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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.

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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.

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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.

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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

Authors and 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.

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Competing interests

The authors declare no competing interests.

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

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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

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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

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