Effects of temperature and ionic strength on the microscopic structure and dynamics of egg white gels.

We investigate the thermal gelation of egg white proteins at different temperatures with varying salt concentrations using x-ray photon correlation spectroscopy in the geometry of ultra-small angle x-ray scattering. Temperature-dependent structural investigation suggests a faster network formation with increasing temperature, and the gel adopts a more compact network, which is inconsistent with the conventional understanding of thermal aggregation. The resulting gel network shows a fractal dimension δ, ranging from 1.5 to 2.2. The values of δ display a non-monotonic behavior with increasing amount of salt. The corresponding dynamics in the q range of 0.002-0.1 nm-1 is observable after major change of the gel structure. The extracted relaxation time exhibits a two-step power law growth in dynamics as a function of waiting time. In the first regime, the dynamics is associated with structural growth, whereas the second regime is associated with the aging of the gel, which is directly linked with its compactness, as quantified by the fractal dimension. The gel dynamics is characterized by a compressed exponential relaxation with a ballistic-type of motion. The addition of salt gradually makes the early stage dynamics faster. Both gelation kinetics and microscopic dynamics show that the activation energy barrier in the system systematically decreases with increasing salt concentration.

Nanoscale Transient Magnetization Gratings Created and Probed by Femtosecond Extreme Ultraviolet Pulses.

We utilize coherent femtosecond extreme ultraviolet (EUV) pulses from a free electron laser (FEL) to generate transient periodic magnetization patterns with periods as short as 44 nm. Combining spatially periodic excitation with resonant probing at the M-edge of cobalt allows us to create and probe transient gratings of electronic and magnetic excitations in a CoGd alloy. In a demagnetized sample, we observe an electronic excitation with a rise time close to the FEL pulse duration and ∼0.5 ps decay time indicative of electron-phonon relaxation. When the sample is magnetized to saturation in an external field, we observe a magnetization grating, which appears on a subpicosecond time scale as the sample is demagnetized at the maxima of the EUV intensity and then decays on the time scale of tens of picoseconds via thermal diffusion. The described approach opens multiple avenues for studying dynamics of ultrafast magnetic phenomena on nanometer length scales.

Microscopic Dynamics of Liquid-Liquid Phase Separation and Domain Coarsening in a Protein Solution Revealed by X-Ray Photon Correlation Spectroscopy.

While the interplay between liquid-liquid phase separation (LLPS) and glass formation in biological systems is highly relevant for their structure formation and thus function, the exact underlying mechanisms are not well known. The kinetic arrest originates from the slowdown at the molecular level, but how this propagates to the dynamics of microscopic phase domains is not clear. Since with diffusion, viscoelasticity, and hydrodynamics, distinctly different mechanisms are at play, the dynamics needs to be monitored on the relevant time and length scales and compared to theories of phase separation. Using x-ray photon correlation spectroscopy, we determine the LLPS dynamics of a model protein solution upon low temperature quenches and find distinctly different dynamical regimes. We observe that the early stage LLPS is driven by the curvature of the free energy and speeds up upon increasing quench depth. In contrast, the late stage dynamics slows down with increasing quench depth, fingerprinting a nearby glass transition. The dynamics observed shows a ballistic type of motion, implying that viscoelasticity plays an important role during LLPS. We explore possible explanations based on the Cahn-Hilliard theory with nontrivial mobility parameters and find that these can only partially explain our findings.

Kinetics of Network Formation and Heterogeneous Dynamics of an Egg White Gel Revealed by Coherent X-Ray Scattering.

The kinetics of heat-induced gelation and the microscopic dynamics of a hen egg white gel are probed using x-ray photon correlation spectroscopy along with ultrasmall-angle x-ray scattering. The kinetics of structural growth reveals a reaction-limited aggregation process with a gel fractal dimension of ≈2 and an average network mesh size of ca. 400 nm. The dynamics probed at these length scales reveals an exponential growth of the characteristic relaxation times followed by an intriguing steady state in combination with a compressed exponential correlation function and a temporal heterogeneity. The degree of heterogeneity increases with decreasing length scale. We discuss our results in the broader context of experiments and models describing attractive colloidal gels.

