Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Few-fs resolution of a photoactive protein traversing a conical intersection

Abstract

The structural dynamics of a molecule are determined by the underlying potential energy landscape. Conical intersections are funnels connecting otherwise separate potential energy surfaces. Posited almost a century ago1, conical intersections remain the subject of intense scientific interest2,3,4,5. In biology, they have a pivotal role in vision, photosynthesis and DNA stability6. Accurate theoretical methods for examining conical intersections are at present limited to small molecules. Experimental investigations are challenged by the required time resolution and sensitivity. Current structure-dynamical understanding of conical intersections is thus limited to simple molecules with around ten atoms, on timescales of about 100 fs or longer7. Spectroscopy can achieve better time resolutions8, but provides indirect structural information. Here we present few-femtosecond, atomic-resolution videos of photoactive yellow protein, a 2,000-atom protein, passing through a conical intersection. These videos, extracted from experimental data by machine learning, reveal the dynamical trajectories of de-excitation via a conical intersection, yield the key parameters of the conical intersection controlling the de-excitation process and elucidate the topography of the electronic potential energy surfaces involved.

This is a preview of subscription content

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Evolution of dynamical modes as a function of pump–probe delay time.
Fig. 2: Topography of the conical intersection and the associated population dynamics in PYP, as deduced from five experimental dynamic trajectories.

Data availability

The structures have been deposited in the Protein Data Bank, together with their respective weighted difference structure factor amplitudes, under accession codes 5HD3, 5HDC, 5HDD, 5HDS and 5HD5Source data are provided with this paper.

Code availability

The code will be made available on request.

References

  1. 1.

    von Neumann, J. & Wigner, E. P. Über das Verhalten von Eigenwerten bei adiabatischen Prozessen Vol. A1 (Springer, 1993).

  2. 2.

    Chang, K. F. et al. Revealing electronic state-switching at conical intersections in alkyl iodides by ultrafast XUV transient absorption spectroscopy. Nat. Commun. 11, 4042 (2020).

    ADS  CAS  Article  Google Scholar 

  3. 3.

    Cerullo, G. & Garavelli, M. A novel spectroscopic window on conical intersections in biomolecules. Proc. Natl Acad. Sci. USA 117, 26553–26555 (2020).

    CAS  Article  Google Scholar 

  4. 4.

    Yang, J. et al. Imaging CF3I conical intersection and photodissociation dynamics with ultrafast electron diffraction. Science 361, 64–67 (2018).

    ADS  CAS  Article  Google Scholar 

  5. 5.

    Tenboer, J. et al. Time-resolved serial crystallography captures high-resolution intermediates of photoactive yellow protein. Science 346, 1242–1246 (2014).

    ADS  CAS  Article  Google Scholar 

  6. 6.

    Nogly, P. et al. Retinal isomerization in bacteriorhodopsin captured by a femtosecond X-ray laser. Science 361, eaat0094 (2018).

    Article  Google Scholar 

  7. 7.

    Yang, J. et al. Simultaneous observation of nuclear and electronic dynamics by ultrafast electron diffraction. Science 368, 885–889 (2020).

    ADS  CAS  Article  Google Scholar 

  8. 8.

    Zinchenko, K. S. et al. Sub-7-femtosecond conical-intersection dynamics probed at the carbon K-edge. Science 371, 489–494 (2021).

    ADS  CAS  Article  Google Scholar 

  9. 9.

    Perman, B. et al. Energy transduction on the nanosecond time scale: early structural events in a xanthopsin photocycle. Science 279, 1946–1950 (1998).

    ADS  CAS  Article  Google Scholar 

  10. 10.

    Pande, K. et al. Femtosecond structural dynamics drives the trans/cis isomerization in photoactive yellow protein. Science 352, 725–729 (2016).

    ADS  CAS  Article  Google Scholar 

  11. 11.

    Polli, D. et al. Conical intersection dynamics of the primary photoisomerization event in vision. Nature 467, 440–443 (2010).

    ADS  CAS  Article  Google Scholar 

  12. 12.

    Van Beeumen, J. J. et al. Primary structure of a photoactive yellow protein from the phototrophic bacterium Ectothiorhodospira halophila, with evidence for the mass and the binding site of the chromophore. Protein Sci. 2, 1114–1125 (1993).

    Article  Google Scholar 

  13. 13.

    Jones, R. O. Density functional theory: its origins, rise to prominence, and future. Rev. Mod. Phys. 87, 897–923 (2015).

    ADS  MathSciNet  Article  Google Scholar 

  14. 14.

    Calegari, F., Sansone, G., Stagira, S., Vozzi, C. & Nisoli, M. Advances in attosecond science. J. Phys. B 49, 062001 (2016).

    ADS  Google Scholar 

  15. 15.

