Geodesic
Computer Simulation of Diffraction of X-ray Pulses by Nanocrystals of Biological Macromolecules Using Unitary Approximation of Nonstationary Atomic Scattering Factors
Matematičeskaâ biologiâ i bioinformatika, Tome 8 (2013) no. 1, pp. 93-118.

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The use of new-generation powerful sources (“X-ray free electron lasers”) in the X-ray diffraction experiment can cause substantial changes in the electronic structure of the object during the experiment. These changes may significantly complicate the solution of the direct problem of X-ray structure analysis, i.e. the prediction of the diffraction pattern, provided an atomic model of the object is available. We suggest below two simplified schemes, which allow the calculation of the diffraction pattern by means of the standard tools of biological (stationary) crystallography, with the accuracy being within the limits achieved nowdays in the study of biological objects. It was found that, at middle resolution and with X-ray pulses of a moderate photon fluence, the photoionization causes an almost simultaneous attenuation of diffracted beams for all Bragg reflections. This allows one to calculate the diffraction pattern by standard crystallographic formulae, by adapting only the general scale factor to the experiment. The use of more powerful X-ray lasers (that are unavailable yet in practice, but are under development) requires the modification of computational schemes. We suggest a modification that takes changes in atomic scattering factors during the experiment into account but retains the computational complexity inherent in standard crystallographic applications. The modification consists in replacing the standard atomic scattering factors by their “effective” counterparts, calculated on the basis of time-dependent scattering factors. The calculation of time-dependent formfactors for X-ray pulse with specified parameters is performed at the preliminary stage of the work. 
@article{MBB_2013_8_1_a6,
     author = {V. Y. Lunin and A. N. Grum-Grzhimailo and E. V. Gryzlova and D. O. Sinitsyn and N. K. Balabaev and N. L. Lunina and T. E. Petrova and K. B. Tereshkina and E. G. Abdulnasyrov and A. S. Stepanov and Y. F. Krupyanskii},
     title = {Computer {Simulation} of {Diffraction} of {X-ray} {Pulses} by {Nanocrystals} of {Biological} {Macromolecules} {Using} {Unitary} {Approximation} of {Nonstationary} {Atomic} {Scattering} {Factors}},
     journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika},
     pages = {93--118},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MBB_2013_8_1_a6/}
}
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AU  - E. G. Abdulnasyrov
AU  - A. S. Stepanov
AU  - Y. F. Krupyanskii
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%A A. S. Stepanov
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V. Y. Lunin; A. N. Grum-Grzhimailo; E. V. Gryzlova; D. O. Sinitsyn; N. K. Balabaev; N. L. Lunina; T. E. Petrova; K. B. Tereshkina; E. G. Abdulnasyrov; A. S. Stepanov; Y. F. Krupyanskii. Computer Simulation of Diffraction of X-ray Pulses by Nanocrystals of Biological Macromolecules Using Unitary Approximation of Nonstationary Atomic Scattering Factors. Matematičeskaâ biologiâ i bioinformatika, Tome 8 (2013) no. 1, pp. 93-118. http://geodesic.mathdoc.fr/item/MBB_2013_8_1_a6/

[1] Barletta W. A., Bisognano J., Corlett J. N., Emma P., Huang Z., Kim K. Z., Lindberg R., Murphy J. B., Neil G. R., Nguyen D. C. et al., “Free electron lasers: Present status and future challenges”, Nucl. Instrum. Methods. Sec. A, 618 (2010), 69–96 | DOI

[2] Chapman H. N., Fromme P., Barty A., White T. A., Kirian R. A., Aquila A., Hunter M. S., