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This talk highlights a proof-of-concept that demonstrates the ability to calculate high-resolution Fourier transforms. These can be combined with multi-scale modeling to simulate scattering over a wide range, from small-angle scattering to XRD and PDF.
The preprint documenting this is available on the ArXiv here:
https://doi.org/10.48550/arXiv.2303.13435
The Jupyter notebook, VASP calculation details and MOUSE measured scattering patterns are available from this Zenodo repository: https://dx.doi.org/10.5281/zenodo.7764045
## Summary:
This notebook and associated datasets (including VASP details) accompany a manuscript available on the ArXiv (https://doi.org/10.48550/arXiv.2303.13435) and hopefully soon in a journal as short communication as well. Most of the details needed to understand this notebook are explained in that paper with the same title as above. For convenience, the abstract is repeated here:
## Paper abstract:
We demonstrate a strategy for simulating wide-range X-ray scattering patterns, which spans the small- and wide scattering angles as well as the scattering angles typically used for Pair Distribution Function (PDF) analysis. Such simulated patterns can be used to test holistic analysis models, and, since the diffraction intensity is presented coupled to the scattering intensity, may offer a novel pathway for determining the degree of crystallinity.
The ``Ultima Ratio'' strategy is demonstrated on a 64-nm Metal Organic Framework (MOF) particle, calculated from $Q<0.01$\,$\mathrm{nm}^{-1}$ up to $Q\approx150$\,$\mathrm{nm}^{-1}$, with a resolution of 0.16\,\AA. The computations exploit a modified 3D Fast Fourier Transform (3D-FFT), whose modifications enable the transformations of matrices at least up to $8000^3$ voxels in size. Multiple of these modified 3D-FFTs are combined to improve the low-$Q$ behaviour.
The resulting curve is compared to a wide-range scattering pattern measured on a polydisperse MOF powder.
While computationally intensive, the approach is expected to be useful for simulating scattering from a wide range of realistic, complex structures, from (poly-)crystalline particles to hierarchical, multicomponent structures such as viruses and catalysts.
The progress in the VAMAS Project #15" Measurement of particle size and shape distribution of bipyramidal titania including deposition from liquid suspension" within TWA 34 Nanoparticle Populations is presented with highlight of the following points:
- Determine and compare particle size and shape distribution by means of:
• electron microscopy (SEM, TEM, STEM-in-SEM)
• atomic force microscopy (AFM)
• small angle X-ray scattering (SAXS)
- Determine uncertainty induced by deposition protocol from liquid suspension with comparison to known values from a prior ILC with already deposited nanoparticles on TEM grids.
- Provide comparative validation of protocols for the techniques other than TEM.
We demonstrate a strategy for simulating wide-range X-ray scattering patterns, which spans the small- and wide scattering angles as well as the scattering angles typically used for Pair Distribution Function (PDF) analysis. Such simulated patterns can be used to test holistic analysis models, and, since the diffraction intensity is on the same scale as the scattering intensity, may offer a novel pathway for determining the degree of crystallinity.
The "Ultima Ratio" strategy is demonstrated on a 64-nm Metal Organic Framework (MOF) particle, calculated from Q < 0.01 1/nm up to Q < 150 1/nm, with a resolution of 0.16 Angstrom. The computations exploit a modified 3D Fast Fourier Transform (3D-FFT), whose modifications enable the transformations of matrices at least up to 8000^3 voxels in size. Multiple of these modified 3D-FFTs are combined to improve the low-Q behaviour. The resulting curve is compared to a wide-range scattering pattern measured on a polydisperse MOF powder. While computationally intensive, the approach is expected to be useful for simulating scattering from a wide range of realistic, complex structures, from (poly-)crystalline particles to hierarchical, multicomponent structures such as viruses and catalysts.
A Round Robin study has been carried out to estimate the impact of the human element in small-angle scattering data analysis. Four corrected datasets were provided to participants ready for analysis. All datasets were measured on samples containing spherical scatterers, with two datasets in dilute dispersions, and two from powders.
Most of the 46 participants correctly identified the number of populations in the dilute dispersions, with half of the population mean entries within 1.5 % and half of the population width entries within 40 %, respectively. Due to the added complexity of the structure factor, much fewer people submitted answers on the powder datasets.
For those that did, half of the entries for the means and widths were within 44 % and 86 % respectively. This Round Robin experiment highlights several causes for the discrepancies, for which solutions are proposed.