    Wolf, T. J. A. et al. The photochemical ring-opening of 1,3-cyclohexadiene imaged by ultrafast electron diffraction. Nat. Chem. 11, 504–509 (2019).

    CAS  Article  Google Scholar 

  16. 16.

    Fung, R. et al. Dynamics from noisy data with extreme timing uncertainty. Nature 532, 471–475 (2016).

    ADS  CAS  Article  Google Scholar 

  17. 17.

    Coifman, R. R. et al. Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. Proc. Natl Acad. Sci. USA 102, 7426–7431 (2005).

    ADS  CAS  Article  Google Scholar 

  18. 18.

    Giannakis, D., Schwander, P. & Ourmazd, A. The symmetries of image formation by scattering. I. Theoretical framework. Opt. Express 20, 12799–12826 (2012).

    ADS  Article  Google Scholar 

  19. 19.

    Giannakis, D. & Majda, A. J. Nonlinear Laplacian spectral analysis for time series with intermittency and low-frequency variability. Proc. Natl Acad. Sci. USA 109, 2222–2227 (2012).

    ADS  MathSciNet  CAS  Article  Google Scholar 

  20. 20.

    Sauer, T., Yorke, J. A. & Casdagli, M. Embedology. J. Stat. Phys. 65, 579–616 (1991).

    ADS  MathSciNet  Article  Google Scholar 

  21. 21.

    Takens, F. in Lecture Notes in Mathematics Vol. 898 (ed. Warwick) 366–381 (Springer-Verlag, 1981).

  22. 22.

    Packard, N., Crutchfield, J., Farmer, J. & Shaw, R. Geometry from a time series. Phys. Rev. Lett. 45, 712–716 (1980).

    ADS  Article  Google Scholar 

  23. 23.

    Fung, R. et al. Achieving accurate estimates of fetal gestational age and personalised predictions of fetal growth based on data from an international prospective cohort study: a population-based machine learning study. Lancet Digit. Health 2, e368–e375 (2020).

    ADS  Article  Google Scholar 

  24. 24.

    Dashti, A. et al. Retrieving functional pathways of biomolecules from single-particle snapshots. Nat. Commun. 11, 4734 (2020).

    ADS  CAS  Article  Google Scholar 

  25. 25.

    Moffat, K. The frontiers of time-resolved macromolecular crystallography: movies and chirped X-ray pulses. Faraday Discuss. 122, 65–77; discussion 79–88 (2003).

    ADS  CAS  Article  Google Scholar 

  26. 26.

    Schmidt, M., Rajagopal, S., Ren, Z. & Moffat, K. Application of singular value decomposition to the analysis of time-resolved macromolecular X-ray data. Biophys. J. 84, 2112–2129 (2003).

    ADS  CAS  Article  Google Scholar 

  27. 27.

    Prieto, G. A., Parker, R. L. & Vernon Iii, F. L. A Fortran 90 library for multitaper spectrum analysis. Comput. Geosci. 35, 1701–1710 (2009).

    ADS  Article  Google Scholar 

  28. 28.

    Mitra, P. & Bokil, H. Observed Brain Dynamics (Oxford Univ. Press, 2008).

  29. 29.

    Jerri, A. J. The Shannon sampling theorem—its various extensions and applications: a tutorial review. Proc. IEEE 65, 1565–1596 (1977).

    ADS  Article  Google Scholar 

  30. 30.

    Grunbein, M. L. et al. Illumination guidelines for ultrafast pump-probe experiments by serial femtosecond crystallography. Nat. Methods 17, 681–684 (2020).

    Article  Google Scholar 

  31. 31.

    Barty, A. et al. Self-terminating diffraction gates femtosecond X-ray nanocrystallography measurements. Nat. Photonics 6, 35–40 (2012).

    ADS  CAS  Article  Google Scholar 

  32. 32.

    Kuramochi, H. et al. Probing the early stages of photoreception in photoactive yellow protein with ultrafast time-domain Raman spectroscopy. Nat. Chem. 9, 660–666 (2017).

    CAS  Article  Google Scholar 

  33. 33.

    Socratese, G. Infrared and Raman Characteristic Group Frequencies: Tables and Charts 3rd edn (Wiiley, 2004).

  34. 34.

    Pandey, S. et al. Time-resolved serial femtosecond crystallography at the European XFEL. Nat. Methods 17, 73–78 (2020).

    Article  Google Scholar 

  35. 35.

    Henry, E. & Hofrichter, J. Singular value decomposition: application to analysis of experimental data. Methods Enzymol. 210, 129–192 (1992).

    CAS  Article  Google Scholar 

  36. 36.

    Fung, R. et al. Dynamics from noisy data with extreme timing uncertainty. Nature 532, 471–475 (2016).

