Unsupervised learning approaches to characterizing heterogeneous samples using X-ray single-particle imaging

Yulong Zhuang; Salah Awel; Anton Barty; Richard Bean; Johan Bielecki; Martin Bergemann; Benedikt J Daurer; Tomas Ekeberg; Armando D Estillore; Hans Fangohr; Klaus Giewekemeyer; Mark S Hunter; Mikhail Karnevskiy; Richard A Kirian; Henry Kirkwood; Yoonhee Kim; Jayanath Koliyadu; Holger Lange; Romain Letrun; Jannik Lübke; Abhishek Mall; Thomas Michelat; Andrew J Morgan; Nils Roth; Amit K Samanta; Tokushi Sato; Zhou Shen; Marcin Sikorski; Florian Schulz; John C H Spence; Patrik Vagovic; Tamme Wollweber; Lena Worbs; P Lourdu Xavier; Oleksandr Yefanov; Filipe R N C Maia; Daniel A Horke; Jochen Küpper; N Duane Loh; Adrian P Mancuso; Henry N Chapman; Kartik Ayyer

doi:10.1107/S2052252521012707

Unsupervised learning approaches to characterizing heterogeneous samples using X-ray single-particle imaging

IUCrJ. 2022 Jan 11;9(Pt 2):204-214. doi: 10.1107/S2052252521012707. eCollection 2022 Mar 1.

Authors

Yulong Zhuang^{1

2}, Salah Awel³, Anton Barty³, Richard Bean⁴, Johan Bielecki⁴, Martin Bergemann⁴, Benedikt J Daurer⁵, Tomas Ekeberg⁶, Armando D Estillore³, Hans Fangohr^{1

2

4

7}, Klaus Giewekemeyer⁴, Mark S Hunter⁸, Mikhail Karnevskiy⁴, Richard A Kirian⁹, Henry Kirkwood⁴, Yoonhee Kim⁴, Jayanath Koliyadu⁴, Holger Lange^{10

11}, Romain Letrun⁴, Jannik Lübke^{3

10

12}, Abhishek Mall^{1

2}, Thomas Michelat⁴, Andrew J Morgan¹³, Nils Roth^{3

12}, Amit K Samanta³, Tokushi Sato⁴, Zhou Shen⁵, Marcin Sikorski³, Florian Schulz^{10

14}, John C H Spence⁹, Patrik Vagovic^{3

4}, Tamme Wollweber^{1

2

10}, Lena Worbs^{3

12}, P Lourdu Xavier^{1

3

10}, Oleksandr Yefanov³, Filipe R N C Maia^{6

15}, Daniel A Horke^{3

10

16}, Jochen Küpper^{3

10

12

17}, N Duane Loh^{5

18}, Adrian P Mancuso^{4

19}, Henry N Chapman^{3

10

12}, Kartik Ayyer^{1

2

10}

Affiliations

¹ Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany.
² Center for Free-Electron Laser Science, 22761 Hamburg, Germany.
³ Center for Free-Electron Laser Science CFEL, Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany.
⁴ European XFEL, 22869 Schenefeld, Germany.
⁵ Center for Bio-Imaging Sciences, National University of Singapore, 117557, Singapore.
⁶ Department of Cell and Molecular Biology, Uppsala University, 75124 Uppsala, Sweden.
⁷ University of Southampton, Southampton SO17 1BJ, United Kingdom.
⁸ Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA.
⁹ Department of Physics, Arizona State University, Tempe, AZ 85287, USA.
¹⁰ Hamburg Center for Ultrafast Imaging, Universität Hamburg, 22761 Hamburg, Germany.
¹¹ Institute of Physical Chemistry, Universität Hamburg, 20146 Hamburg, Germany.
¹² Department of Physics, Universität Hamburg, 22761 Hamburg, Germany.
¹³ Department of Physics, University of Melbourne, Victoria 3010, Australia.
¹⁴ Institute of Nanostructure and Solid State Physics, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany.
¹⁵ NERSC, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
¹⁶ Institute for Molecules and Materials, Radboud University, 6525 AJ Nijmegen, Netherlands.
¹⁷ Department of Chemistry, Universität Hamburg, 20146 Hamburg, Germany.
¹⁸ Department of Physics, National University of Singapore, 117551, Singapore.
¹⁹ Department of Chemistry and Physics, La Trobe Institute for Molecular Science, La Trobe University, Melbourne, Victoria 3086, Australia.

Abstract

One of the outstanding analytical problems in X-ray single-particle imaging (SPI) is the classification of structural heterogeneity, which is especially difficult given the low signal-to-noise ratios of individual patterns and the fact that even identical objects can yield patterns that vary greatly when orientation is taken into consideration. Proposed here are two methods which explicitly account for this orientation-induced variation and can robustly determine the structural landscape of a sample ensemble. The first, termed common-line principal component analysis (PCA), provides a rough classification which is essentially parameter free and can be run automatically on any SPI dataset. The second method, utilizing variation auto-encoders (VAEs), can generate 3D structures of the objects at any point in the structural landscape. Both these methods are implemented in combination with the noise-tolerant expand-maximize-compress (EMC) algorithm and its utility is demonstrated by applying it to an experimental dataset from gold nanoparticles with only a few thousand photons per pattern. Both discrete structural classes and continuous deformations are recovered. These developments diverge from previous approaches of extracting reproducible subsets of patterns from a dataset and open up the possibility of moving beyond the study of homogeneous sample sets to addressing open questions on topics such as nanocrystal growth and dynamics, as well as phase transitions which have not been externally triggered.

Keywords: XFELs; coherent X-ray diffractive imaging (CXDI); single particles.

Grants and funding

This work was funded by Deutsche Forschungsgemeinschaft grants 194651731 and 390715994; European Research Council, FP7 Ideas: European Research Council grant ERC-614507-Küpper; Helmholtz-Gemeinschaft; National Science Foundation, BioXFEL Science and Technology Center grant STC-1231306 to John C. H. Spence and Richard A. Kirian; Vetenskapsrådet; Carl Tryggers Stiftelse för Vetenskaplig Forskning; Joachim Herz Stiftung; Human Frontier Science Program grant RGP0010/2017 to P. Lourdu Xavier and Henry N. Chapman.