Ferroelectric domain wall dynamics characterized with X-ray photon correlation spectroscopy.

Technologically important properties of ferroic materials are determined by their intricate response to external stimuli. This response is driven by distortions of the crystal structure and/or by domain wall motion. Experimental separation of these two mechanisms is a challenging problem which has not been solved so far. Here, we apply X-ray photon correlation spectroscopy (XPCS) to extract the contribution of domain wall dynamics to the overall response. Furthermore, we show how to distinguish the dynamics related to the passing of domain walls through the periodic (Peierls) potential of the crystal lattice and through the random potential caused by lattice defects (pinning centers). The approach involves the statistical analysis of correlations between X-ray speckle patterns produced by the interference of coherent synchrotron X-rays scattered from different nanosize volumes of the crystal and identification of Poisson-type contribution to the statistics. We find such a contribution in the thermally driven response of the monoclinic phase of a ferroelectric PbZr0.55Ti0.45O3 crystal and calculate the number of domain wall jumps in the studied microvolume.

Towards molecular movies with X-ray photon correlation spectroscopy.

In this perspective article we highlight research opportunities and challenges in probing structural dynamics of molecular systems using X-ray Photon Correlation Spectroscopy (XPCS). The development of new X-ray sources, such as 4th generation storage rings and X-ray free-electron lasers (XFELs), provides promising new insights into molecular motion. Employing XPCS at these sources allows to capture a very broad range of timescales and lengthscales, spanning from femtoseconds to minutes and atomic scales to the mesoscale. Here, we discuss the scientific questions that can be addressed with these novel tools for two prominent examples: the dynamics of proteins in biomolecular condensates and the dynamics of supercooled water. Finally, we provide practical tips for designing and estimating feasibility of XPCS experiments as well as on detecting and mitigating radiation damage.

Implications of disturbed photon-counting statistics of Eiger detectors for X-ray speckle visibility experiments.

This paper reports on coherent scattering experiments in the low-count regime with less than one photon per pixel per acquisition on average, conducted with two detectors based on the Eiger single-photon-counting chip. The obtained photon-count distributions show systematic deviations from the expected Poisson-gamma distribution, which result in a strong overestimation of the measured speckle contrast. It is shown that these deviations originate from an artificial increase of double-photon events, which is proportional to the detected intensity and inversely proportional to the exposure time. The observed miscounting effect may have important implications for new coherent scattering experiments emerging with the advent of high-brilliance X-ray sources. Different correction schemes are discussed in order to obtain the correct photon distributions from the data. A successful correction is demonstrated with the measurement of Brownian motion from colloidal particles using X-ray speckle visibility spectroscopy.

Low Dose X-Ray Speckle Visibility Spectroscopy Reveals Nanoscale Dynamics in Radiation Sensitive Ionic Liquids.

X-ray radiation damage provides a serious bottleneck for investigating microsecond to second dynamics on nanometer length scales employing x-ray photon correlation spectroscopy. This limitation hinders the investigation of real time dynamics in most soft matter and biological materials which can tolerate only x-ray doses of kGy and below. Here, we show that this bottleneck can be overcome by low dose x-ray speckle visibility spectroscopy. Employing x-ray doses of 22-438 kGy and analyzing the sparse speckle pattern of count rates as low as 6.7×10^{-3} per pixel, we follow the slow nanoscale dynamics of an ionic liquid (IL) at the glass transition. At the prepeak of nanoscale order in the IL, we observe complex dynamics upon approaching the glass transition temperature T_{G} with a freezing in of the alpha relaxation and a multitude of millisecond local relaxations existing well below T_{G}. We identify this fast relaxation as being responsible for the increasing development of nanoscale order observed in ILs at temperatures below T_{G}.

Nano-beam X-ray microscopy of dried colloidal films.

We report on a nano-beam small angle X-ray scattering study on densely-packed, dried binary films made out of spherical silica particles with radii of 11.2 and 19.3 nm. For these three-dimensional thin films prepared by drop casting, only a finite number of colloidal particles contributes to the scattering signal due to the small beam size of 400 × 400 nm(2). By scanning the samples, the structure and composition of the silica particle films are determined spatially resolved revealing spatial heterogeneities in the films. Three different types of domains were identified: regions containing mainly large particles, regions containing mainly small particles, and regions where both particle species are mixed. Using the new angular X-ray cross-correlations analysis (XCCA) approach, spatial maps of the local type and degree of orientational order within the silica particle films are obtained. Whereas the mixed regions have dominant two-fold order, weaker four-fold and marginal six-fold order, regions made out of large particles are characterized by an overall reduced orientational order. Regions of small particles are highly ordered showing actually crystalline order. Distinct differences in the local particle order are observed by analyzing sections through the intensity and XCCA maps. The different degree of order can be understood by the different particle size polydispersities. Moreover, we show that preferential orientations of the particle domains can be studied by cross-correlation analysis yielding information on particle film formation. We find patches of preferential order with an average size of 8-10 µm. Thus, by this combined X-ray cross-correlation microscopy (XCCM) approach the structure and orientational order of films made out of nanometer sized colloids can be determined. This method will allow to reveal the local structure and order of self-assembled structures with different degree of order in general.

(Sub-)Picosecond Surface Correlations of Femtosecond Laser Excited Al-Coated Multilayers Observed by Grazing-Incidence X-ray Scattering.

Femtosecond high-intensity laser pulses at intensities surpassing 1014 W/cm2 can generate a diverse range of functional surface nanostructures. Achieving precise control over the production of these functional structures necessitates a thorough understanding of the surface morphology dynamics with nanometer-scale spatial resolution and picosecond-scale temporal resolution. In this study, we show that single XFEL pulses can elucidate structural changes on surfaces induced by laser-generated plasmas using grazing-incidence small-angle X-ray scattering (GISAXS). Using aluminium-coated multilayer samples we distinguish between sub-picosecond (ps) surface morphology dynamics and subsequent multi-ps subsurface density dynamics with nanometer-depth sensitivity. The observed subsurface density dynamics serve to validate advanced simulation models representing matter under extreme conditions. Our findings promise to open new avenues for laser material-nanoprocessing and high-energy-density science.

Nanocrystallites Modulate Intermolecular Interactions in Cryoprotected Protein Solutions.

Studying protein interactions at low temperatures has important implications for optimizing cryostorage processes of biological tissue, food, and protein-based drugs. One of the major issues is related to the formation of ice nanocrystals, which can occur even in the presence of cryoprotectants and can lead to protein denaturation. The presence of ice nanocrystals in protein solutions poses several challenges since, contrary to microscopic ice crystals, they can be difficult to resolve and can complicate the interpretation of experimental data. Here, using a combination of small- and wide-angle X-ray scattering (SAXS and WAXS), we investigate the structural evolution of concentrated lysozyme solutions in a cryoprotected glycerol-water mixture from room temperature (T = 300 K) down to cryogenic temperatures (T = 195 K). Upon cooling, we observe a transition near the melting temperature of the solution (T ≈ 245 K), which manifests both in the temperature dependence of the scattering intensity peak position reflecting protein-protein length scales (SAXS) and the interatomic distances within the solvent (WAXS). Upon thermal cycling, a hysteresis is observed in the scattering intensity, which is attributed to the formation of nanocrystallites in the order of 10 nm. The experimental data are well described by the two-Yukawa model, which indicates temperature-dependent changes in the short-range attraction of the protein-protein interaction potential. Our results demonstrate that the nanocrystal growth yields effectively stronger protein-protein attraction and influences the protein pair distribution function beyond the first coordination shell.

X-ray driven and intrinsic dynamics in protein gels.

We use X-ray photon correlation spectroscopy to investigate how structure and dynamics of egg white protein gels are affected by X-ray dose and dose rate. We find that both, changes in structure and beam-induced dynamics, depend on the viscoelastic properties of the gels with soft gels prepared at low temperatures being more sensitive to beam-induced effects. Soft gels can be fluidized by X-ray doses of a few kGy with a crossover from stress relaxation dynamics (Kohlrausch-Williams-Watts exponents [Formula: see text] to 2) to typical dynamical heterogeneous behavior ([Formula: see text]1) while the high temperature egg white gels are radiation-stable up to doses of 15 kGy with [Formula: see text]. For all gel samples we observe a crossover from equilibrium dynamics to beam induced motion upon increasing X-ray fluence and determine the resulting fluence threshold values [Formula: see text]. Surprisingly small threshold values of [Formula: see text] s[Formula: see text] nm[Formula: see text] can drive the dynamics in the soft gels while for stronger gels this threshold is increased to [Formula: see text] s[Formula: see text] nm[Formula: see text]. We explain our observations with the viscoelastic properties of the materials and can connect the threshold dose for structural beam damage with the dynamic properties of beam-induced motion. Our results suggest that soft viscoelastic materials can display pronounced X-ray driven motion even for low X-ray fluences. This induced motion is not detectable by static scattering as it appears at dose values well below the static damage threshold. We show that intrinsic sample dynamics can be separated from X-ray driven motion by measuring the fluence dependence of the dynamical properties.

Exploring non-equilibrium processes and spatio-temporal scaling laws in heated egg yolk using coherent X-rays.

The soft-grainy microstructure of cooked egg yolk is the result of a series of out-of-equilibrium processes of its protein-lipid contents; however, it is unclear how egg yolk constituents contribute to these processes to create the desired microstructure. By employing X-ray photon correlation spectroscopy, we investigate the functional contribution of egg yolk constituents: proteins, low-density lipoproteins (LDLs), and yolk-granules to the development of grainy-gel microstructure and microscopic dynamics during cooking. We find that the viscosity of the heated egg yolk is solely determined by the degree of protein gelation, whereas the grainy-gel microstructure is controlled by the extent of LDL aggregation. Overall, protein denaturation-aggregation-gelation and LDL-aggregation follows Arrhenius-type time-temperature superposition (TTS), indicating an identical mechanism with a temperature-dependent reaction rate. However, above 75 °C TTS breaks down and temperature-independent gelation dynamics is observed, demonstrating that the temperature can no longer accelerate certain non-equilibrium processes above a threshold value.

Coherent X-ray Scattering Reveals Nanoscale Fluctuations in Hydrated Proteins.

Hydrated proteins undergo a transition in the deeply supercooled regime, which is attributed to rapid changes in hydration water and protein structural dynamics. Here, we investigate the nanoscale stress-relaxation in hydrated lysozyme proteins stimulated and probed by X-ray Photon Correlation Spectroscopy (XPCS). This approach allows us to access the nanoscale dynamics in the deeply supercooled regime (T = 180 K), which is typically not accessible through equilibrium methods. The observed stimulated dynamic response is attributed to collective stress-relaxation as the system transitions from a jammed granular state to an elastically driven regime. The relaxation time constants exhibit Arrhenius temperature dependence upon cooling with a minimum in the Kohlrausch-Williams-Watts exponent at T = 227 K. The observed minimum is attributed to an increase in dynamical heterogeneity, which coincides with enhanced fluctuations observed in the two-time correlation functions and a maximum in the dynamic susceptibility quantified by the normalized variance χT. The amplification of fluctuations is consistent with previous studies of hydrated proteins, which indicate the key role of density and enthalpy fluctuations in hydration water. Our study provides new insights into X-ray stimulated stress-relaxation and the underlying mechanisms behind spatiotemporal fluctuations in biological granular materials.

High wavevector temporal speckle correlations at the Linac Coherent Light Source.

We report on the feasibility of high wavevector temporal speckle correlation measurements at the world's first hard x-ray free electron laser, the Linac Coherent Light Source (LCLS). Due to the chaotic nature of LCLS, the spectral profile of the x-ray radiation fluctuates on a pulse-to-pulse basis. Its impact on the determination of the single shot speckle contrast in a wide angle x-ray scattering geometry is investigated by analyzing FEL power spectra that are simulated based on the nominal operational parameters of LCLS. Ultimately, a potential scheme to deliver a single-mode hard x-ray pulse is proposed by using a narrow bandpass crystal monochromator.

Femtosecond single-shot imaging of nanoscale ferromagnetic order in Co/Pd multilayers using resonant x-ray holography.