    ADS  CAS  Article  Google Scholar 

  37. 37.

    Schwander, P., Giannakis, D., Yoon, C. H. & Ourmazd, A. The symmetries of image formation by scattering. II. Applications. Opt. Express 20, 12827–12849 (2012).

    ADS  Article  Google Scholar 

  38. 38.

    Winn, M. D. et al. Overview of the CCP4 suite and current developments. Acta Crystallogr. D 67, 235–242 (2011).

    CAS  Google Scholar 

  39. 39.

    Emsley, P., Lohkamp, B., Scott, W. G. & Cowtan, K. Features and development of Coot. Acta Crystallogr. D 66, 486-501 (2010).

    CAS  Google Scholar 

  40. 40.

    Köppel, H., Domcke, W. & Cederbaum, L. S. in Advances in Chemical Physics (eds Rice, S. et al.) 59–246 (2007).

  41. 41.

    Domcke, W., Yarkony, D. R. & Köppel, H. Conical Intersections (WorldScientific, 2004).

  42. 42.

    Gromov, E. V. et al. Theoretical study of excitations in furan: spectra and molecular dynamics. J. Chem. Phys. 121, 4585–4598 (2004).

    ADS  CAS  Article  Google Scholar 

  43. 43.

    Faraji, S., Meyer, H. D. & Koppel, H. Multistate vibronic interactions in difluorobenzene radical cations. II. Quantum dynamical simulations. J. Chem. Phys. 129, 074311 (2008).

    ADS  Article  Google Scholar 

  44. 44.

    Arnold, C., Vendrell, O., Welsch, R. & Santra, R. Control of nuclear dynamics through conical intersections and electronic coherences. Phys. Rev. Lett. 120, 123001 (2018).

    ADS  CAS  Article  Google Scholar 

  45. 45.

    The MCTDH package v.8.4.18 (2019).

  46. 46.

    Beck, M. The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets. Phys. Rep. 324, 1–105 (2000).

    ADS  CAS  Article  Google Scholar 

  47. 47.

    Meyer, H. D., Manthe, U. & Cederbaum, L. S. The multi-configurational time-dependent Hartree approach. Chem. Phys. Lett. 165, 73–78 (1990).

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

We acknowledge valuable discussions with E. Lattman, K. Moffat, T. Martinez and past and present members of the UWM data science group. The development of underlying techniques was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under award DE-SC0002164 (underlying dynamical techniques) and by the US National Science Foundation under awards STC-1231306 (underlying data analytical techniques) and DBI-2029533 (underlying analytical models). N.B. and R. Santra were supported by the Cluster of Excellence ‘CUI: Advanced Imaging of Matter’ of Deutsche Forschungsgemeinschaft (DFG)–EXC 2056–project no. 390715994.

Author information

Affiliations

Authors

Contributions

A.O. designed this study. A.O., A.H., P.S., R.F. and R. Sepehr co-defined the algorithm and the data-analytical pipeline. A.H. and R.F. performed analytical and computational work, and tested and validated the algorithm with participation by A.O. N.B. and R. Santra performed the quantum-dynamics simulations. M.S. provided experimental data and expertise in crystallographic data analysis. All authors contributed to the manuscript.

Corresponding author

Correspondence to A. Ourmazd.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks the anonymous reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 PYP chromophore in trans configuration and structure dynamical modes obtained by our approach.

a, The PYP chromophore in the trans configuration. The oval contains the primary structure-dynamically active region, with the numbered atoms and aromatic structures identified. C: carbon, N: nitrogen, O: oxygen, S: sulfur. b, c, The structure dynamical modes obtained by our approach can be combined to yield the more intuitive torsional angle, which is commonly chosen as the primary reaction coordinate for isomerization in PYP. Changes in the torsional angle and the bend of the chromophore axis relative to equilibrium values necessarily increase the energy of the ground state structure. Near the CI the structure on the ground state PES and that on the excited state PES are essentially identical with very similar energies. The structure on the excited state PES determined at 615 fs is therefore an excellent model for the electronic ground state structure near the PYP conical intersection.

Extended Data Fig. 2 Dynamical trajectories near the conical intersection.

Unless otherwise stated, arbitrary units. a, b, Time evolutions (chronos) of modes 3 and 4, respectively. c, The experimental dynamical trajectory (in black) obtained from modes 3 and 4 as collective variables x and y, respectively, and the best-fit simulated trajectory, with color showing the passage of time (see color bar). The red dot indicates the position of the conical intersection. For additional trajectories, see Supplementary Information. d, The calculated de-excitation dynamics as reflected in the electronic state population for the trajectory shown in Panel c above. The brown and blue curves represent the populations of the upper and the lower adiabatic electronic states, respectively.

