Multi-speckle X-ray photon correlation spectroscopy in the ultra-small-angle X-ray scattering range

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.

Spatially-resolved nanometer-scale measurement of cartilage extracellular matrix mobility

OBJECTIVE

Tissues have complex structures, comprised of solid and fluid phases. Improved understanding of interactions between joint fluid and extracellular matrix (ECM) is required in models of cartilage mechanics. X-ray photon correlation spectroscopy (XPCS) directly measures nanometer-scale dynamics and can provide insight into biofluid-biosolid interactions in cartilage. This study applies XPCS to evaluate dynamic interactions between intact cartilage and biofluids.

DESIGN

Cartilage biopsies were collected from bovine femoral condyles. During XPCS measurements, cartilage samples were exposed to different fluids: deionized water, PBS, synovial fluid, or sonicated synovial fluid. ECM-biofluid interactions were also assessed at different length scales and different depths from the cartilage surface.

RESULTS

Using XPCS, cartilage ECM mobility was detected at length scales from 50 to 207 nm. As length scale decreased, time scale for autocorrelation decay decreased, suggesting smaller ECM components are more mobile. ECM dynamics were slowed by dehydrating the sample, demonstrating XPCS assesses matrix mobility in hydrated environments. At all length scales, the matrix was more mobile in deionized water and slowest in synovial fluid. Using the 207 nm length scale assessment, ECM dynamics in synovial fluid were fastest at the cartilage surface and progressively slowed as depth into the sample increased, demonstrating XPCS can assess spatial distribution of ECM dynamics. Finally, ECM mobility increased for degraded synovial fluid.

CONCLUSIONS

This study demonstrates the potential of XPCS to provide unique insights into nanometer-scale cartilage ECM mobility in a spatially resolved manner and illustrates the importance of biosolid-biofluid interactions in dictating ECM dynamics.

From Femtoseconds to Hours—Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays

X-ray photon correlation spectroscopy (XPCS) enables the study of sample dynamics between micrometer and atomic length scales. As a coherent scattering technique, it benefits from the increased brilliance of the next-generation synchrotron radiation and Free-Electron Laser (FEL) sources. In this article, we will introduce the XPCS concepts and review the latest developments of XPCS with special attention on the extension of accessible time scales to sub-μs and the application of XPCS at FELs. Furthermore, we will discuss future opportunities of XPCS and the related technique X-ray speckle visibility spectroscopy (XSVS) at new X-ray sources. Due to its particular signal-to-noise ratio, the time scales accessible by XPCS scale with the square of the coherent flux, allowing to dramatically extend its applications. This will soon enable studies over more than 18 orders of magnitude in time by XPCS and XSVS.

X-ray photon correlation spectroscopy of protein dynamics at nearly diffraction-limited storage rings

This study explores the possibility of measuring the dynamics of proteins in solution using X-ray photon correlation spectroscopy (XPCS) at nearly diffraction-limited storage rings (DLSRs). We calculate the signal-to-noise ratio (SNR) of XPCS experiments from a concentrated lysozyme solution at the length scale of the hydrodynamic radius of the protein molecule. We take into account limitations given by the critical X-ray dose and find expressions for the SNR as a function of beam size, sample-to-detector distance and photon energy. Specifically, we show that the combined increase in coherent flux and coherence lengths at the DLSR PETRA IV yields an increase in SNR of more than one order of magnitude. The resulting SNR values indicate that XPCS experiments of biological macromolecules on nanometre length scales will become feasible with the advent of a new generation of synchrotron sources. Our findings provide valuable input for the design and construction of future XPCS beamlines at DLSRs.

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.

Dynamics of proteins in solution

The dynamics of proteins in solution includes a variety of processes, such as backbone and side-chain fluctuations, interdomain motions, as well as global rotational and translational (i.e. center of mass) diffusion. Since protein dynamics is related to protein function and essential transport processes, a detailed mechanistic understanding and monitoring of protein dynamics in solution is highly desirable. The hierarchical character of protein dynamics requires experimental tools addressing a broad range of time- and length scales. We discuss how different techniques contribute to a comprehensive picture of protein dynamics, and focus in particular on results from neutron spectroscopy. We outline the underlying principles and review available instrumentation as well as related analysis frameworks.

