Skip to main content
SpringerLink
Log in

Nonlinear Network Model of Energy Transfer and Localisation in FMO

  • Chapter
  • First Online:
Ultrafast Quantum Effects and Vibrational Dynamics in Organic and Biological Systems

Part of the book series: Springer Theses ((Springer Theses))

  • 399 Accesses

Abstract

In this final chapter I take some first steps towards building a microscopic description of protein vibrations and clarifying their role in the archetypal light harvesting system, the Fenna-Matthews-Olson complex.

Using a term like nonlinear science is like referring to the bulk of zoology as the study of non-elephant animals.

Stanislaw Ulam, quoted in Campbell et al. [1]

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Campbell, D., Crutchfield, J., Farmer, J., Jen, E.: Experimental mathematics: the role of computation in nonlinear science. Commun. Assoc. Comput. Mach. 28, 374–84 (1985)

    MathSciNet  Google Scholar 

  2. Fassioli, F., Nazir, A., Olaya-Castro, A.: Quantum state tuning of energy transfer in a correlated environment. J. Phys. Chem. Lett. 1, 2139–2143 (2010)

    Article  Google Scholar 

  3. Chin, A., Prior, J., Rosenbach, R., Caycedo-Soler, F., Huelga, S., Plenio, M.: The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment-protein complexes. Nat. Phys. 9, 113–118 (2013)

    Article  Google Scholar 

  4. Mourokh, L.G., Nori, F.: Energy transfer efficiency in the chromophore network strongly coupled to a vibrational mode. Phys. Rev. E 92, 052720 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  5. Hu, X., Hong, L., Smith, M.D., Neusius, T., Cheng, X., Smith, J.C.: The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time. Nat. Phys. 12, 171–174 (2016)

    Article  Google Scholar 

  6. Levy, R.M., Perahia, D., Karplus, M.: Molecular dynamics of an \(\alpha \)-helical polypeptide: Temperature dependence and deviation from harmonic behavior. Proc. Natl. Acad. Sci. 79, 1346–1350 (1982)

    Article  ADS  Google Scholar 

  7. Hayward, S., Kitao, A., Go, N.: Harmonicity and anharmonicity in protein dynamics: a normal mode analysis and principal component analysis. Proteins 23, 177–186 (1995)

    Article  Google Scholar 

  8. Juanico, B., Sanejouand, Y., Piazza, F., Rios, P.D.L.: Discrete breathers in nonlinear network models of proteins. Phys. Rev. Lett. 99, 238104 (2007)

    Article  ADS  Google Scholar 

  9. Piazza, F., Sanejouand, Y.-H.: Discrete breathers in protein structures. Phys. Biol. 5, 026001 (2008)

    Article  ADS  Google Scholar 

  10. Luccioli, S., Imparato, A., Lepri, S., Piazza, F., Torcini, A.: Discrete breathers in a realistic coarse-grained model of proteins. Phys. Biol. 8, 046008 (2011)

    Article  ADS  Google Scholar 

  11. Caraglio, M., Imparato, A.: Energy transfer in molecular devices. Phys. Rev. E 90, 062712 (2014)

    Article  ADS  Google Scholar 

  12. Kopidakis, G., Aubry, S., Tsironis, G.P.: Targeted energy transfer through discrete breathers in nonlinear systems. Phys. Rev. Lett. 87, 165501 (2001)

    Article  ADS  Google Scholar 

  13. Renger, T., Klinger, A., Steinecker, F., am Busch, M. S., Numata, J., Müh, F.: Normal mode analysis of the spectral density of the Fenna-Matthews-Olson light-harvesting protein: How the protein dissipates the excess energy of excitons. J. Phys. Chem. B 116, 14565–14580 (2012)

    Google Scholar 

  14. Cole, D.J., Chin, A.W., Hine, N.D.M., Haynes, P.D., Payne, M.C.: Toward Ab initio optical spectroscopy of the Fenna-Matthews-Olson complex. J. Phys. Chem. Lett. 4, 4206–4212 (2013)

