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 ago
, conical intersections remain the subject of intense scientific interest
. In biology, they have a pivotal role in vision, photosynthesis and DNA stability
. 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 longer
. Spectroscopy can achieve better time resolutions
, 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.
We describe a new generation of algorithms capable of mapping the structure and conformations of macromolecules and their complexes from large ensembles of heterogeneous snapshots, and demonstrate ...the feasibility of determining both discrete and continuous macromolecular conformational spectra. These algorithms naturally incorporate conformational heterogeneity without resort to sorting and classification, or prior knowledge of the type of heterogeneity present. They are applicable to single-particle diffraction and image datasets produced by X-ray lasers and cryo-electron microscopy, respectively, and particularly suitable for systems not easily amenable to purification or crystallization.
The advent of the X-ray free-electron laser (XFEL) has made it possible to record diffraction snapshots of biological entities injected into the X-ray beam before the onset of radiation damage. ...Algorithmic means must then be used to determine the snapshot orientations and thence the three-dimensional structure of the object. Existing Bayesian approaches are limited in reconstruction resolution typically to 1/10 of the object diameter, with the computational expense increasing as the eighth power of the ratio of diameter to resolution. We present an approach capable of exploiting object symmetries to recover three-dimensional structure to high resolution, and thus reconstruct the structure of the satellite tobacco necrosis virus to atomic level. Our approach offers the highest reconstruction resolution for XFEL snapshots to date and provides a potentially powerful alternative route for analysis of data from crystalline and nano-crystalline objects.
Imperfect knowledge of the times at which 'snapshots' of a system are recorded degrades our ability to recover dynamical information, and can scramble the sequence of events. In X-ray free-electron ...lasers, for example, the uncertainty--the so-called timing jitter--between the arrival of an optical trigger ('pump') pulse and a probing X-ray pulse can exceed the length of the X-ray pulse by up to two orders of magnitude, marring the otherwise precise time-resolution capabilities of this class of instruments. The widespread notion that little dynamical information is available on timescales shorter than the timing uncertainty has led to various hardware schemes to reduce timing uncertainty. These schemes are expensive, tend to be specific to one experimental approach and cannot be used when the record was created under ill-defined or uncontrolled conditions such as during geological events. Here we present a data-analytical approach, based on singular-value decomposition and nonlinear Laplacian spectral analysis, that can recover the history and dynamics of a system from a dense collection of noisy snapshots spanning a sufficiently large multiple of the timing uncertainty. The power of the algorithm is demonstrated by extracting the underlying dynamics on the few-femtosecond timescale from noisy experimental X-ray free-electron laser data recorded with 300-femtosecond timing uncertainty. Using a noisy dataset from a pump-probe experiment on the Coulomb explosion of nitrogen molecules, our analysis reveals vibrational wave-packets consisting of components with periods as short as 15 femtoseconds, as well as more rapid changes, which have yet to be fully explored. Our approach can potentially be applied whenever dynamical or historical information is tainted by timing uncertainty.
Intense femtosecond x-ray pulses from free-electron laser sources allow the imaging of individual particles in a single shot. Early experiments at the Linac Coherent Light Source (LCLS) have led to ...rapid progress in the field and, so far, coherent diffractive images have been recorded from biological specimens, aerosols, and quantum systems with a few-tens-of-nanometers resolution. In March 2014, LCLS held a workshop to discuss the scientific and technical challenges for reaching the ultimate goal of atomic resolution with single-shot coherent diffractive imaging. This paper summarizes the workshop findings and presents the roadmap toward reaching atomic resolution, 3D imaging at free-electron laser sources.
Amongst the promised capabilities of fourth-generation x-ray sources currently under construction is the ability to record diffraction patterns from individual biological molecules. One version of ...such an experiment would involve directing a stream of molecules into the x-ray beam and sequentially recording the scattering from each molecule of a short, but intense, pulse of radiation. The pulses are sufficiently short that the diffraction pattern is that due to scattering from identical molecules 'frozen' in random orientations. Each diffraction pattern may be thought of as a section through the 3D reciprocal space of the molecule, of unknown, random, orientation. At least two algorithms have been proposed for finding the relative orientations from just the measured diffraction data. The 'common-line' method, also employed in 3D electron microscopy, appears not best suited to the very low mean photon count per diffraction pattern pixel expected in such experiments. A manifold embedding technique has been used to reconstruct the 3D diffraction volume and hence the electron density of a small protein at the signal level expected of the scattering of an x-ray free electron laser pulse from a 500 kD biomolecule. In this paper, we propose an alternative algorithm which raises the possibility of reconstructing the 3D diffraction volume of a molecule without determining the relative orientations of the individual diffraction patterns. We discuss why such an algorithm may provide a practical and computationally convenient method of extracting information from very weak diffraction patterns. We suggest also how such a method may be adapted to the problem of finding the variations of a structure with time in a time-resolved pump-probe experiment.
It is demonstrated that a common‐line method can assemble a three‐dimensional oversampled diffracted intensity distribution suitable for high‐resolution structure solution from a set of measured ...two‐dimensional diffraction patterns, as proposed in experiments with an X‐ray free‐electron laser (XFEL) Neutze et al. (2000). Nature (London), 406, 752–757. Even for a flat Ewald sphere, it is shown how the ambiguities due to Friedel's law may be overcome. The method breaks down for photon counts below about 10 per detector pixel, almost three orders of magnitude higher than expected for scattering by a 500 kDa protein with an XFEL beam focused to a 0.1 µm diameter spot. Even if 103 orientationally similar diffraction patterns could be identified and added to reach the requisite photon count per pixel, the need for about 106 orientational classes for high‐resolution structure determination suggests that about 109 diffraction patterns must be recorded. Assuming pulse and readout rates of ∼100 Hz, such measurements would require ∼107 s, i.e. several months of continuous beam time.
Single-particle structure recovery without crystals or radiation damage is a revolutionary possibility offered by X-ray free-electron lasers, but it involves formidable experimental and ...data-analytical challenges. Many of these difficulties were encountered during the development of cryogenic electron microscopy of biological systems. Electron microscopy of biological entities has now reached a spatial resolution of about 0.3 nm, with a rapidly emerging capability to map discrete and continuous conformational changes and the energy landscapes of biomolecular machines. Nonetheless, single-particle imaging by X-ray free-electron lasers remains important for a range of applications, including the study of large "electron-opaque" objects and time-resolved examination of key biological processes at physiological temperatures. After summarizing the state of the art in the study of structure and conformations by cryogenic electron microscopy, we identify the primary opportunities and challenges facing X-ray-based single-particle approaches, and possible means for circumventing them.
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