D+: software for high-resolution hierarchical modeling of solution X-ray scattering from complex structures

This paper presents the computer program D+ (https://scholars.huji.ac.il/uriraviv/book/d-0), where the reciprocal-grid (RG) algorithm is implemented. D+ efficiently computes, at high-resolution, the X-ray scattering curves from complex structures that are isotropically distributed in random orientations in solution. Structures are defined in hierarchical trees in which subunits can be represented by geometric or atomic models. Repeating subunits can be docked into their assembly symmetries, describing their locations and orientations in space. The scattering amplitude of the entire structure can be calculated by computing the amplitudes of the basic subunits on 3D reciprocal-space grids, moving up in the hierarchy, calculating the RGs of the larger structures, and repeating this process for all the leaves and nodes of the tree. For very large structures (containing over 100 protein subunits), a hybrid method can be used to avoid numerical artifacts. In the hybrid method, only grids of smaller subunits are summed and used as subunits in a direct computation of the scattering amplitude. D+ can accurately analyze both small- and wide-angle solution X-ray scattering data. This article describes how D+ applies the RG algorithm, accounts for rotations and translations of subunits, processes atomic models, accounts for the contribution of the solvent as well as the solvation layer of complex structures in a scalable manner, writes and accesses RGs, interpolates between grid points, computes numerical integrals, enables the use of scripts to define complicated structures, applies fitting algorithms, accounts for several coexisting uncorrelated populations, and accelerates computations using GPUs. D+ may also account for different X-ray energies to analyze anomalous solution X-ray scattering data. An accessory tool that can identify repeating subunits in a Protein Data Bank file of a complex structure is provided. The tool can compute the orientation and translation of repeating subunits needed for exploiting the advantages of the RG algorithm in D+. A Python wrapper (https://scholars.huji.ac.il/uriraviv/book/python-api) is also available, enabling more advanced computations and integration of D+ with other computational tools. Finally, a large number of tests are presented. The results of D+ are compared with those of other programs when possible, and the use of D+ to analyze solution scattering data from dynamic microtubule structures with different protofilament number is demonstrated. D+ and its source code are freely available for academic users and developers (https://bitbucket.org/uriraviv/public-dplus/src/master/).

D+: software for high-resolution hierarchical modeling of solution X-ray scattering from complex structures

This paper presents the computer program D+ (https://scholars.huji.ac.il/uriraviv/book/d-0), where the reciprocal-grid (RG) algorithm is implemented. D+ efficiently computes, at high-resolution, the X-ray scattering curves from complex structures that are isotropically distributed in random orientations in solution. Structures are defined in hierarchical trees in which subunits can be represented by geometric or atomic models. Repeating subunits can be docked into their assembly symmetries, describing their locations and orientations in space. The scattering amplitude of the entire structure can be calculated by computing the amplitudes of the basic subunits on 3D reciprocal-space grids, moving up in the hierarchy, calculating the RGs of the larger structures, and repeating this process for all the leaves and nodes of the tree. For very large structures (containing over 100 protein subunits), a hybrid method can be used to avoid numerical artifacts. In the hybrid method, only grids of smaller subunits are summed and used as subunits in a direct computation of the scattering amplitude. D+ can accurately analyze both small- and wide-angle solution X-ray scattering data. This article describes how D+ applies the RG algorithm, accounts for rotations and translations of subunits, processes atomic models, accounts for the contribution of the solvent as well as the solvation layer of complex structures in a scalable manner, writes and accesses RGs, interpolates between grid points, computes numerical integrals, enables the use of scripts to define complicated structures, applies fitting algorithms, accounts for several coexisting uncorrelated populations, and accelerates computations using GPUs. D+ may also account for different X-ray energies to analyze anomalous solution X-ray scattering data. An accessory tool that can identify repeating subunits in a Protein Data Bank file of a complex structure is provided. The tool can compute the orientation and translation of repeating subunits needed for exploiting the advantages of the RG algorithm in D+. A Python wrapper (https://scholars.huji.ac.il/uriraviv/book/python-api) is also available, enabling more advanced computations and integration of D+ with other computational tools. Finally, a large number of tests are presented. The results of D+ are compared with those of other programs when possible, and the use of D+ to analyze solution scattering data from dynamic microtubule structures with different protofilament number is demonstrated. D+ and its source code are freely available for academic users and developers (https://bitbucket.org/uriraviv/public-dplus/src/master/).

