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We present a computational case study of X-ray single-particle imaging of hydrated proteins on an example of 2-Nitrogenase–Iron protein covered with water layers of various thickness, using a start-to-end simulation platform and experimental parameters of the SPB/SFX instrument at the European X-ray Free-Electron Laser facility. The simulations identify an optimal thickness of the water layer at which the effective resolution for imaging the hydrated sample becomes significantly higher than for the non-hydrated sample. This effect is lost when the water layer becomes too thick. Even though the detailed results presented pertain to the specific sample studied, the trends which we identify should also hold in a general case. We expect these findings will guide future single-particle imaging experiments using hydrated proteins.

X-ray free-electron lasers (XFELs) enable crystallographic structure determination beyond the limitations imposed upon synchrotron measurements by radiation damage. The need for very short XFEL pulses is relieved through gating of Bragg diffraction by loss of crystalline order as damage progresses, but not if ionization events are spatially non-uniform due to underlying elemental distributions, as in biological samples. Indeed, correlated movements of iron and sulfur ions were observed in XFEL-irradiated ferredoxin microcrystals using unusually long pulses of 80 fs. Here, we report a femtosecond time-resolved X-ray pump/X-ray probe experiment on protein nanocrystals. We observe changes in the protein backbone and aromatic residues as well as disulfide bridges. Simulations show that the latter’s correlated structural dynamics are much slower than expected for the predicted high atomic charge states due to significant impact of ion caging and plasma electron screening. This indicates that dense-environment effects can strongly affect local radiation damage-induced structural dynamics. The local X-ray-induced dynamics that occur in protein crystals during serial femtosecond crystallography (SFX) measurements at XFELs are not well understood. Here the authors performed a time-resolved X-ray pump X-ray probe SFX experiment, and they observe distinct structural changes in the disulfide bridges and peptide backbone of proteins; complementing theoretical approaches allow them to further characterize the details of the X-ray induced ionization and local structural dynamics.

Single particle imaging at atomic resolution is perhaps one of the most desired goals for ultrafast X-ray science with X-ray free-electron lasers. Such a capability would create great opportunity within the biological sciences, as high-resolution structural information of biosamples that may not crystallize is essential for many research areas therein. In this paper, we report on a comprehensive computational study of diffraction image formation during single particle imaging of a macromolecule, containing over one hundred thousand non-hydrogen atoms. For this study, we use a dedicated simulation framework, SIMEX, available at the European XFEL facility. Our results demonstrate the full feasibility of computational single-particle imaging studies for biological samples of realistic size. This finding is important as it shows that the SIMEX platform can be used for simulations to inform relevant single-particle-imaging experiments and help to establish optimal parameters for these experiments. This will enable more focused and more efficient single-particle-imaging experiments at XFEL facilities, making the best use of the resource-intensive XFEL operation.

The charged environment within a dense plasma leads to the phenomenon of ionization-potential depression (IPD) for ions embedded in the plasma. Accurate predictions of the IPD effect are of crucial importance for modeling atomic processes occurring within dense plasmas. Several theoretical models have been developed to describe the IPD effect, with frequently discrepant predictions. Only recently, first experiments on IPD in Al plasma have been performed with an x-ray free-electron laser, where their results were found to be in disagreement with the widely used IPD model by Stewart and Pyatt. Another experiment on Al, at the Orion laser, showed disagreement with the model by Ecker and Kröll. This controversy shows a strong need for a rigorous and consistent theoretical approach to calculate the IPD effect. Here, we propose such an approach: a two-step Hartree-Fock-Slater model. With this parameter-free model, we can accurately and efficiently describe the experimental Al data and validate the accuracy of standard IPD models. Our model can be a useful tool for calculating atomic properties within dense plasmas with wide-ranging applications to studies on warm dense matter, shock experiments, planetary science, inertial confinement fusion, and nonequilibrium plasmas created with x-ray free-electron lasers.

In this work, we report on incorporating for the first time tree-algorithm based solvers into the molecular dynamics code, XMDYN. XMDYN was developed to describe the interaction of ultrafast X-ray pulses with atomic assemblies. It is also a part of the simulation platform, SIMEX, developed for computational single-particle imaging studies at the SPB/SFX instrument of the European XFEL facility. In order to improve the XMDYN performance, we incorporated the existing tree-algorithm based Coulomb solver, PEPC, into the code, and developed a dedicated tree-algorithm based secondary ionization solver, now also included in the XMDYN code. These extensions enable computationally efficient simulations of X-ray irradiated large atomic assemblies, e.g., large protein systems or viruses that are of strong interest for ultrafast X-ray science. The XMDYN-based preparatory simulations can now guide future single-particle-imaging experiments at the free-electron-laser facility, EuXFEL.