    Article  Google Scholar 

  15. Morgan, S., Cole, D., Chin, A.: Nonlinear network model analysis of vibrational energy transfer and localisation in the Fenna-Matthews-Olson complex. Nat. Sci. Rep. 6, 36703 (2016)

    Article  ADS  Google Scholar 

  16. Imhoff, J. F. Biology of Green Sulfur Bacteria (eLS, 2014)

    Google Scholar 

  17. Fenna, R.E., Matthews, B.W.: Chlorophyll arrangement in a bacteriochlorophyll protein from chlorobium limicola. Nature 258, 573–577 (1975)

    Article  ADS  Google Scholar 

  18. Adolphs, J., Renger, T.: How proteins trigger excitation energy transfer in the FMO complex of green sulfur bacteria. Biophys. J. 91, 2778–2797 (2006)

    Article  ADS  Google Scholar 

  19. Müh, F., Madjet, M.E.-A., Adolphs, J., Abdurahman, A., Rabenstein, B., Ishikita, H., Knapp, E.-W., Renger, T.: \(\alpha \)-helices direct excitation energy flow in the Fenna-Matthews-Olson protein. Proc. Natl. Acad. Sci. 104, 16862–16867 (2007)

    Article  ADS  Google Scholar 

  20. Jia, X., Mei, Y., Zhang, J.Z., Mo, Y.: Hybrid QM/MM study of FMO complex with polarized protein-specific charge. Sci. Rep. 5, 17096 (2015)

    Article  ADS  Google Scholar 

  21. Blankenship, R. Molecular Mechanisms of Photosynthesis, 2nd edn Wiley-Blackwell (2014)

    Google Scholar 

  22. Savikhin, S., Buck, D.R., Struve, W.S.: Oscillating anisotropies in a bacteriochlorophyll protein: evidence for quantum beating between exciton levels. Chem. Phys. 223, 303–312 (1997)

    Article  ADS  Google Scholar 

  23. Engel, G., Calhourn, T., Read, E., Ahn, T.-K., Mancal, T., Cheng, Y.-C., Blankenship, R., Fleming, G.: Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446, 782–786 (2007)

    Article  ADS  Google Scholar 

  24. Panitchayangkoon, G., Hayes, D., Fransted, K., Caram, J., Harel, E., Wen, J., Blankenship, R., Engel, G.: Long-lived quantum coherence in photosynthetic complexes at physiological temperature. Proc. Natl. Acad. Sci. 107, 12766–12770 (2010)

    Article  ADS  Google Scholar 

  25. Tiwari, V., Peters, W.K., Jonas, D.M.: Electronic resonance with anticorrelated pigment vibrations drives photosynthetic energy transfer outside the adiabatic framework. Proc. Natl. Acad. Sci. 110, 1203–1208 (2013)

    Article  ADS  Google Scholar 

  26. Renger, T., Marcus, R.A.: On the relation of protein dynamics and exciton relaxation in pigment-protein complexes: an estimation of the spectral density and a theory for the calculation of optical spectra. J. Chem. Phys. 116, 9997 (2002)

    Article  ADS  Google Scholar 

  27. Tirion, M.M.: Large amplitude elastic motions in proteins from a single-parameter, atomic analysis. Phys. Rev. Lett. 77, 1905 (1996)

    Article  ADS  Google Scholar 

  28. Hinsen, K.: Analysis of domain motions by approximate normal mode calculations. Proteins 33, 417–429 (1998)

    Article  Google Scholar 

  29. Krebs, W.G., Alexandrov, V., Wilson, C.A., Echols, N., Yu, H., Gerstein, M.: Normal mode analysis of macromolecular motions in a database framework: developing mode concentration as a useful classifying statistic. Proteins 48, 682–695 (2002)

    Article  Google Scholar 

  30. Bahar, I., Rader, A.: Coarse-grained normal mode analysis in structural biology. Curr. Opin. Struct. Biol. 15, 586–592 (2005)

