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We simulated Coulomb explosion dynamics due to fast ionization induced by high-intensity x-rays in six proteins that share similar atomic content and shape. We followed and projected the trajectory of the fragments onto a virtual detector, providing a unique explosion footprint. After collecting 500 explosion footprints for each protein, we utilized principal component analysis and 𝑡-distributed stochastic neighbor embedding to classify these. Results show that the classification algorithms were able to separate proteins on the basis of explosion footprints from structurally similar proteins into distinct groups. The explosion footprints, therefore, provide a unique identifier for each protein. We envision that method could be used concurrently with single-particle coherent imaging experiments to provide additional information on shape, mass, or conformation.

We describe a method to compute photon–matter interaction and atomic dynamics with x-ray lasers using a hybrid code based on classical molecular dynamics and collisional-radiative calculations. The forces between the atoms are dynamically determined based on changes to their electronic occupations and the formation of a free electron cloud created from the irradiation of photons in the x-ray spectrum. The rapid transition from neutral solid matter to dense plasma phase allows the use of screened potentials, reducing the number of non-bonded interactions. In combination with parallelization through domain decomposition, the hybrid code handles large-scale molecular dynamics and ionization. This method is applicable for large enough samples (solids, liquids, proteins, viruses, atomic clusters, and crystals) that, when exposed to an x-ray laser pulse, turn into a plasma in the first few femtoseconds of the interaction. We present four examples demonstrating the applicability of the method. We investigate the non-thermal heating and scattering of bulk water and damage-induced dynamics of a protein crystal using an x-ray pump–probe scheme. In both cases, we compare to the experimental data. For single particle imaging, we simulate the ultrafast dynamics of a methane cluster exposed to a femtosecond x-ray laser. In the context of coherent diffractive imaging, we study the fragmentation as given by an x-ray pump–probe setup to understand the evolution of radiation damage in the time range of hundreds of femtoseconds.

Biological structure determination has had new avenues of investigation opened due to the introduction of X-ray free-electron lasers (XFELs). These X-ray lasers provide an extreme amount of photons on ultrafast timescales used to probe matter, and in particular biomolecules. The high intensity of the X-rays destroys the sample, though not before structural information has been acquired. The unique properties of the probe provide the unprecedented opportunity to study the un-crystallized form of biological macromolecules, small crystals of biomolecules and their dynamics. 

In this work, we study processes in XFEL imaging experiments that could affect the achievable resolution of the protein structure in a diffraction experiment. Elastic scattering is the process which provides structural information and leaves the sample unperturbed. This interaction occurs far less often compared to damage inducing processes, such as photoabsorption, which leads to rapid ionization of the studied sample. By using density functional theory, we study the effect of ultrahigh charge states in small systems, such as amino acids and peptides, on the subsequent bond breaking and charge dynamics. Reproducible fragmentation patterns are studied in order to find features that could be understood in larger systems, such as proteins. 

Biomolecules are dynamical systems, and the currently used pulse duration is not short enough to outrun the movement of the atoms. The diffraction patterns acquired in an experiment are therefore an incoherent sum of slightly different conformations of the same system. Water can help to reduce these structural variations, but the water molecules themselves will then be a source of noise. Using classical molecular dynamics, we study the optimal amount of water that should be used to achieve the highest resolution. 

To simulate ultrafast molecular dynamics of larger systems such as proteins, we develop a hybrid Monte Carlo/molecular dynamics model. We utilize it to simulate the fragmentation dynamics of small proteins and investigate the possibility to extract structural information from the fragmentation patterns. For larger systems exposed to X-ray lasers, such as viruses and crystals, we develop a hybrid collisional-radiative and classical molecular dynamics approach. The method is used in several projects, both in theoretical studies and to support experiments conducted at XFEL facilities. In particular, we simulate the interaction of hexagonal ice with an X-ray laser, and show the structure makes a phase transition from the native crystal state to a plasma, while still partly retaining structural order. Furthermore, we note that the structural changes occur in an anisotropic manner, where different local structural configurations in ice decay on different time-scales. 

Preliminary experimental results show this anisotropic dynamics in an X-ray pump-probe serial femtosecond X-ray crystallography experiment performed on  I3C crystals. The real space dynamics as a function of probe delay given by our theoretical model and the experiment both show good agreement, where the iodine atoms exhibit correlated motion. The model is also used to calculate the expected atomic displacement and ionization in a hemoglobin crystal, revealing the time and length scales of the dynamics in the protein during the experiment. 

Water and ice are routinely studied with X-rays to reveal their diverse structures and anomalous properties. We employ a hybrid collisional-radiative/molecular-dynamics method to explore how femtosecond X-ray pulses interact with hexagonal ice. We find that ice makes a phase transition into a crystalline plasma where its initial structure is maintained up to tens of femtoseconds. The ultrafast melting process occurs anisotropically, where different geometric configurations of the structure melt on different time scales. The transient state and anisotropic melting of crystals can be captured by X-ray diffraction, which impacts any study of crystalline structures probed by femtosecond X-ray lasers.