Small-angle X-ray scattering (SAXS) can be used for structural determination of biological macromolecules and polymers in their native states (e.g. liquid phase). This means that the structural changes of (bio-)polymers, such as proteins and DNA, can be monitored in situ to understand their sensitivity to changes in chemical environments. In an attempt to improve the reliability of such experiments, the reduction of radiation damage occurring from exposure to X-rays is required. One such method, is to use scavenger molecules to protect macromolecules against radicals produced during radiation exposure, such as reactive oxygen species (ROS). In this study we investigate the feasibility of applying the compatible solute, osmolyte and radiation protector Ectoine (THP(B)), as a scavenger molecule during SAXS measurements of the single-stranded DNA-binding protein Gene-V Protein (G5P/GVP). In this case, we monitor the radiation induced changes of G5P during bio-SAXS measurments and the resulting microscopic energy-damage relation was determined from microdosimetric calculations by Monte-Carlo based particle scattering simulations with TOPAS/Geant4 and a custom target-model. This resulted in a median-lethal energy deposit of pure G5P at 4 mg mL−1 of E1/2 = 7 ± 5 eV, whereas a threefold increase of energy-deposit was needed under the presence of Ectoine to reach the same level of damage. This indicates that Ectoine increases the possible exposure time before radiation-damage to G5P is observed. Furthermore, the dominant type of damage shifted from aggregation in pure solutions towards a fragmentation for solutions containing Ectoine as a cosolute. These results are interpreted in terms of indirect radiation damage by reactive secondary species, as well as post-irradiation effects, related to preferential-exclusion of the cosolute from the protein surface. Hence, Ectoine is shown to provide a non-disturbing way to improve structure-determination of proteins via bio-SAXS in future studies.
Showcasing research from the Federal Institute for Material Research and Testing Berlin and Fraunhofer Institute for Celltherapy and Immunology Branch Bioanalytics and Bioprocesses Potsdam.
Bio-SAXS of single-stranded DNA-binding proteins: Radiation protection by the compatible solute ectoine.
We aimed to increase the possible undisturbed exposure time during bio-SAXS measurements of single-stranded DNA-binding proteins. Therefore small angle X-ray scattering was performed on Gene-V Protein (G5P/GVP), which is involved in DNA repair processes. To achieve this, irradiations were performed in presence and absence of the hydroxyl-radical scavenger and osmolyte Ectoine, which showed efficient radiation protection and prevented protein aggregation, thus allows for a non-disturbing way to improve structure-determination of biomolecules.
X-ray scattering datasets for samples described in the 2022 publication "Side chain length dependent dynamics and conductivity in self assembled ion channels". This dataset includes both raw and processed X-ray scattering data for samples ILC8, ILC10, ILC12, ILC14 and ILC16 alongside background measurement files (BKG).
X-ray scattering datasets for samples described in the 2022 publication "Molecular Mobility of Polynorbornenes with Trimethylsiloxysilyl side groups: Influence of the Polymerization Mechanism". This dataset includes both raw and processed X-ray scattering data for samples APTCN and MPTCN, alongside background measurements files (BKG).
X-ray scattering datasets for samples described in the 2020 publication "Molecular Dynamics of Janus Polynorbornenes: Glass Transitions and Nanophase Separation". This dataset includes both raw and processed X-ray scattering data for samples PTCHSiO-Pr, Bu, Hx, Oc and De, alongside background measurements files (BKG). This data was collected using the MOUSE project (instrument and methodology).
Large, ink-bottle-shaped pores in mesocellular foams (MCFs) are desired for various applications requiring enhanced mass transfer or the immobilization of larger compounds. Hence, the cylindrical pores of COK-12, an ordered mesoporous silica structurally comparable to SBA-15 but synthesized at room-temperature at quasi-neutral pH, are chemically swollen into ink-bottle pores. Therefore, p-xylene is used as a more sustainable swelling agent compared to popular alternatives. Its high boiling point allows for an additional thermal aging step to amplify the mesostructure enlargement without needing additional chemicals. For COK-12, the MCFs obtained at room temperature reach an unprecedented plateau for the modal mesopore cell and window diameter of 19.9 and 5.5 nm, respectively, with an underlying broad pore size distribution and distorted hexagonal lattice up to 14.5 nm, involving hexagonal and spherical structures. The combined chemical and thermal swelling resulted in the selective enlargement of the window diameter to more than 200% and a slightly increased cell diameter, pore size distribution, and hexagonal lattice distortion in comparison to the room temperature synthesis. Such materials are thought to be promising alternatives to SBA-15-based MCFs, often utilizing toxic catalysts during synthesis. The presented results pave the way for enhanced adsorptive, catalytic, and drug delivery performances for COK-12-based materials.
