Geodesic
Single particle study by X-ray diffraction: crystallographic approach
Matematičeskaâ biologiâ i bioinformatika, Tome 14 (2019) no. 2, pp. 500-516.

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An increase in the power of X-ray sources, in particular, the commissioning of X-ray free electron lasers, opens up the possibility of recording the diffraction by single macromolecular biological particles. These opportunities open the way to weakening, and, ideally, removal, of the main limitation of X-ray structure analysis, namely, the need to prepare the sample in the single-crystal form. However, the possibility of the practical recording of diffraction by a single particle is currently limited to a very low-resolution zone, what is one of the main obstacles in the development of this approach. This paper discusses the similarities and differences in the study of crystal samples and single particles. It is shown that the problem of the determination of the structure of a single particle can be formulated as a standard problem of biological crystallography, namely, as the problem of retrieval the electron density distribution in some unit cell from the magnitudes of its Fourier coefficients. This makes it possible to apply the entire range of the methods of biological crystallography to the study of isolated particles. At the same time, the possibility of recording continuous diffraction pattern for a single particle (as opposed to a discrete set of Bragg reflections in the case of a crystal) significantly increases the amount of information derived from the experiment. The analytical properties of the continuous diffraction pattern create a potential opportunity both to restore the structure factors phases (lost in the diffraction experiment), and to extrapolate the experimentally observed pattern onto a wider area, which allows to increase the resolution of Fourier syntheses for the electron density distribution. 
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V. Yu. Lunin; N. L. Lunina; T. E. Petrova. Single particle study by X-ray diffraction: crystallographic approach. Matematičeskaâ biologiâ i bioinformatika, Tome 14 (2019) no. 2, pp. 500-516. http://geodesic.mathdoc.fr/item/MBB_2019_14_2_a14/

[1] P. D. Adams, P. V. Afonine, G. Bunkóczi, V. B. Chen, I. W. Davis, N. Echols, J. J. Headd, L. W. Hung, G. J. Kapral, R. W. Grosse-Kunstleve et al, “PHENIX: a comprehensive Python-based system for macromolecular structure solution”, Acta Crystallographica D, 66 (2010), 213–221 | DOI

[2] M. D. Winn, C. C. Ballard, K. D. Cowtan, E. J. Dodson, P. Emsley, P. R. Evans, R. M. Keegan, E. B. Krissinel, A. G. W. Leslie, A. McCoy et al, “Overview of the CCP4 suite and current developments”, Acta Crystallographica D, 67 (2011), 235–242 | DOI

[3] G. M. Sheldrick, “A short history of SHELX”, Acta Crystallographica A, 64 (2008), 112–122 | DOI | Zbl

[4] G. Bricogne, C. Vonrhein, C. Flensburg, M. Schiltz, W. Paciorek, “Generation, representation and flow of phase information in structure determination: recent developments in and around SHARP 2.0”, Acta Crystallographica D, 59 (2003), 2023–2030 | DOI

[5] E. Blanc, P. Roversi, C. Vonrhein, C. Flensburg, S. M. Lea, G. Bricogne, “Refinement of severely incomplete structures with maximum likelihood in BUSTER-TNT”, Acta Crystallographica D, 60 (2004), 2210–2221 | DOI

[6] W. Minor, M. Cymborowski, Z. Otwinowski, M. Chruszcz, “HKL-3000: the integration of data reduction and structure solution-from diffraction images to an initial model in minutes”, Acta Crystallographica D, 62 (2006), 859–866 | DOI

[7] H. M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T. N. Bhat, H. Weissig, I. N. Shindyalov, P. E. Bourne, “The Protein Data Bank”, Nucleic Acids Research, 28 (2000), 235–242 | DOI

[8] V. Y. Lunin, N. L. Lunina, T. E. Petrova, “The biological crystallography without crystals”, Mathematical Biology and Bioinformatics, 12:1 (2017), 55–72 | DOI

[9] J. C.H. Spence, “XFELs for structure and dynamics in biology”, IUCrJ, 4 (2017), 322–339 | DOI

[10] J. Standfuss, J. Spence, “Serial crystallography at synchrotrons and X-ray lasers”, IUCrJ, 4 (2017), 100–101 | DOI

[11] A. Aquila, A. Barty, C. Bostedt, S. Boutet, G. Carini, D. dePonte, P. Drell, S. Doniach, K. H. Downing, T. Earnest et al, “The linac coherent light source single particle imaging road map”, Structural Dynamics, 2 (2015) | DOI

[12] K. Ayyer, G. Geloni, V. Kocharyan, E. Saldin, S. Serkez, O. Yefanov, I. Zagorodnov, “Perspectives for imaging single protein molecules with the present design of the European XFEL”, Structural Dynamics, 2 (2015) | DOI | Zbl

[13] B. J. Daurer, K. Okamoto, J. Bielecki, F. R.N. C. Maia, K. Muhlig, M. M. Seibert, M. F. Hantke, C. Nettelblad, W. H. Benner, M. Svenda et al, “Experimental strategies for imaging bioparticles with femtosecond hard X-ray pulses”, IUCrJ, 4 (2017), 251–262 | DOI

[14] L. D. Landau, E. M. Lifshitz, Mechanics, 3d edition, Butterworth-Heinemann, 1976, 224 pp. | MR

[15] L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields, 4th edition, Butterworth-Heinemann, 1980, 402 pp. | MR

[16] A. G. Urzhumtsev, V. Y. Lunin, “Introduction to crystallographic refinement of macromolecular atomic models”, Crystallography Reviews, 25 (2019), 164–262 | DOI

[17] L. Urzhumtseva, B. Klaholz, A. Urzhumtsev, “On effective and optical resolutions of diffraction data sets”, Acta Crystallographica D, 69 (2013), 1921–1934 | DOI

[18] W. Rudin, Functional analysis, McGraw-Hill Book Company, 1973 | MR | Zbl

[19] J. A. Rodriguez, R. Xu, C. C. Chen, Z. Huang, H. Jiang, A. L. Chen, K. S. Raines, Jr. A. Pryor, D. Nam, L. Wiegart et al, “Three-dimensional coherent X-ray diffractive imaging of whole frozen-hydrated cells”, IUCrJ, 2 (2015), 575–583 | DOI

[20] T. Ekeberg, M. Svenda, C. Abergel, F. R. N. C. Maia, V. Seltzer, J. M. Claverie, M. Hantke, O. Jönsson, C. Nettelblad, G. van der Schot et al, “Three-Dimensional Reconstruction of the Giant Mimivirus Particle with an X-Ray Free-Electron Laser”, Physical Review Letters, 114 (2015) | DOI

[21] A. Munke, J. Andreasson, A. Aquila, S. Awel, K. Ayyer, A. Barty, R. J. Bean, P. Berntsen, J. Bielecki, S. Boutet et al, “Coherent diffraction of single Rice Dwarf virus particles using hard X-rays at the Linac Coherent Light Source”, Scientific Data, 3 (2016) | DOI

[22] V. Y. Lunin, N. L. Lunina, T. E. Petrova, M. W. Baumstark, A. G. Urzhumtsev, “Maskbased approach to phasing of single-particle diffraction data”, Acta Crystallographica D, 72 (2016), 147–157 | DOI

[23] V. Y. Lunin, N. L. Lunina, T. E. Petrova, M. W. Baumstark, A. G. Urzhumtsev, “Maskbased approach to phasing of single-particle diffraction data. II. Likelihood-based selection criteria”, Acta Crystallographica D, 75 (2019), 79–89 | DOI

[24] E. Meijering, “A chronology of interpolation: from ancient astronomy to modern signal and image processing”, Proceedings of the IEEE, 90 (2002), 319–342 | DOI

[25] V. A. Kotel'nikov, “On the transmission capacity of 'ether' and wire in electric communications”, Physics-Uspekhi, 49:7 (2006), 736–744 | DOI

[26] D. Sayre, “Some implications of a theorem due to Shannon”, Acta Crystallographica, 5 (1952), 843 | DOI

[27] G. Bricogne, “Geometric sources of redundancy in intensity data and their use for phase determination”, Acta Crystallographica A, 30 (1974), 395–405 | DOI

[28] G. Bricogne, “Methods and programs for direct-space exploitation of geometric redundancies”, Acta Crystallographica A, 32 (1976), 832–847 | DOI

[29] V. Y. Lunin, N. L. Lunina, “Repairing of the diffraction pattern in the X-ray freeelectron laser study of biological particles”, Advanced Mathematical Models Applications, 3 (2018), 117–127

[30] A. Misnovs, A. Mishnev, “On phasing of oversampled diffraction data”, 32-nd European Crystallographic Meeting, Book of abstracts (Vienna, Austria, 18.–23.08), 2019, 706 (accessed 06.11.2019) https://ecm2019.org/fileadmin/user_upload/k_ecm2019/images/Programm/ECM32AbstractBooklet_18.08.2019.pdf | MR

[31] V. Y. Lunin, N. L. Lunina, T. E. Petrova, “The use of connected masks for reconstructing the single particle image from X-ray diffraction data”, Mathematical Biology and Bioinformatics, 10, Suppl. (2014), t1–t19 | DOI

[32] N. L. Lunina, T. E. Petrova, A. G. Urzhumtsev, V. Y. Lunin, “The use of connected masks for reconstructing the single particle image from X-ray diffraction data. II. The dependence of the accuracy of the solution on the sampling step of experimental data”, Mathematical Biology and Bioinformatics, 10, Suppl. (2015), t56–t72 | DOI

[33] N. L. Lunina, T. E. Petrova, A. G. Urzhumtsev, V. Y. Lunin, “The Use of Connected Masks for Reconstructing the Single Particle Image from X-Ray Diffraction Data. III. Maximum-Likelihood Based Strategies to Select Solution of the Phase Problem”, Mathematical Biology and Bioinformatics, 13:Suppl. (2018), t70–t83 | DOI