Source data

Extended Data Fig. 3 Frequency content of a typical chrono, in this case chrono-4.

a, Fourier power spectrum. b, Multi-taper analysis. The vertical axis of the latter essentially represents the signal-to-noise ratio. Each chrono displays a characteristic frequency spectrum.

Source data

Extended Data Fig. 4 Dynamical trajectories near the conical intersection.

Unless otherwise stated, arbitrary units. a, b, Time evolutions (chronos) of modes 2 and 3, respectively. c, The experimental dynamical trajectory (in black) obtained from modes 2 and 3 as collective variables x and y, respectively, and the best-fit simulated trajectory, with color showing the passage of time (see color bar). The red dot indicates the position of the conical intersection. d, The calculated de-excitation dynamics as reflected in the electronic state population for the trajectory shown in Panel c above. The brown and blue curves represent the populations of the upper and the lower adiabatic electronic states, respectively.

Source data

Extended Data Fig. 5 Dynamical trajectories near the conical intersection.

Unless otherwise stated, arbitrary units. a, b, Time evolutions (chronos) of modes 2 and 4, respectively. c, The experimental dynamical trajectory (in black) obtained from modes 2 and 4 as collective variables x and y, respectively, and the best-fit simulated trajectory, with color showing the passage of time (see color bar). The red dot indicates the position of the conical intersection. d, The calculated de-excitation dynamics as reflected in the electronic state population for the trajectory shown in Panel c. The brown and blue curves represent the populations of the upper and the lower adiabatic electronic states, respectively.

Source data

Extended Data Fig. 6 Dynamical trajectories near the conical intersection.

Unless otherwise stated, arbitrary units. a, b, Time evolutions (chronos) of modes 2 and 5, respectively. c, The experimental dynamical trajectory (in black) obtained from modes 2 and 5 as collective variables x and y, respectively, and the best-fit simulated trajectory, with color showing the passage of time (see color bar). The red dot indicates the position of the conical intersection. d, The calculated de-excitation dynamics as reflected in the electronic state population for the trajectory shown in Panel c above. The brown and blue curves represent the populations of the upper and the lower adiabatic electronic states, respectively.

Source data

Extended Data Fig. 7 Dynamical trajectories near the conical intersection.

Unless otherwise stated, arbitrary units. a, b, Time evolutions (chronos) of modes 4 and 5, respectively. c, The experimental dynamical trajectory (in black) obtained from modes 4 and 5 as collective variables x and y, respectively, and the best-fit simulated trajectory, with color showing the passage of time (see color bar). The red dot indicates the position of the conical intersection. d, The calculated de-excitation dynamics as reflected in the electronic state population for the trajectory shown in Panel c above. The brown and blue curves represent the populations of the upper and the lower adiabatic electronic states, respectively.

Source data

Extended Data Fig. 8 Comparing modes from light and dark data.

a, The first five chronos obtained from light data ordered according to pump-probe delay. b, The first five chronos obtained from dark data lexicographically sorted according to run numbers followed by event numbers. The first two chronos are identical, except for scale. This is a hallmark of a one-parameter process. Correlation analysis shows the single-parameter process correlates with the integrated Bragg spot intensity (Pearson correlation: 0.93), most likely pertaining to drift in the incident beam intensity. The subsequent chronos represent noise.

Source data

Extended Data Table 1 Peak positions obtained from multi-taper Fourier analysis of the chronos before the encounter with the conical intersection vs. peak positions obtained from time-resolved Raman spectra of PYP, all in THz
Extended Data Table 2 Parameters of the potential energy surface and parametric grid of simulated trajectories near the conical intersection

Supplementary information

Supplementary Information

This file contains Supplementary Information sections 1–4 and Supplementary Figs. 1–5.

Reporting Summary

Supplementary Data

This file contains source data for Supplementary Figs. 1, 3, 4 and 5.

Peer Review File

Supplementary Video 1

Difference electron density video along mode 2

Supplementary Video 2

Difference electron density video along mode 3

Supplementary Video 3

Difference electron density video along mode 4

Supplementary Video 4

Difference electron density video along mode 5

Supplementary Video 5

Difference electron density video along trajectory of mode 2/mode 3

Supplementary Video 6

Difference electron density video along trajectory of mode 2/mode 4

Supplementary Video 7

Difference electron density video along trajectory of mode 2/mode 5

Supplementary Video 8

Difference electron density video along trajectory of mode 3/mode 4

Supplementary Video 9

Difference electron density video along trajectory of mode 4/mode 5

Source data

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hosseinizadeh, A., Breckwoldt, N., Fung, R. et al. Few-fs resolution of a photoactive protein traversing a conical intersection. Nature 599, 697–701 (2021). https://doi.org/10.1038/s41586-021-04050-9

Download citation

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing