Geodesic
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
Matematičeskaâ biologiâ i bioinformatika, Tome 10 (2015), pp. t56-t72.

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Advances in the methodology of the X-ray diffraction experiments leads to a possibility to register the rays scattered by large isolated biological particles (viruses and individual cells) but not only by crystalline samples. The experiment with an isolated particle provides researchers with the intensities of the scattered rays for the continuous spectrum of scattering vectors. Such experiment gives much more experimental data than an experiment with a crystalline sample where the information is limited to a set of Bragg reflections. This opens up additional opportunities in solving underlying problem of X-ray crystallography, namely, calculating phase values for the scattered waves needed to restore the structure of the object under study. In practice, the original continuous diffraction pattern is sampled, reduced to the values at grid points in the space of scattering vectors (in the reciprocal space). The sampling step determines the amount of the information involved in solving the phase problem and the complexity of the necessary calculations. In this paper, we investigate the effect of the sampling step on the accuracy of the phase problem solution obtained by the method proposed earlier by the authors. It is shown that an expected improvement of the accuracy of the solution with the reducing the sampling step continues even after crossing the 'Nyquist limit' defined as the inverse of the double size of the object under study. 
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     title = {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},
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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. Matematičeskaâ biologiâ i bioinformatika, Tome 10 (2015), pp. t56-t72. http://geodesic.mathdoc.fr/item/MBB_2015_10_a4/

[1] Miao J., Kirz J., Sayre D., “The oversampling phasing method”, Acta Crystallographica Section D: Biological Crystallography, 56 (2000), 1312–1315 <ext-link ext-link-type='doi' href='https://doi.org/10.1107/S0907444900008970'>10.1107/S0907444900008970</ext-link>

[2] Thibault P., Elser V., Jacobsen C., Shapiro D., Sayre D., “Reconstruction of a yeast cell from X-ray diffraction data”, Acta Crystallographica Section A: Foundations of Crystallography, 62 (2006), 248–261 <ext-link ext-link-type='doi' href='https://doi.org/10.1107/S0108767306016515'>10.1107/S0108767306016515</ext-link>

[3] Song C., Jiang H., Mancuso A., Amirbekian B., Peng L., Sun R., Shah S. S., Zhou Z. H., Ishikawa T., Miao J., “Quantitative Imaging of Single, Unstained Viruses with Coherent X Rays”, Physical Review Letters, 101 (2008), 158101 <ext-link ext-link-type='doi' href='https://doi.org/10.1103/PhysRevLett.101.158101'>10.1103/PhysRevLett.101.158101</ext-link>

[4] Maia F. R. N., Ekeberg T., van der Spoel D., Hajdu J., Journal of Applied Crystallography, 43 (2010), 1535–1539 <ext-link ext-link-type='doi' href='https://doi.org/10.1107/S0021889810036083'>10.1107/S0021889810036083</ext-link>

[5] Seibert M. M., Ekeberg T., Maia F. R. N. C., Svenda M., Andreasson J., Jonsson O., Odic D., Iwan B., Rocker A., Westphall D. et al., “Single mimivirus particles intercepted and imaged with an X-ray laser”, Nature, 470 (2011), 78–82 <ext-link ext-link-type='doi' href='https://doi.org/10.1038/nature09748'>10.1038/nature09748</ext-link>

[6] Van der Schot G., Svenda M., Maia F. R. N. C., Hantke M., DePonte D., Seibert M. M., Aquila A., Schulz J., Kirian R., Liang M. et al., “Imaging single cells in a beam of live cyanobacteria with an X-ray laser”, Nature Communication, 6 (2015), 5704 <ext-link ext-link-type='doi' href='https://doi.org/10.1038/ncomms6704'>10.1038/ncomms6704</ext-link>

[7] Feigin L. A., Svergun D. I., Structure Analysis by Small-Angle X-ray and Neutron Scattering, Shpringer, 1987

[8] Berman H. M., Westbrook J., Feng Z., Gilliland G., Bhat T. N., Weissig H., Shindyalov I. N., Bourne P. E., “The Protein Data Bank”, Nucleic Acids Research, 28 (2000), 235–242 (data obrascheniya: 22.11.2015) <ext-link ext-link-type='uri' href='http://www.rcsb.org/'>http://www.rcsb.org/</ext-link><ext-link ext-link-type='doi' href='https://doi.org/10.1093/nar/28.1.235'>10.1093/nar/28.1.235</ext-link>

[9] Sayre D., “Some implications of a theorem due to Shannon”, Acta Crystallographica, 5 (1952), 843 <ext-link ext-link-type='doi' href='https://doi.org/10.1107/S0365110X52002276'>10.1107/S0365110X52002276</ext-link>

[10] Bricogne G., “Geometric sources of redundancy in intensity data and their use for phase determination”, Acta Crystallographica Section A: Foundations of Crystallography, 30 (1974), 349–405

[11] Bricogne G., “Methods and programs for direct-space exploitation of geometric redundancies”, Acta Crystallographica Section A: Foundations of Crystallography, 32 (1976), 832–847 <ext-link ext-link-type='doi' href='https://doi.org/10.1107/S0567739476001691'>10.1107/S0567739476001691</ext-link>

[12] Fienup J. R., “Reconstruction of an object from the modulus of its Fourier transform”, Optics Letters, 3:1 (1978), 27–29 <ext-link ext-link-type='doi' href='https://doi.org/10.1364/OL.3.000027'>10.1364/OL.3.000027</ext-link>

[13] Zhang K. Y. J., Cowtan K. D., Main P., “Phase improvement by iterative density modification”, International Tables for Crystallography, F (2012), 385–400 <ext-link ext-link-type='doi' href='https://doi.org/10.1107/97809553602060000847'>10.1107/97809553602060000847</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=817988'>817988</ext-link>

[14] Lunin V. Y., Lunina N. L., Petrova T. E., “The use of connected masks for reconstructing the single particle image from X-ray diffraction data”, Mathematical Biology and Bioinformatics, 10, Suppl. (2015), t1–t19

[15] Lunin V. Y., Lunina N. L., Petrova T. E., Baumstark M. W., Urzhumtsev A. G., “Maskbased approach to phasing of single-particle diffraction data”, Acta Crystallographica Section D: Biological Crystallography, 72 (2016) (to appear)

[16] Jordan P., Fromme P., Witt H. T., Klukas O., Saenger W., Krauß N., “Three-dimensional structure of cyanobacterial photosystem I at 2.5 A resolution”, Nature, 411 (2001), 909–917 <ext-link ext-link-type='doi' href='https://doi.org/10.1038/35082000'>10.1038/35082000</ext-link>

[17] Rossmann M. G., Arnold E., “Noncrystallographic symmetry averaging of electron density for molecular-replacement phase refinement and extension”, International Tables for Crystallography, F (2012), 352–363 <ext-link ext-link-type='doi' href='https://doi.org/10.1107/97809553602060000842'>10.1107/97809553602060000842</ext-link>

[18] Matthews B. M., “Solvent content of protein crystals”, Journal of Molecular Biology, 33 (1968), 491–497 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/0022-2836(68)90205-2'>10.1016/0022-2836(68)90205-2</ext-link>

[19] Weichenberger C. X., Rupp B., “Ten years of probabilistic estimates of biocrystal solvent content: new insights via nonparametric kernel density estimate”, Acta Crystallographica Section D: Biological Crystallography, 70 (2014), 1579–1588 <ext-link ext-link-type='doi' href='https://doi.org/10.1107/S1399004714005550'>10.1107/S1399004714005550</ext-link>