A multipurpose instrument for time-resolved ultra-small-angle and coherent X-ray scattering

This article presents the main technical features and performance of the upgraded beamline ID02 at the ESRF. The beamline combines different small-angle X-ray scattering techniques in one unique instrument, enabling static and kinetic investigations from ångström to micrometre size scales and time resolution down to the sub-millisecond range. The main component of the instrument is an evacuated detector tube of length 34 m and diameter 2 m. Several different detectors are housed inside a motorized wagon that travels along a rail system, allowing an automated change of the sample-detector distance from about 1 to 31 m as well as selection of the desired detector. For optional combined wide-angle scattering measurements, a wide-angle detector is installed at the entrance cone of the tube. A scattering vector (of magnitude q) range of 0.002 ≤ q ≤ 50 nm-1 is covered with two sample-detector distances and a single-beam setting for an X-ray wavelength of 1 Å. In the high-resolution mode, two-dimensional ultra-small-angle X-ray scattering patterns down to q < 0.001 nm-1 can be recorded, and the resulting one-dimensional profiles have superior quality as compared to those measured with an optimized Bonse-Hart instrument. In the highest-resolution mode, the beam is nearly coherent, thereby permitting multispeckle ultra-small-angle X-ray photon correlation spectroscopy measurements. The main applications of the instrument include the elucidation of static and transient hierarchical structures, and nonequilibrium dynamics in soft matter and biophysical systems.

Anomalous Dynamics of Magnetic Anisotropic Colloids Studied by XPCS

The influence of an applied magnetic field on the collective dynamics of novel anisotropic colloidal particles whose shape resembles peanuts is reported. Being made up of hematite cores and silica shells, these micrometer-sized particles align in a direction perpendicular to the applied external magnetic field, and assemble into chains along the field direction. The anisotropic dynamics of these particles is investigated using multispeckle ultrasmall-angle X-ray photon correlation spectroscopy (USA-XPCS). The results indicate that along the direction of the magnetic field, the particle dynamics strongly depends on the length scale probed. Here, the relaxation of the intermediate scattering function follows a compressed exponential behavior at large distances, while it appears diffusive at distances comparable or smaller than the particle size. Perpendicular to the applied field (and along the direction of gravity), the experimental data can be quantitatively reproduced by a combination of an advective term originating from sedimentation and a purely diffusive one that describes the thermal diffusion of the assembled chains and individual particles.

Ultra-small-angle X-ray photon correlation spectroscopy using the Eiger detector

Successful implementation of the single-photon-counting Eiger 500k pixel array detector for sub-millisecond X-ray photon correlation spectroscopy (XPCS) measurements in the ultra-small-angle scattering region is reported. The performance is demonstrated by measuring the dynamics of dilute silica colloids in aqueous solvents when the detector is operated at different counter depths, 4, 8 and 12 bit. In the fastest mode involving 4 bit parallel readout, a stable frame rate of 22 kHz is obtained that enabled measurement of intensity-intensity autocorrelation functions with good statistics down to the 50 µs range for a sample with sufficient scattering power. The high frame rate and spatial resolution together with large number of pixels of the detector facilitate the investigation of sub-millisecond dynamics over a broad length scale by multispeckle XPCS. This is illustrated by an example involving phoretic motion of colloids during the phase separation of the solvent.

