Comparison of EMC and CM methods for orienting diffraction images in single-particle imaging experiments.

Miklós Tegze,Gábor Bortel

doi:10.1107/s205225252100868x

Abstract

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.

Highlights

The short and intense pulses of X-ray free-electron lasers (XFELs) make diffraction experiments on single particles possible (Neutze et al, 2000; Huldt et al, 2003)
In a singleparticle imaging (SPI) experiment, identical particles are injected into the X-ray beam with random orientations and diffraction patterns can be recorded in a 2D detector before the particle is destroyed by radiation damage
We tested the efficiency of two methods, expansion maximization compression (EMC) and correlation maximization (CM), for orienting the noisy SPI patterns and reconstructing a consistent 3D intensity distribution

Summary

Introduction

The short and intense pulses of X-ray free-electron lasers (XFELs) make diffraction experiments on single particles possible (Neutze et al, 2000; Huldt et al, 2003). We consider two methods for orientating the measured diffraction patterns and reconstructing the 3D scattering intensity distribution: the expansion maximization compression (EMC) algorithm (Loh & Elser, 2009; Loh et al, 2010) and the correlation maximization (CM) algorithm (Tegze & Bortel, 2012, 2013, 2016, 2018). The most timeconsuming step of the EMC algorithm is the calculation of the probabilities of all possible orientations for all measured diffraction patterns. In the CM method, the time-consuming expectation-maximization step is replaced by a search for the orientation with the highest correlation (Fig. 2) This is practically equivalent to setting the largest weight among the possible orientations of a diffraction pattern to one and all the others to zero in the EMC method. The calculations were executed on a single workstation (2 Â Intel Xeon Gold 6146 computing processor unit) reinforced with a group of graphics processors (8 Â Nvidia Geforce RTX 2080 Ti)

Simulation of diffraction patterns

Orientation problem in one dimension

Phase retrieval

Conclusions

Findings

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