    Article  Google Scholar 

  31. Bahar, I., Lezon, T.R., Yang, L.-W., Eyal, E.: Global dynamics of proteins: Bridging between structure and function. Annu. Rev. Biophys. 39, 23–42 (2010)

    Article  Google Scholar 

  32. Darmstadt, T. U.: Gaussian network model (2016). http://2012.igem.org/Team:TU_Darmstadt/Modeling_GNM

  33. Xie, A., van der Meer, L., Hoff, W., Austin, R.H.: Long-lived amide I vibrational modes in myoglobin. Phys. Rev. Lett. 84, 5435 (2000)

    Article  ADS  Google Scholar 

  34. Piazza, F.: Nonlinear excitations match correlated motions unveiled by NMR in proteins: a new perspective on allosteric cross-talk. Phys. Biol. 11, 036003 (2014)

    Article  ADS  Google Scholar 

  35. Tronrud, D. E., Wen, J., Gay, L., Blankenship, R. E.: The structural basis for the difference in absorbance spectra for the FMO antenna protein from various green sulfur bacteria. Photosynth. Res. 100, 79–87 (2009)

    Google Scholar 

  36. Hayward, S., de Groot, B.: Normal modes and essential dynamics. Methods Mol. Biol. 443, 89–106 (2008)

    Article  Google Scholar 

  37. Swope, W.C., Andersen, H.C., Berens, P.H., Wilson, K.R.: A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters. J. Chem. Phys. 76, 637 (1982)

    Article  ADS  Google Scholar 

  38. Dostál, J., Ps̆enc̆ík, J., Zigmantas, D.: In situ mapping of the energy flow through the entire photosynthetic apparatus. Nat. Chem. (2016). Advance Online Publication

    Google Scholar 

  39. Acbas, G., Niessen, K.A., Snell, E.H., Markelz, A.: Optical measurements of long-range protein vibrations. Nat. Commun. 5, 3076 (2014)

    Article  ADS  Google Scholar 

  40. Wendling, M., Pullerits, T., Przyjalgowski, M.A., Vulto, S.I.E., Aartsma, T.J., van Grondelle, R., van Amerongen, H.: 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, 5825–5831 (2000)

    Article  Google Scholar 

  41. Nalbach, P., Mujica-Martinez, C.A., Thorwart, M.: Vibronically coherent speed-up of the excitation energy transfer in the Fenna-Matthews-Olson complex. Phys. Rev. E 91, 022706 (2015)

    Article  ADS  Google Scholar 

  42. Fokas, A.S., Cole, D.J., Chin, A.W.: Constrained geometric dynamics of the Fenna-Matthews-Olson complex: the role of correlated motion in reducing uncertainty in excitation energy transfer. Photosynth. Res. 122, 275–292 (2014)

    Article  Google Scholar 

  43. Hayes, D., Engel, G.S.: Extracting the excitonic Hamiltonian of the Fenna-Matthews-Olson complex using three-dimensional third-order electronic spectroscopy. Biophys. J. 100, 2043–2052 (2011)

    Article  ADS  Google Scholar 

  44. Zuehlsdorff, T.J., Hine, N.D.M., Payne, M.C., Haynes, P.D.: Linear-scaling time-dependent density-functional theory beyond the Tamm-Dancoff approximation: obtaining efficiency and accuracy with in situ optimised local orbitals. J. Chem. Phys. 143, 204107 (2015)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theory of Condensed Matter Group, Department of Physics, University of Cambridge, Cambridge, UK

    Sarah Elizabeth Morgan

Authors
  1. Sarah Elizabeth Morgan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sarah Elizabeth Morgan .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Morgan, S.E. (2017). Nonlinear Network Model of Energy Transfer and Localisation in FMO. In: Ultrafast Quantum Effects and Vibrational Dynamics in Organic and Biological Systems. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-63399-2_5

Download citation

Publish with us

Policies and ethics

Search

Navigation