Microstructure and dynamics of Janus particles in a phase separating medium

The evolution of interactions and dynamics of Janus colloidal particles suspended in quasi-binary liquid mixtures undergoing phase separation is presented. The experimental system consisted of silica-nickel Janus particles dispersed in mixtures of 3-methylpyridine, water, and heavy water. Colloidal microstructure and dynamics were probed by ultra-small-angle X-ray scattering and ultra-small-angle X-ray photon correlation spectroscopy, respectively. The observed static and dynamic behaviors are significantly different from those found for Stöber silica colloids in this mixture. The Janus particles manifest a slow aggregation below the coexistence temperature and become strongly attractive upon phase separation of the solvent mixture. In the two-phase region, particles tend to display surfactant-like behavior with silica and nickel surfaces likely preferring water and 3-methylpyridine rich phases, respectively. While the onset of diffusiophoretic motion is evident in the dynamics, it is gradually suppressed by particle clustering at the investigated colloid volume fractions.

Effective interactions and dynamics of small passive particles in an active bacterial medium

This article presents an investigation of the interparticle interactions and dynamics of submicron silica colloids suspended in a bath of motile Escherichia coli bacteria. The colloidal microstructure and dynamics were probed by ultra-small-angle x-ray scattering and multi-speckles x-ray photon correlation spectroscopy, respectively. Both static and hydrodynamic interactions were obtained for different colloid volume fractions and bacteria concentrations as well as when the interparticle interaction potential was modified by the motility buffer. Results suggest that motile bacteria reduce the effective attractive interactions between passive colloids and enhance their dynamics at high colloid volume fractions. The enhanced dynamics under different static interparticle interactions can be rationalized in terms of an effective viscosity of the medium and unified by means of an empirical effective temperature of the system. While the influence of swimming bacteria on the colloid dynamics is significantly lower for small particles, the role of motility buffer on the static and dynamic interactions becomes more pronounced.

Multiple-scattering effects in SAXS and XPCS measurements in the ultra-small-angle region

An experimental study of the influence of multiple-scattering events on data acquired by small-angle X-ray scattering (SAXS) and X-ray photon correlation spectroscopy (XPCS) techniques in the ultra-small-angle range is presented. Both techniques rely on the single-scattering assumption and any deviation may lead to erroneous interpretation of structural and dynamical results. Typical effects of multiple scattering on measured static and dynamic scattering from model colloidal suspensions are presented, and it is demonstrated that the same information content as in a single-scattering experiment can be extracted after applying appropriate corrections. The perturbations induced by multiple scattering on resolution, photon statistics and speckle visibility are evaluated and the required optimal experimental conditions are discussed. In many cases, multiple scattering might be tolerable to a certain extent, especially if any shortcomings are outweighed by beneficial effects from counting statistics, acquisition time and signal-to-background ratio. The presented study may help to optimize future experiments and serve as a guide for data evaluation for this type of system.

Development of combined microstructure and structure characterization facility for in situ and operando studies at the Advanced Photon Source

Following many years of evolutionary development, first at the National Synchrotron Light Source, Brookhaven National Laboratory, and then at the Advanced Photon Source (APS), Argonne National Laboratory, the APS ultrasmall-angle X-ray scattering (USAXS) facility has been transformed by several new developments. These comprise a conversion to higher-order crystal optics and higher X-ray energies as the standard operating mode, rapid fly scan measurements also as a standard operational mode, automated contiguous pinhole small-angle X-ray scattering (SAXS) measurements at intermediate scattering vectors, and associated rapid wide-angle X-ray scattering (WAXS) measurements for X-ray diffraction without disturbing the sample geometry. With each mode using the USAXS incident beam optics upstream of the sample, USAXS/SAXS/WAXS measurements can now be made within 5 min, allowing in situ and operando measurement capabilities with great flexibility under a wide range of sample conditions. These developments are described, together with examples of their application to investigate materials phenomena of technological importance. Developments of two novel USAXS applications, USAXSbased X-ray photon correlation spectroscopy and USAXS imaging, are also briefly reviewed.

