The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment–protein complexes

Journal name:
Nature Physics
Volume:
9,
Pages:
113–118
Year published:
DOI:
doi:10.1038/nphys2515
Received
Accepted
Published online

Abstract

Recent observations of oscillatory features in the optical response of photosynthetic complexes have revealed evidence for surprisingly long-lasting electronic coherences which can coexist with energy transport. These observations have ignited multidisciplinary interest in the role of quantum effects in biological systems, including the fundamental question of how electronic coherence can survive in biological surroundings. Here we show that the non-trivial spectral structures of protein fluctuations can generate non-equilibrium processes that lead to the spontaneous creation and sustenance of electronic coherence, even at physiological temperatures. Developing new advanced simulation tools to treat these effects, we provide a firm microscopic basis to successfully reproduce the experimentally observed coherence times in the Fenna–Matthews–Olson complex, and illustrate how detailed quantum modelling and simulation can shed further light on a wide range of other non-equilibrium processes which may be important in different photosynthetic systems.

At a glance

Figures

  1. The generic organization of the early stages of light-harvesting in natural photosynthesis.
    Figure 1: The generic organization of the early stages of light-harvesting in natural photosynthesis.

    Excitons created in the antenna complexes migrate via dipolar coupling between chromophores in different pigment–protein complexes and are finally transferred to a reaction centre where charge separation occurs. Under the low-light conditions where light-harvesting is most efficient, most of the intermediate pigment–protein complexes transport only single excitons at a time and each complex functions independently. Chromophores are modelled as having a ground state |gright fence and an optically excited state |iright fence. Couplings between chromophores leads to the formation of delocalized excitonic eigenstates |eiright fence, with transitions between these states mediated by environmental fluctuations.

  2. Electronic coherence from the semiclassical model.
    Figure 2: Electronic coherence from the semiclassical model.

    a,b, Results at T=77K. a, Inter-exciton coherence Re(ρe1e2(t))for an initial exciton state 2ρ(0)=|e1right fenceleft fencee1|+|e2right fenceleft fencee2|+|e1right fenceleft fencee2|+|e2right fenceleft fencee1|. b, Ground-excited coherences Abs(ρe1g(t)) (in red) and Abs(ρe2g(t))(in black) for an initial exciton state 2ρ(0)=|eiright fenceleft fenceei|+|gright fenceleft fenceg|+|eiright fenceleft fenceg|+|gright fenceleft fenceei| (i=1,2), respectively. Note that the optical high-frequency oscillations of the ρeig(t) coherences have been suppressed by taking the absolute value. Exciton population dynamics following the injection of an excitation on site 1 of the FMO complex were also computed at this temperature, showing that excitons relax to the lowest energy states localized around sites 3 and 4 after 3 ps (not shown). This is in line with the experimental transport times of several picoseconds35. c,d, Semiclassical results at T=277K. The same quantities and initial conditions as a,b are plotted and used in c,d, respectively. The results at T=277K in c,d are plotted on the interval [0.2,0.8] ps to highlight the long lived coherences in the presence of the resonant 180cm−1 mode on a timescale relevant for experiments at this temperature. In all the plots, results including and excluding the resonant 180cm−1 mode are shown as solid and dashed lines, respectively.

  3. Numerical exact results of electronic coherence for cryogenic and physiological temperatures.
    Figure 3: Numerical exact results of electronic coherence for cryogenic and physiological temperatures.

    a,b, TEDOPA results at T=77K. a, Inter-exciton coherence Re(ρe1e2(t))for an initial exciton state 2ρ(0)=|e1right fenceleft fencee1|+|e2right fenceleft fencee2|+|e1right fenceleft fencee2|+|e2right fenceleft fencee1|. b, Ground-excited coherences Abs(ρe1g(t)) (in red) and Abs(ρe2g(t))(in black) for an initial exciton state 2ρ(0)=|eiright fenceleft fenceei|+|gright fenceleft fenceg|+|eiright fenceleft fenceg|+|gright fenceleft fenceei|(i=1,2), respectively. Note that the optical high-frequency oscillations of the ρeig(t) coherences have been suppressed by taking the absolute value. Weak revivals of Abs(ρe2g(t)) (on top of faster amplitude modulations) in the interval [0.3, 0.6]ps arise from coherent population transfer (against the energy gradient) and match similar features seen in Fig. 4a. c,d, TEDOPA results at T=277K. The same quantities and initial conditions as a,b are plotted and used in c,d, respectively. The results at T=277K in c,d are plotted on the interval [0.2, 0.8]ps to highlight the long lived coherences in the presence of the resonant 180cm−1 mode on a timescale relevant for experiments at this temperature. In all the plots, results including and excluding the resonant 180cm−1 mode are shown as solid and dashed lines, respectively.