Despite their inherent instability, 4n π systems have recently received significant attention due to their unique optical and electronic properties. In dibenzopentalene (DBP), benzanellation stabilizes the highly antiaromatic pentalene core, without compromising its amphoteric redox behavior or small HOMO−LUMO energy gap. However, incorporating such molecules in organic devices as discrete small molecules or amorphous polymers can limit the performance (e.g., due to solubility in the battery electrolyte solution or low internal surface area). Covalent organic frameworks (COFs), on the contrary, are highly ordered, porous, and crystalline materials that can provide a platform to align molecules with specific properties in a well-defined, ordered environment. We synthesized the first antiaromatic framework materials and obtained a series of three highly crystalline and porous COFs based on DBP. Potential applications of such antiaromatic bulk materials were explored: COF films show a conductivity of 4 × 10−8 S cm−1 upon doping and exhibit photoconductivity upon irradiation with visible light. Application as positive electrode materials in Li-organic batteries demonstrates a significant enhancement of performance when the antiaromaticity of the DBP unit in the COF is exploited in its redox activity with a discharge capacity of 26 mA h g−1 at a potential of 3.9 V vs. Li/Li+ . This work showcases antiaromaticity as a new design principle for functional framework materials.
Small-angle X-ray scattering (SAXS) can be used for structural determination of biological macromolecules and polymers in their native states (e.g. liquid phase). This means that the structural changes of (bio-)polymers, such as proteins and DNA, can be monitored in situ to understand their sensitivity to changes in chemical environments. In an attempt to improve the reliability of such experiments, the reduction of radiation damage occurring from exposure to X-rays is required. One such method, is to use scavenger molecules to protect macromolecules against radicals produced during radiation exposure, such as reactive oxygen species (ROS). In this study we investigate the feasibility of applying the compatible solute, osmolyte and radiation protector Ectoine (THP(B)), as a scavenger molecule during SAXS measurements of the single-stranded DNA-binding protein Gene-V Protein (G5P/GVP). In this case, we monitor the radiation induced changes of G5P during bio-SAXS measurments and the resulting microscopic energy-damage relation was determined from microdosimetric calculations by Monte-Carlo based particle scattering simulations with TOPAS/Geant4 and a custom target-model. This resulted in a median-lethal energy deposit of pure G5P at 4 mg mL−1 of E1/2 = 7 ± 5 eV, whereas a threefold increase of energy-deposit was needed under the presence of Ectoine to reach the same level of damage. This indicates that Ectoine increases the possible exposure time before radiation-damage to G5P is observed. Furthermore, the dominant type of damage shifted from aggregation in pure solutions towards a fragmentation for solutions containing Ectoine as a cosolute. These results are interpreted in terms of indirect radiation damage by reactive secondary species, as well as post-irradiation effects, related to preferential-exclusion of the cosolute from the protein surface. Hence, Ectoine is shown to provide a non-disturbing way to improve structure-determination of proteins via bio-SAXS in future studies.
X-ray scattering and sorption data associated with the publication "Antiaromatic Covalent Organic Frameworks Based on Dibenzopentalenes". X-ray scattering data is provided for COF and POP materials, including data from stability tests, as three-column ascii files with columns q (nm-1), I (m-1) and uncertainty on I, as well as being provided in 2θ.
This dataset contains the processed and analysed small-angle X-ray scattering data associated with all samples from the publications "Bio-SAXS of Single-Stranded DNA-Binding Proteins: Radiation Protection by the Compatible Solute Ectoine" (https://doi.org/10.1039/D2CP05053F).
Files associated with McSAS3 analyses are included, alongside the relevant SAXS data, with datasets labelled in accordance to the protein (G5P), its concentration (1, 2 or 4 mg/mL), and if Ectoine is present (Ect) or absent (Pure). PEPSIsaxs simulations of the GVP monomer (PDB structure: 1GV5 ) and dimer are also included.
TOPAS-bioSAXS-dosimetry extension for TOPAS-nBio based particle scattering simulations can be obtained from https://github.com/MarcBHahn/TOPAS-bioSAXS-dosimetry which is further described in https://doi.org/10.26272/opus4-55751.
