scholarly journals The correlation of single-particle diffraction patterns as a continuous function of particle orientation

2014 ◽  
Vol 369 (1647) ◽  
pp. 20130329 ◽  
Author(s):  
Andrew V. Martin

A statistical model for X-ray scattering of a non-periodic sample to high angles is introduced. It is used to calculate analytically the correlation of distinct diffraction measurements of a particle as a continuous function of particle orientation. Diffraction measurements with shot-noise are also considered. This theory provides a general framework for a deeper understanding of single particle imaging techniques used at X-ray free-electron lasers. Many of these techniques use correlations as a measure of diffraction-pattern similarity in order to determine properties of the sample, such as particle orientation.

IUCrJ ◽  
2021 ◽  
Vol 8 (6) ◽  
Author(s):  
Miklós Tegze ◽  
Gábor Bortel

In single-particle imaging (SPI) experiments, diffraction patterns of identical particles are recorded. The particles are injected into the X-ray free-electron laser (XFEL) beam in random orientations. The crucial step of the data processing of SPI is finding the orientations of the recorded diffraction patterns in reciprocal space and reconstructing the 3D intensity distribution. Here, two orientation methods are compared: the expansion maximization compression (EMC) algorithm and the correlation maximization (CM) algorithm. To investigate the efficiency, reliability and accuracy of the methods at various XFEL pulse fluences, simulated diffraction patterns of biological molecules are used.


2016 ◽  
Vol 49 (4) ◽  
pp. 1320-1335 ◽  
Author(s):  
Kartik Ayyer ◽  
Ti-Yen Lan ◽  
Veit Elser ◽  
N. Duane Loh

Single-particle imaging (SPI) with X-ray free-electron lasers has the potential to change fundamentally how biomacromolecules are imaged. The structure would be derived from millions of diffraction patterns, each from a different copy of the macromolecule before it is torn apart by radiation damage. The challenges posed by the resultant data stream are staggering: millions of incomplete, noisy and un-oriented patterns have to be computationally assembled into a three-dimensional intensity map and then phase reconstructed. In this paper, theDragonflysoftware package is described, based on a parallel implementation of the expand–maximize–compress reconstruction algorithm that is well suited for this task. Auxiliary modules to simulate SPI data streams are also included to assess the feasibility of proposed SPI experiments at the Linac Coherent Light Source, Stanford, California, USA.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Zhou Shen ◽  
Colin Zhi Wei Teo ◽  
Kartik Ayyer ◽  
N. Duane Loh

AbstractWe propose an encryption–decryption framework for validating diffraction intensity volumes reconstructed using single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) when the ground truth volume is absent. This conceptual framework exploits each reconstructed volumes’ ability to decipher latent variables (e.g. orientations) of unseen sentinel diffraction patterns. Using this framework, we quantify novel measures of orientation disconcurrence, inconsistency, and disagreement between the decryptions by two independently reconstructed volumes. We also study how these measures can be used to define data sufficiency and its relation to spatial resolution, and the practical consequences of focusing XFEL pulses to smaller foci. This conceptual framework overcomes critical ambiguities in using Fourier Shell Correlation (FSC) as a validation measure for SPI. Finally, we show how this encryption-decryption framework naturally leads to an information-theoretic reformulation of the resolving power of XFEL-SPI, which we hope will lead to principled frameworks for experiment and instrument design.


2018 ◽  
Vol 8 (1) ◽  
pp. 132 ◽  
Author(s):  
Zhibin Sun ◽  
Jiadong Fan ◽  
Haoyuan Li ◽  
Huaidong Jiang

2018 ◽  
Vol 74 (5) ◽  
pp. 512-517
Author(s):  
Miklós Tegze ◽  
Gábor Bortel

In coherent-diffraction-imaging experiments X-ray diffraction patterns of identical particles are recorded. The particles are injected into the X-ray free-electron laser (XFEL) beam in random orientations. If the particle has symmetry, finding the orientation of a pattern can be ambiguous. With some modifications, the correlation-maximization method can find the relative orientations of the diffraction patterns for the case of symmetric particles as well. After convergence, the correlation maps show the symmetry of the particle and can be used to determine the symmetry elements and their orientations. The C factor, slightly modified for the symmetric case, can indicate the consistency of the assembled three-dimensional intensity distribution.


IUCrJ ◽  
2017 ◽  
Vol 4 (5) ◽  
pp. 560-568 ◽  
Author(s):  
Carsten Fortmann-Grote ◽  
Alexey Buzmakov ◽  
Zoltan Jurek ◽  
Ne-Te Duane Loh ◽  
Liubov Samoylova ◽  
...  

Single-particle imaging with X-ray free-electron lasers (XFELs) has the potential to provide structural information at atomic resolution for non-crystalline biomolecules. This potential exists because ultra-short intense pulses can produce interpretable diffraction data notwithstanding radiation damage. This paper explores the impact of pulse duration on the interpretability of diffraction data using comprehensive and realistic simulations of an imaging experiment at the European X-ray Free-Electron Laser. It is found that the optimal pulse duration for molecules with a few thousand atoms at 5 keV lies between 3 and 9 fs.


2021 ◽  
Vol 11 (Suppl_1) ◽  
pp. S11-S11
Author(s):  
Grigoriy Armeev ◽  
Alexey Shaytan ◽  
Mikhail Vorovich ◽  
Alexey Egorov ◽  
Aydar Ishmukhametov ◽  
...  

Background: Tick-borne encephalitis virus (TBEV) is a dangerous human pathogen which envelope structure is already known from cryoEM study. TBEV mature viral particle size (~50 nm in diameter) makes it suitable for single-particle imaging (SPI) on X-ray free-electron laser (XFEL). XFEL SPI studies are at the early stages of development; thus, a well-described and conformationally homogeneous sample is required to develop approaches for experimental setup and data analysis. Here we present the image analysis results of data collected in October 2019 during the European XFEL experiment #2316. Methods: The detector was placed at 1.62 m from the injector; photon energy was around 6 keV, pulse energy 4 mJ, beam diameter ~ 500 nm. All runs were processed to detect hits with threshold filter (5th percentile of lit pixels) and further filtered to omit low-intensity images and images that lack detector modules. Filtered hits were background and geometry corrected with SPImage library and custom python scripts. Then hits were azimuthally integrated using PyFAI library. Scattering profiles were further clustered using the affinity propagation algorithm with cosine similarity metric in log space. Extracted classes were used to build averaged images. All hit profiles were fitted with model scattering to estimate the diameter of the particle. Simulated diffraction patterns were prepared using Condor from the cryoEM electron density map (EMDB ID 3752). Results: During the analysis after the filtering, only 276 clean and bright hits were collected per 135 min of injection (from 27287 hits detected via lit pixels threshold). Thus the hit rate was around ~ 2 hits/min, which is expected to rise in the future. The majority of hits correspond to the 40-50 nm particles (Fig. 1a), which is expected for TBEV. However, the exact size may vary due to solvent evaporation, ion condensation, and possible variability in the sample. Conclusion: The averaged images and their scattering profiles correlate with the simulated scattering patterns, though not ideally (Fig. 1 bc). Such discrepancy is expected due to the absence of electron density in the center of modeled viral structures.


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