Velocity Fluctuations in Sedimenting Brownian Particles

We report a gradual transition of dynamics in sedimenting suspensions of charge stabilized Brownian particles prior to the onset of the macroscopic sedimentation front. Using multispeckle ultrasmall-angle x-ray photon correlation spectroscopy (USA-XPCS), we show that well-defined advective motions dominate the colloid dynamics during the early stages of sedimentation. With elapsing time, these advective currents decay and diffusive motions become the dominating contribution in the dynamics. Probing the temporal development of these fluctuations at smaller Peclet numbers (<1) provides a new perspective for the mechanism determining the transient nature of velocity fluctuations in sedimentation and demonstrates new experimental capabilities enabled by multispeckle USA-XPCS.

Phoretic motion of colloids in a phase separating medium

The enhanced motion of dispersed particles driven by a concentration gradient is the basis for diffusiophoresis. Here we present the dynamics of colloids in a phase separating medium probed by X-Ray Photon Correlation Spectroscopy (XPCS) in the ultra-small angle scattering range. Charge stabilized silica colloids suspended in a binary mixture of 3-methylpyridine and water/heavy water are preferentially wetted by 3-methylpyridine and consequently display a phoretic motion towards that phase upon demixing. This activity lasts for hundreds of seconds before the phase separation is complete and the enhanced motion is arrested as the colloids return to normal diffusive dynamics.

On the use of two-time correlation functions for X-ray photon correlation spectroscopy data analysis

Multi-time correlation functions are especially well suited to study non-equilibrium processes. In particular, two-time correlation functions are widely used in X-ray photon correlation experiments on systems out of equilibrium. One-time correlations are often extracted from two-time correlation functions at different sample ages. However, this way of analysing two-time correlation functions is not unique. Here, two methods to analyse two-time correlation functions are scrutinized, and three illustrative examples are used to discuss the implications for the evaluation of the correlation times and functional shape of the correlations.

Structure and Dynamics of Bimodal Colloidal Dispersions in a Low-Molecular-Weight Polymer Solution

We present an experimental study of the structural and dynamical properties of bimodal, micrometer-sized colloidal dispersions (size ratio ≈ 2) in an aqueous solution of low-molecular-weight polymer (polyethylene glycol 2000) using synchrotron ultra-small angle X-ray scattering (USAXS) and USAXS-based X-ray photon correlation spectroscopy. We fixed the volume fraction of the large particles at 5% and systematically increased the volume fraction of the small particles from 0 to 5% to evaluate their effects on the structure and dynamics. The bimodal dispersions were homogenous through the investigated parameter space. We found that the partial structure factors can be satisfactorily retrieved for the bimodal colloidal dispersions using a Percus-Yevick hard-sphere potential when the size distributions of the particles were taken into account. We also found that the partial structure factor between the large particles did not exhibit a significant variation with increasing volume fraction of the small particles, whereas the isothermal compressibility of the binary mixture was found to decrease with increasing volume fraction of the small particles. The dynamics of single-component large-particle dispersion obey the principles of de Gennes narrowing, where the wave vector dependence of the interparticle diffusion coefficient is inversely proportional to the interparticle structure factor. The dynamics of the bimodal dispersions demonstrate a strong dependence on the fraction of small particles. We also made a comparison between the experimental effective dynamic viscosity of the bimodal dispersion with the theoretical predictions, which suggest that the complex mutual interactions between the large and small particles have a strong effect on the dynamic behaviors of bimodal dispersions.

A sub-ms pressure jump setup for time-resolved X-ray scattering

We present a new experimental setup for time-resolved solution small-angle X-ray scattering (SAXS) studies of kinetic processes induced by sub-ms hydrostatic pressure jumps. It is based on a high-force piezo-stack actuator, with which the volume of the sample can be dynamically compressed. The presented setup has been designed and optimized for SAXS experiments with absolute pressures of up to 1000 bars, using transparent diamond windows and an easy-to-change sample capillary. The pressure in the cell can be changed in less than 1 ms, which is about an order of magnitude faster jump than previously obtained by dynamic pressure setups for SAXS. An additional temperature control offers the possibility for automated mapping of p-T phase diagrams. Here we present the technical specifications and first experimental data taken together with a preview of new research opportunities enabled by this setup.