This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under grant number 442240902 (HA 8528/2-1 and SE 2999/2-1). We acknowledge Diamond Light Source for time on Beamline B21 under Proposal SM29806. This work has been supported by iNEXT-Discovery, grant number 871037, funded by the Horizon 2020 program of the European Commission.
These are four datasets that were made available to the participants of the Small-angle Scattering data analysis round robin. The intent was to find out how comparable results from different researchers are, who analyse exactly the same processed, corrected dataset.
In this repository, there are:
1) a PDF document with more details for the study,
2) the datasets for people to try and fit,
3) an Excel spreadsheet to document the results.
Datasets 1 and 2 were modified from: Deumer, Jerome, & Gollwitzer, Christian. (2022). npSize_SAXS_data_PTB (Version 5) [Data set]. Zenodo. https://doi.org/10.5281/zenodo.5886834
Datasets 3 and 4 were collected in-house on the MOUSE instrument.
Continuing progress in the field of X-ray scattering methods empowers scientists with new possibilities to capture the most important piece of information about the structure of the sample - its 3D electron density.
Although the first methods appeared almost a century ago, recovering the density structure of a sample is still very problematic. Most avail-able imaging techniques transform a 3D electron density of a realspace structure into the 2D Fourier Transform of the intensity of scattered waves in the reciprocal space. This process causes a loss of information.
Firstly, instead of a 3D sample, a 2D image is created, and secondly, the phase information of the scattered waves is lost. The latter is known as the ”phase problem” and poses a serious obstacle on a way to recover a 3D electron density. In this work, we draw attention to the problem of forward and inverse Small Angle X-Ray Scattering. In the first, forward, part, we rethink the existing pipelines to computationally simulate such scattering experiments. Although there are efficient implementations of fast Fourier transformation, they often have some drawbacks. For instance, to calculate a 3D fast Fourier transform it is required to place its density in the RAM. For high-resolution structures of size > 1024 3 , this becomes very problematic, as the whole density structure requires more than 16 GB of memory.
CUDA solution allows for a very fast and parallelizable implementation of high-resolution data on hundreds of last-generation machines.
Such computations are very pricy and inaccessible for most scientists.
To bypass this limitation, we propose a solution for a split-up 3D fast Fourier transform, which is implemented as a sequence of 2D and 1D operations. We compare our implementation on the simulated 3D shapes and show the result of a proof-of-concept on 4096 3 Metallorganic framework density structure. In the second, inverse problem, we train an invertible neural network, that given scattering data can predict the shape and its parameters. The architecture is built such, that the inverse problem is learned together with the forward process - the Fourier Transformation. We achieved very good results with this architecture, nonetheless, further testing is required, as the current training set only encompasses three simple shapes: sphere, hard sphere and cylinder.
All code to reproduce and analyze the results is available at https: //github.com/sofyalaski/SAXS-simulations.
Technical drawings and documents for building a compact, heated, vacuum compatible flow-through sample holder. This holder is in use at the BAM MOUSE instrument as well as at the I22 beamline at the Diamond Light Source (see references for instrument details).
This holder has several features:
- The holder can be used in vacuum environments as well as in atmosphere
- It has two G 1/4" UNF fittings to attach HPLC tubing for (optionally) flowing a medium through the sample cell
- There are two additional (unflowed) sample positions for backgrounds and calibrants, held at the same temperature
- The low-mass design coupled with a 250W heating element can achieve heating rates of 1 degree C per second, when coupled (for example) with an Omron E5CC PID controller.
- The sample holder insert can be made from various materials depending on the application. Sealing the sample from the vacuum can be achieved using kapton, teflon or Magic tape, depending on the temperature requirements. The inlet and outlet holes will need to be punctured with a needle to enable flow.
- Large exit cones ensure a clear exit angle of at least 45 degrees two theta.
- It has been tested with temperatures up to 400 degrees C.
- Compression area has been raised and polished to ensure a good vacuum seal.
OpenSCAD, STL and technical drawings for the solid sample rack designed primarily for use with The MOUSE instruments.
This solid sample rack can be used in conjunction with:
- Laser-cut sample holder (10.5281/zenodo.7499437)
- Modular sample holder (10.5281/zenodo.7499416)
- Capillary flow-cell for liquid samples (10.5281/zenodo.7499421)