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

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 interest2-5. 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.

Fiber diffraction without fibers.

Postprocessing of diffraction patterns of completely randomly oriented helical particles, as measured, for example, in so-called "diffract-and-destroy" experiments with an x-ray free electron laser can yield "fiber diffraction" patterns expected of fibrous bundles of the particles. This will allow "single-axis alignment" to be performed computationally, thus obviating the need to do this by experimental means such as forming fibers and laser or flow alignment. The structure of such particles may then be found by either iterative phasing methods or standard methods of fiber diffraction.

Reconstructing an icosahedral virus from single-particle diffraction experiments.

The first experimental data from single-particle scattering experiments from free electron lasers (FELs) are now becoming available. The first such experiments are being performed on relatively large objects such as viruses, which produce relatively low-resolution, low-noise diffraction patterns in so-called "diffract-and-destroy" experiments. We describe a very simple test on the angular correlations of measured diffraction data to determine if the scattering is from an icosahedral particle. If this is confirmed, the efficient algorithm proposed can then combine diffraction data from multiple shots of particles in random unknown orientations to generate a full 3D image of the icosahedral particle. We demonstrate this with a simulation for the satellite tobacco necrosis virus (STNV), the atomic coordinates of whose asymmetric unit is given in Protein Data Bank entry 2BUK.

Single-particle imaging by x-ray free-electron lasers-How many snapshots are needed?

X-ray free-electron lasers (XFELs) open the possibility of obtaining diffraction information from a single biological macromolecule. This is because XFELs can generate extremely intense x-ray pulses that are so short that diffraction data can be collected before the sample is destroyed. By collecting a sufficient number of single-particle diffraction patterns, the three-dimensional electron density of a molecule can be reconstructed ab initio. The quality of the reconstruction depends largely on the number of patterns collected at the experiment. This paper provides an estimate of the number of diffraction patterns required to reconstruct the electron density at a targeted spatial resolution. This estimate is verified by simulations for realistic x-ray fluences, repetition rates, and experimental conditions available at modern XFELs. Employing the bacterial phytochrome as a model system, we demonstrate that sub-nanometer resolution is within reach.

Simulations on time-resolved structure determination of uncrystallized biomolecules in the presence of shot noise.

Determination of fast structural changes of biomolecules is usually performed on crystalline samples in a time-resolved pump-probe experiment. Changes in the structure are found by the difference Fourier method using phases of a known reference structure. As we showed recently, such changes can also be determined from diffraction of uncrystallized molecules in random orientations. In this case, the difference in the angular correlations of the diffraction patterns is used to find structural changes. Similar to the difference Fourier method, there is no need for iterative phasing. We validated this approach previously with simulations in the absence of noise. In this paper, we show that the effects of noise can be adequately suppressed by averaging over a sufficiently large ensemble as they can be obtained using an X-ray free electron laser.

Single-particle structure determination by X-ray free-electron lasers: Possibilities and challenges.

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.

Conformations of macromolecules and their complexes from heterogeneous datasets.

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.

Deducing fast electron density changes in randomly orientated uncrystallized biomolecules in a pump-probe experiment.

We propose a method for deducing time-resolved structural changes in uncrystallized biomolecules in solution. The method relies on measuring the angular correlations of the intensities, when averaged over a large number of diffraction patterns from randomly oriented biomolecules in solution in a liquid solvent. The experiment is somewhat like a pump-probe version of an experiment on small angle X-ray scattering, except that the data expected by the algorithm are not just the radial variation of the averaged intensities. The differences of these correlation functions as measured from a photoexcited and dark structure enable the direct calculation of the difference electron density with a knowledge of only the dark structure. We exploit a linear relation we derive between the difference in these correlation functions and the difference electron density, applicable for small structural changes.

High-resolution structure of viruses from random diffraction snapshots.

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.