- Single particle imaging using X-ray lasers is a technique aiming to capture atomic resolution structures of biomolecules in their native state. Knowing the particle's orientation during exposure is crucial for method enhancement. It has been shown that the trajectories of sulfur atoms in a Coulomb exploding lysozyme are reproducible, providing orientation information. This study explores if sulfur atom depth influences explosion trajectory. Employing a hybrid collisional-radiative/molecular dynamics model, we analyze the X-ray laser-induced dynamics of a single sulfur ion at varying depths in water. Our findings indicate that the ion spread-depth relationship depends on pulse parameters. At a photon energy of 2 keV, high-charge states are obtained, resulting in an increase of the spread with depth. However, at 8 keV photon energy, where lower charge states are obtained, the spread is essentially independent with depth. Finally, lower ion mass results in less reproducible trajectories, opening a promising route for determining protein orientation through the introduction of heavy atoms.

MS SPIDOC is a novel sample delivery system designed for single (isolated) particle imaging at X-ray Free-Electron Lasers that is adaptable towards most large-scale facility beamlines. Biological samples can range from small proteins to MDa particles. Following nano-electrospray ionization, ionic samples can be m/z-filtered and structurally separated before being oriented at the interaction zone. Here, we present the simulation package developed alongside this prototype. The first part describes how the front-to-end ion trajectory simulations have been conducted. Highlighted is a quadrant lens; a simple but efficient device that steers the ion beam within the vicinity of the strong DC orientation field in the interaction zone to ensure spatial overlap with the X-rays. The second part focuses on protein orientation and discusses its potential with respect to diffractive imaging methods. Last, coherent diffractive imaging of prototypical T = 1 and T = 3 norovirus capsids is shown. We use realistic experimental parameters from the SPB/SFX instrument at the European XFEL to demonstrate that low-resolution diffractive imaging data (q < 0.3 nm⁻¹) can be collected with only a few X-ray pulses. Such low-resolution data are sufficient to distinguish between both symmetries of the capsids, allowing to probe low abundant species in a beam if MS SPIDOC is used as sample delivery.

X-ray free-electrons lasers have revolutionized the method of imaging biological macromolecules such as proteins, viruses and cells by opening the door to structural determination of both single particles and crystals at room temperature. By utilizing high intensity X-ray pulses on femtosecond timescales, the effects of radiation damage can be reduced. Achieving high resolution structures will likely require knowledge of how radiation damage affects the structure on an atomic scale, since the experimentally obtained electron densities will be reconstructed in the presence of radiation damage. Detailed understanding of the expected damage scenarios provides further information, in addition to guiding possible corrections that may need to be made to obtain a damage free reconstruction. In this work, we have quantified the effects of ionizing photon-matter interactions using first principles molecular dynamics. We utilize density functional theory to calculate bond breaking and charge dynamics in three ultracharged molecules and two different structural conformations that are important to the structural integrity of biological macromolecules, comparing to our previous studies on amino acids. The effects of the ultracharged states and subsequent bond breaking in real space are studied in reciprocal space using coherent diffractive imaging of an ensemble of aligned biomolecules in the gas phase.

X-rays are routinely used for structural studies through scattering, and femtosecond X-ray lasers can probe ultrafast dynamics. We aim to capture the femtosecond dynamics of liquid samples using simulations and deconstruct the interplay of ionization and atomic motion within the X-ray laser pulse. This deconstruction is resolution dependent, as ionization influences the low momentum transfers through changes in scattering form factors, while atomic motion has a greater effect at high momentum transfers through loss of coherence. Our methodology uses a combination of classical molecular dynamics and plasma simulation on a protic ionic liquid to quantify the contributions to the scattering signal and how these evolve with time during the X-ray laser pulse. Our method is relevant for studies of organic liquids, biomolecules in solution or any low-Z materials at liquid densities that quickly turn into a plasma while probed with X-rays.

One of the challenges facing single particle imaging with ultrafast X-ray pulses is the structural heterogeneity of the sample to be imaged. For the method to succeed with weakly scattering samples, the diffracted images from a large number of individual proteins need to be averaged. The more the individual proteins differ in structure, the lower the achievable resolution in the final reconstructed image. We use molecular dynamics to simulate two globular proteins in vacuum, fully desolvated as well as with two different solvation layers, at various temperatures. We calculate the diffraction patterns based on the simulations and evaluate the noise in the averaged patterns arising from the structural differences and the surrounding water. Our simulations show that the presence of a minimal water coverage with an average 3 Å thickness will stabilize the protein, reducing the noise associated with structural heterogeneity, whereas additional water will generate more background noise.

Historically, structure determination of nanocrystals, proteins, and macromolecules required the growth of high-quality crystals sufficiently large to diffract X-rays efficiently while withstanding radiation damage. The development of the X-ray free-electron laser has opened the path toward high resolution single particle imaging, and the extreme intensity of the X-rays ensures that enough diffraction statistics are collected before the sample is destroyed by radiation damage. Still, recovery of the structure is a challenge, in part due to the partial fragmentation of the sample during the diffraction event. In this study, we use first-principles based methods to study the impact of radiation induced ionization of six amino acids on the reconstruction process. In particular, we study the fragmentation and charge rearrangement to elucidate the time scales involved and the characteristic fragments occurring.