Gordon R (1968) Correlation functions for molecular motion, vol 3. Advances in magnetic and optical resonance. Academic press inc., Cambridge, pp 1–42. https://doi.org/10.1016/B978-1-4832-3116-7.50008-4

  15. Hamm P, Zanni MT (2011) Concepts of 2D spectroscopy. Cambridge University Press, Cambridge

  16. Hein B, Kreisbeck C, Kramer T, Rodríguez M (2012) Modelling of oscillations in two-dimensional echo-spectra of the Fenna–Matthews–Olson complex. New J Phys 14(2):023018–023018. https://doi.org/10.1088/1367-2630/14/2/023018

  17. Hochstrasser RM (2001) Two-dimensional IR-spectroscopy: polarization anisotropy effects. Chem Phys 266(2–3):273–284. https://doi.org/10.1016/S0301-0104(01)00232-4

  18. Ishizaki A, Fleming GR (2009) On the adequacy of the Redfield equation and related approaches to the study of quantum dynamics in electronic energy transfer. J Chem Phys 130(23):234110–234110. https://doi.org/10.1063/1.3155214

  19. Kramer T, Kreisbeck C (2014) Modelling excitonic-energy transfer in light-harvesting complexes. AIP Conf Proc 1575:111–135. https://doi.org/10.1063/1.4861701

  20. Kramer T, Rodriguez M (2017) Two-dimensional electronic spectra of the photosynthetic apparatus of green sulfur bacteria. Sci Rep 7:45245–45245. https://doi.org/10.1038/srep45245

  21. Kramer T, Noack M, Reimers JR, Reinefeld A, Rodríguez M, Yin S (2018a) Energy flow in the Photosystem I supercomplex: comparison of approximative theories with DM-HEOM. Chem Phys 515:262–271. https://doi.org/10.1016/j.chemphys.2018.05.028

  22. Kramer T, Noack M, Reinefeld A, Rodríguez M, Zelinskyy Y (2018b) Efficient calculation of open quantum system dynamics and time-resolved spectroscopy with distributed memory HEOM (DM-HEOM). J Comput Chem 39(22):1779. https://doi.org/10.1002/jcc.25354

  23. Kreisbeck C, Kramer T (2012) Long-lived electronic coherence in dissipative exciton dynamics of light-harvesting complexes. J Phys Chem Lett 3(19):2828–2833. https://doi.org/10.1021/jz3012029

  24. Kreisbeck C, Kramer T, Rodríguez M, Hein B (2011) High-performance solution of hierarchical equations of motion for studying energy transfer in light-harvesting complexes. J Chem Theory Comput 7(7):2166–2174. https://doi.org/10.1021/ct200126d

  25. Kreisbeck C, Kramer T, Aspuru-Guzik A (2013) Disentangling electronic and vibronic coherences in two-dimensional echo spectra. J Phys Chem B 117(32):9380–9385. https://doi.org/10.1021/jp405421d

  26. Kreisbeck C, Kramer T, Aspuru-Guzik A (2014) Scalable high-performance algorithm for the simulation of exciton dynamics. Application to the light-harvesting complex II in the presence of resonant vibrational modes. J Chem Theory Comput 10:4045–4054. https://doi.org/10.1021/ct500629s

  27. Lambrev PH, Akhtar P, Tan HS (2019) Insights into the mechanisms and dynamics of energy transfer in plant light-harvesting complexes from two-dimensional electronic spectroscopy. Biochimica et Biophysica Acta (BBA) - Bioenergetics. https://doi.org/10.1016/j.bbabio.2019.07.005

  28. Lindorfer D, Renger T (2018) Theory of anisotropic circular dichroism of excitonically coupled systems: application to the baseplate of green sulfur bacteria. J Phys Chem B 122(10):2747–2756. https://doi.org/10.1021/acs.jpcb.7b12832

  29. May V, Kühn O (2008) Optical field control of charge transmission through a molecular wire I. Generalized master equation description. Phys Rev B 77(11):115439–115439. https://doi.org/10.1103/PhysRevB.77.115439

  30. Mukamel S (1995) Principles of nonlinear optical spectroscopy. Oxford University Press, Oxford

  31. Noack M, Reinefeld A, Kramer T, Steinke T (2018) DM-HEOM: a portable and scalable solver-framework for the hierarchical equations of motion. In: 2018 IEEE international parallel and distributed processing symposium workshops (IPDPSW) p 947. https://doi.org/10.1109/IPDPSW.2018.00149

  32. Novoderezhkin VI, van Grondelle R (2017) Modeling of excitation dynamics in photosynthetic light-harvesting complexes: exact versus perturbative approaches. J Phys B Atomic Mol Opt Phys 50(12):124003–124003. https://doi.org/10.1088/1361-6455/aa6b87

  33. Nuernberger P, Ruetzel S, Brixner T (2015) Multidimensional electronic spectroscopy of photochemical reactions. Angew Chem Int Ed 54(39):11368–11386. https://doi.org/10.1002/anie.201502974