  4. Spontaneous generation of excitonic coherence.
    Figure 4: Spontaneous generation of excitonic coherence.

    a, Population dynamics, showing ρe2e2(t) for the electronic and mode parameters given in the text. The initial state was ρ(0)=|e2right fenceleft fencee2| and the environment was at T=77K. Weak, oscillatory revival of population in the |e2right fence state between 0.3 and 0.6ps matches the revival dynamics of ρe2g in Fig. 3b, indicating coherent population (and coherence) transfer. b, Spontaneous electronic coherences Re(ρe1e2(t)) for same parameters and initial conditions. c, Average displacement left fenceX1right fence(t) for same parameters and initial conditions. df. The same as for ac, respectively, but with the environment initially at T=277K. In all the plots, results including and excluding the resonant 180cm−1 mode are shown as solid and dashed lines, respectively.

References

  1. Blankenship, R. Molecular Mechanisms of Photosynthesis (Wiley-Blackwell, 2002).
  2. Van Amerongen, H., Valkunas, L. & van Grondelle, R. Photosynthetic Excitons (World Scientific, 2000).
  3. Scholes, G., Fleming, G., Olaya-Castro, A. & van Grondelle, R. Lessons from nature about solar light harvesting. Nature Chem. 3, 763774 (2011).
  4. Engel, G. S. et al. Evidence for wavelike energy transfer through quantum coherence in photosynthetic complexes. Nature 446, 782786 (2007).
  5. Panitchayangkoon, G. et al. Long-lived quantum coherence in photosynthetic complexes at physiological temperature. Proc. Natl Acad. Sci. USA 107, 1276612770 (2010).
  6. Calhoun, T. et al. Quantum coherence enabled determination of the energy landscape in light-harvesting complex II. J. Phys. Chem. B 113, 1629116295 (2009).
  7. Hayes, D. et al. Dynamics of electronic dephasing in the Fenna–Matthews–Olson complex. New J. Phys. 12, 065042 (2010).
  8. Collini, E. et al. Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature. Nature 463, 644647 (2010).
  9. Mohseni, M., Rebentrost, P., Lloyd, S. & Aspuru-Guzik, A. Environment-assisted quantum walks in photosynthetic energy transfer. J. Chem. Phys. 129, 174106 (2008).
  10. Plenio, M. B. & Huelga, S. F. Dephasing-assisted transport: Quantum networks and biomolecules. New J. Phys. 10, 113019 (2008).
  11. Caruso, F., Chin, A. W., Datta, A., Huelga, S. F. & Plenio, M. B. Highly efficient energy excitation transfer in light-harvesting complexes: The fundamental role of noise-assisted transport. J. Chem. Phys. 131, 105106 (2009).
  12. Ishizaki, A., Calhoun, T., Schlau-Cohen, G. & Fleming, G. R. Quantum coherence and its interplay with protein environments in photosynthetic electronic energy transfer. Phys. Chem. Chem. Phys. 12, 73197337 (2010).
  13. Olaya-Castro, A., Lee, C., Olsen, F. & Johnson, N. Efficiency of energy transfer in a light-harvesting system under quantum coherence. Phys. Rev. B 78, 085115 (2008).
  14. Prior, J., Chin, A. W., Huelga, S. F. & Plenio, M. B. Efficient simulation of strong system-environment interactions. Phys. Rev. Lett. 105, 050404 (2010).
  15. Chin, A. W., Rivas, A., Huelga, S. F. & Plenio, M. B. Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials. J. Math. Phys. 51, 092109 (2010).
  16. Chin, A. W., Huelga, S. F. & Plenio, M. B. Chain representations of open quantum systems and their numerical simulation with time-adapative density matrix renormalisation group methods. Semiconduct. Semimet. 85, 115143 (2011).
  17. Matsuzaki, S., Zazubovich, V., Rätsep, M., Hayes, J. & Small, G. Energy transfer kinetics and low energy vibrational structure of the three lowest energy Qy-states of the Fenna-Matthews-Olson antenna complex. J. Phys. Chem. B 104, 95649572 (2000).
  18. Wending, M. et al. Electron-vibrational coupling in the Fenna-Matthews-Olson complex of Prosthecochloris aestuarii determined by temperature-dependent absorption and fluorescence line-narrowing measurements. J. Phys. Chem. B 104, 58255831 (2000).
  19. Rätsep, M., Blankenship, R. E. & Small, G. J. Energy transfer and spectral dynamics of the three lowest energy Qy-states of the Fenna-Matthews-Olson antenna complex. J. Phys. Chem. B 103, 57365741 (1999).
  20. Rätsep, M. & Freiberg, A. Electron–phonon and vibronic couplings in the FMO bacteriochlorophyll a antenna complex studied by difference fluorescence line narrowing. J. Lumin. 127, 251259 (2007).
  21. Pachón, P. A. & Brumer, P. The physical basis for long-lived electronic coherence in photosynthetic light harvesting systems. J. Phys. Chem. Lett. 2, 27282732 (2011).