We present the first single-shot images of ferromagnetic, nanoscale spin order taken with femtosecond x-ray pulses. X-ray-induced electron and spin dynamics can be outrun with pulses shorter than 80 fs in the investigated fluence regime, and no permanent aftereffects in the samples are observed below a fluence of 25 mJ/cm(2). Employing resonant spatially muliplexed x-ray holography results in a low imaging threshold of 5 mJ/cm(2). Our results open new ways to combine ultrafast laser spectroscopy with sequential snapshot imaging on a single sample, generating a movie of excited state dynamics.

X-ray cross correlation analysis uncovers hidden local symmetries in disordered matter.

We explore the different local symmetries in colloidal glasses beyond the standard pair correlation analysis. Using our newly developed X-ray cross correlation analysis (XCCA) concept together with brilliant coherent X-ray sources, we have been able to access and classify the otherwise hidden local order within disorder. The emerging local symmetries are coupled to distinct momentum transfer (Q) values, which do not coincide with the maxima of the amorphous structure factor. Four-, 6-, 10- and, most prevalently, 5-fold symmetries are observed. The observation of dynamical evolution of these symmetries forms a connection to dynamical heterogeneities in glasses, which is far beyond conventional diffraction analysis. The XCCA concept opens up a fascinating view into the world of disorder and will definitely allow, with the advent of free electron X-ray lasers, an accurate and systematic experimental characterization of the structure of the liquid and glass states.

Reverse-engineering method for XPCS studies of non-equilibrium dynamics.

X-ray photon correlation spectroscopy (XPCS) is a powerful tool in the investigation of dynamics covering a broad time and length scale. It has been widely used to probe dynamics for systems in both equilibrium and non-equilibrium states; in particular, for systems undergoing a phase transition where the structural growth kinetics and the microscopic dynamics are strongly intertwined. The resulting time-dependent dynamic behavior can be described using the two-time correlation function (TTC), which, however, often contains more interesting features than the component along the diagonal, and cannot be easily interpreted via the classical simulation methods. Here, a reverse engineering (RE) approach is proposed based on particle-based heuristic simulations. This approach is applied to an XPCS measurement on a protein solution undergoing a liquid-liquid phase separation. It is demonstrated that the rich features of experimental TTCs can be well connected with the key control parameters including size distribution, concentration, viscosity and mobility of domains. The dynamic information obtained from this RE analysis goes beyond the existing theory. The RE approach established in this work is applicable for other processes such as film growth, coarsening or evolving systems.

Automated matching of two-time X-ray photon correlation maps from phase-separating proteins with Cahn-Hilliard-type simulations using auto-encoder networks.

Machine learning methods are used for an automated classification of experimental two-time X-ray photon correlation maps from an arrested liquid-liquid phase separation of a protein solution. The correlation maps are matched with correlation maps generated with Cahn-Hilliard-type simulations of liquid-liquid phase separations according to two simulation parameters and in the last step interpreted in the framework of the simulation. The matching routine employs an auto-encoder network and a differential evolution based algorithm. The method presented here is a first step towards handling large amounts of dynamic data measured at high-brilliance synchrotron and X-ray free-electron laser sources, facilitating fast comparison with phase field models of phase separation.

Resolving molecular diffusion and aggregation of antibody proteins with megahertz X-ray free-electron laser pulses.

X-ray free-electron lasers (XFELs) with megahertz repetition rate can provide novel insights into structural dynamics of biological macromolecule solutions. However, very high dose rates can lead to beam-induced dynamics and structural changes due to radiation damage. Here, we probe the dynamics of dense antibody protein (Ig-PEG) solutions using megahertz X-ray photon correlation spectroscopy (MHz-XPCS) at the European XFEL. By varying the total dose and dose rate, we identify a regime for measuring the motion of proteins in their first coordination shell, quantify XFEL-induced effects such as driven motion, and map out the extent of agglomeration dynamics. The results indicate that for average dose rates below 1.06 kGy µs-1 in a time window up to 10 µs, it is possible to capture the protein dynamics before the onset of beam induced aggregation. We refer to this approach as correlation before aggregation and demonstrate that MHz-XPCS bridges an important spatio-temporal gap in measurement techniques for biological samples.