The noise caused by sample heterogeneity (including sample solvent) has been identified as one of the determinant factors for a successful X-ray single-particle imaging experiment. It influences both the radiation damage process that occurs during illumination as well as the scattering patterns captured by the detector. Here, we investigate the impact of water layer thickness and radiation damage on orientation recovery from diffraction patterns of the nitrogenase iron protein. Orientation recovery is a critical step for single-particle imaging. It enables to sort a set of diffraction patterns scattered by identical particles placed at unknown orientations and assemble them into a 3D reciprocal space volume. The recovery quality is characterized by a “disconcurrence” metric. Our results show that while a water layer mitigates protein damage, the noise generated by the scattering from it can introduce challenges for orientation recovery and is anticipated to cause problems in the phase retrieval process to extract the desired protein structure. Compared to these disadvantageous effects due to the thick water layer, the effects of radiation damage on the orientation recovery are relatively small. Therefore, minimizing the amount of residual sample solvent should be considered a crucial step in improving the fidelity and resolution of X-ray single-particle imaging experiments.

The interaction of a high intensity x-ray pulse with matter causes ionization of the constituent atoms through various atomic processes, and the system eventually goes through a complex structural dynamics. Understanding this whole process is important from the perspective of structure determination of molecules using single particle imaging. XMDYN, which is a classical molecular dynamics-Monte Carlo based hybrid approach, has been successful in simulating the dynamical evolution of various systems under intense irradiation over the past years. The present study aims for extending the XMDYN toolkit to treat chemical bonds using the reactive force field. In order to study its impact, a highly intense x-ray pulse was made to interact with the simplest amino acid, glycine. Different model variants were used to highlight the consequences of charge rearrangement and chemical bonds on the time evolution. The charge-rearrangement-enhanced x-ray ionization of molecules effect is also discussed to address the capability of a classical MD based approach, i.e., XMDYN, to capture such a molecular phenomenon.

An accurate description of the interaction of intense hard X-ray pulses with heavy atoms, which is crucial for many applications of free-electron lasers, represents a hitherto unresolved challenge for theory because of the enormous number of electronic configurations and relativistic effects, which need to be taken into account. Here we report results on multiple ionization of xenon atoms by ultra-intense (about 10 19  W/cm 2 ) femtosecond X-ray pulses at photon energies from 5.5 to 8.3 keV and present a theoretical model capable of reproducing the experimental data in the entire energy range. Our analysis shows that the interplay of resonant and relativistic effects results in strongly structured charge state distributions, which reflect resonant positions of relativistically shifted electronic levels of highly charged ions created during the X-ray pulse. The theoretical approach described here provides a basis for accurate modeling of radiation damage in hard X-ray imaging experiments on targets with high- Z constituents. Availability of intense hard X-ray pulses allows exploration of multiple ionization effects in heavier elements. Here, the authors measure the complex charge state distributions of xenon and found a reasonable agreement by comparing with the model including the relativistic and resonance effects.

The advent of newer, brighter, and more coherent X-ray sources, such as X-ray Free-Electron Lasers (XFELs), represents a tremendous growth in the potential to apply coherent X-rays to determine the structure of materials from the micron-scale down to the Angstrom-scale. There is a significant need for a multi-physics simulation framework to perform source-to-detector simulations for a single particle imaging experiment, including (i) the multidimensional simulation of the X-ray source; (ii) simulation of the wave-optics propagation of the coherent XFEL beams; (iii) atomistic modelling of photon-material interactions; (iv) simulation of the time-dependent diffraction process, including incoherent scattering; (v) assembling noisy and incomplete diffraction intensities into a three-dimensional data set using the Expansion-Maximisation-Compression (EMC) algorithm and (vi) phase retrieval to obtain structural information. We demonstrate the framework by simulating a single-particle experiment for a nitrogenase iron protein using parameters of the SPB/SFX instrument of the European XFEL. This exercise demonstrably yields interpretable consequences for structure determination that are crucial yet currently unavailable for experiment design.

In this work, we analyze the application of X-ray diffraction imaging techniques to follow ultrafast structural transitions in solid materials using the example of an X-ray pump–X-ray probe experiment with a single-crystal silicon performed at a Linac Coherent Light Source. Due to the spatially non-uniform profile of the X-ray beam, the diffractive signal recorded in this experiment included contributions from crystal parts experiencing different fluences from the peak fluence down to zero. With our theoretical model, we could identify specific processes contributing to the silicon melting in those crystal regions, i.e., the non-thermal and thermal melting whose occurrences depended on the locally absorbed X-ray doses. We then constructed the total volume-integrated signal by summing up the coherent signal contributions (amplitudes) from the various crystal regions and found that this significantly differed from the signals obtained for a few selected uniform fluence values, including the peak fluence. This shows that the diffraction imaging signal obtained for a structurally damaged material after an impact of a non-uniform X-ray pump pulse cannot be always interpreted as the material’s response to a pulse of a specific (e.g., peak) fluence as it is sometimes believed. This observation has to be taken into account in planning and interpreting future experiments investigating structural changes in materials with X-ray diffraction imaging.