  22. Kreisbeck, C. & Kramer, T. Long-lived electronic coherence in dissipative exciton-dynamics of light-harvesting complexes. J. Phys. Chem. Lett. 3, 28282833 (2012).
  23. Scully, M. O., Chaplin, K. R., Dorfman, E., Kim, M. B. & Svidzinsky, A. Quantum heat engine power can be increased by noise-induced coherence. Proc. Natl Acad. Sci. USA 108, 1509715100 (2011).
  24. Plenio, M. B. & Huelga, S. F. Entangled light from white noise. Phys. Rev. Lett. 88, 197901 (2002).
  25. Eisert, J., Plenio, M. B., Bose, S. & Hartley, J. Towards quantum entanglement in nanoelectromechanical devices. Phys. Rev. Lett. 93, 190402 (2004).
  26. Huelga, S. F. & Plenio, M. B. Stochastic resonance phenomena in quantum many-body systems. Phys. Rev. Lett. 98, 170601 (2007).
  27. Hartmann, L., Dür, W. & Briegel, H-J. Entanglement and its dynamics in open, dissipative systems. New J. Phys. 9, 230 (2007).
  28. Cai, J. M., Briegel, H. J. & Popescu, S. Dynamic entanglement in oscillating molecules and potential biological implications. Phys. Rev. E 82, 021921 (2010).
  29. Semião, F. L., Furuya, K. & Milburn, G. J. Vibration-enhanced quantum transport. New J. Phys. 12, 083033 (2010).
  30. Sarovar, M., Cheng, Y. & Whaley, K. Environmental correlation effects on excitation energy transfer in photosynthetic light harvesting. Phys. Rev. E 83, 011906 (2011).
  31. Chin, A. W., Huelga, S. F. & Plenio, M. B. Coherence and decoherence in biological systems: Principles of noise-assisted transport and the origin of long-lived coherences. Phil. Trans. Act. R. Soc. A 370, 36383657 (2012).
  32. Caycedo-Soler, F., Chin, A. W., Almeida, J., Huelga, S. F. & Plenio, M. B. The nature of the low energy band of the Fenna-Matthews-Olson complex: Vibronic signatures. J. Chem. Phys. 136, 155102 (2012).
  33. Christensson, N., Kauffmann, H., Pullerits, T. & Mancal, T. Origin of long-lived coherences in light-harvesting complexes. J. Phys. Chem. B 116, 74497454 (2012).
  34. Novoderezhkin, V. I., Yakovlev, A. G., van Grondelle, R. & Shuvalov, V. A. Coherent nuclear and electronic dynamics in primary charge separation in photosynthetic reaction centers: A redfield theory approach. J. Chem. Phys. B 108, 74457457 (2004).
  35. Adolphs, J. & Renger, T. How proteins trigger excitation energy transfer in the fmo complex of green sulfur bacteria. Biophys. J. 91, 27782797 (2006).
  36. Louwve, R. J. W. & Aartsma, T. J. On the nature of energy transfer at low temperatures in the bchl a pigment-protein complex of green sulfur bacteria. J. Chem. Phys. B 101, 72217226 (1997).
  37. Hildner, R., Brinks, D. & van Hulst, N. Femtosecond coherence and quantum control of single molecules at room temperature. Nature Phys. 7, 172177 (2010).
  38. Theiss, C. et al. Pigment-pigment and pigment-protein interactions in recombinant water-soluble chlorophyll proteins (WSCP) from cauliflower. J. Phys. Chem. B 111, 1332513335 (2007).
  39. Panitchayangkoon, G. et al. Direct evidence of quantum transport in photosynthetic light-harvesting complexes. Proc. Natl Acad. Sci. USA 108, 2090820912 (2011).
  40. Collini, E. & Scholes, G. Coherent intrachain energy migration in a conjugated polymer at room temperature. Science 323, 369373 (2009).
  41. Collini, E. & Scholes, G. Electronic and vibrational coherences in resonance energy transfer along MEH-PPV chains at room temperature. J. Phys. Chem. A 113, 42234241 (2009).

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Author information

Affiliations

  1. Institute of Theoretical Physics, Universität Ulm, Albert-Einstein-Allee 11, 89069 Ulm, Germany

    • A. W. Chin,
    • R. Rosenbach,
    • F. Caycedo-Soler,
    • S. F. Huelga &
    • M. B. Plenio
  2. Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge, CB3 0HE,UK

    • A. W. Chin
  3. Departamento de Física Aplicada, Universidad Politécnica de Cartagena, Cartagena 30202, Spain

    • J. Prior

Contributions

S.F.H. and M.B.P. designed the research with input from A.W.C.; A.W.C. and F.C-S. carried out the analytical calculations with advice from S.F.H. and M.B.P.; J.P. and R.R. developed the numerical codes and carried out the numerical simulations with guidance from A.W.C. and M.B.P. All authors discussed the results. S.F.H. and M.B.P. led the project. A.W.C., F.C.S., S.F.H. and M.B.P. wrote the manuscript with input of all authors.

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The authors declare no competing financial interests.

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