  34. Olbrich C, Jansen TLC, Liebers J, Aghtar M, Strümpfer J, Schulten K, Knoester J, Kleinekathöfer U (2011) From atomistic modeling to excitation transfer and two-dimensional spectra of the FMO light-harvesting complex. J Phys Chem B 115(26):8609–8621. https://doi.org/10.1021/jp202619a

  35. Olson JM, Romano CA (1962) A new chlorophyll from green bacteria. Biochim Biophys Acta 59(3):726–728. https://doi.org/10.1016/0006-3002(62)90659-5

  36. Panitchayangkoon G, Hayes D, a Fransted K, Caram JR, Harel E, Wen J, Blankenship RE, Engel GS, (2010) Long-lived quantum coherence in photosynthetic complexes at physiological temperature. In: Proceedings of the National Academy of Sciences of the United States of America 107(29):12766–70. https://doi.org/10.1073/pnas.1005484107

  37. Rodríguez M, Kramer T (2019) Machine learning of two-dimensional spectroscopic data. Chem Phys 520:52–60. https://doi.org/10.1016/j.chemphys.2019.01.002

  38. Schlau-Cohen GS, Ishizaki A, Calhoun TR, Ginsberg NS, Ballottari M, Bassi R, Fleming GR (2012) Elucidation of the timescales and origins of quantum electronic coherence in LHCII. Nat Chem 4(5):389–395. https://doi.org/10.1038/nchem.1303

  39. Tanimura Y, Kubo R (1989) Time evoultion of a quantum system in contact with a nearly Gaussian–Markoffian noise bath. J Phys Soc Jpn 58(1):101–114. https://doi.org/10.1143/JPSJ.58.101

  40. Thyrhaug E, Žídek K, Dostál J, Bína D, Zigmantas D (2016) Exciton structure and energy transfer in the Fenna–Matthews–Olson complex. J Phys Chem Lett 7(9):1653–1660. https://doi.org/10.1021/acs.jpclett.6b00534

  41. Thyrhaug E, Tempelaar R, Alcocer MJP, Žídek K, Bína D, Knoester J, Jansen TLC, Zigmantas D (2018) Identification and characterization of diverse coherences in the Fenna–Matthews–Olson complex. Nat Chem 10(7):780–786. https://doi.org/10.1038/s41557-018-0060-5

  42. Tiwari V, Peters WK, Jonas DM (2013) Electronic resonance with anticorrelated pigment vibrations drives photosynthetic energy transfer outside the adiabatic framework. Proc Natl Acad Sci 110(4):1203–1208. https://doi.org/10.1073/pnas.1211157110

  43. Tronrud DE, Wen J, Gay L, Blankenship RE (2009) The structural basis for the difference in absorbance spectra for the FMO antenna protein from various green sulfur bacteria. Photosynth Res 100(2):79–87. https://doi.org/10.1007/s11120-009-9430-6

  44. Vulto SIE, de Baat MA, Louwe RJW, Permentier HP, Neef T, Miller M, van Amerongen H, Aartsma TJ (1998) Exciton simulations of optical spectra of the FMO complex from the green sulfur bacterium chlorobium tepidum at 6 K. J Phys Chem B 102(47):9577–9582. https://doi.org/10.1021/jp982095l

  45. Vulto SIE, de Baat MA, Neerken S, Nowak FR, van Amerongen H, Amesz J, Aartsma TJ (1999) Excited state dynamics in FMO antenna complexes from photosynthetic green sulfur bacteria: a kinetic model. J Phys Chem B 103(38):8153–8161. https://doi.org/10.1021/jp984702a

  46. Westenhoff S, Palecek D, Edlund P, Smith P, Zigmantas D (2012) Coherent picosecond exciton dynamics in a photosynthetic reaction center. J Am Chem Soc 134(40):16484–16487. https://doi.org/10.1021/ja3065478

  47. Yuen-Zhou J, Krich JJ, Kassal I, Johnson A, Aspuru-Guzik A (2014) Ultrafast spectroscopy. IOP Publ. https://doi.org/10.1088/978-0-750-31062-8

  48. Zanni MT, Ge NH, Kim YS, Hochstrasser RM (2001) Two-dimensional IR spectroscopy can be designed to eliminate the diagonal peaks and expose only the crosspeaks needed for structure determination. Proc Natl Acad Sci 98(20):11265–11270. https://doi.org/10.1073/pnas.201412998

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The work was supported by the German Research Foundation (DFG) grants KR 2889 and RE 1389 (“Realistic Simulations of Photoactive Systems on HPC Clusters with Many Core Processors”). We acknowledge compute time allocation by the North German Supercomputing Alliance (HLRN). M.R. has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant agreement No. 707636.

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Correspondence to Tobias Kramer.

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Kramer, T., Rodríguez, M. Effect of disorder and polarization sequences on two-dimensional spectra of light-harvesting complexes. Photosynth Res (2019). https://doi.org/10.1007/s11120-019-00699-6

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  • Two-dimensional spectroscopy
  • Light-harvesting complex
  • FMO (Fenna–Matthews–Olson complex)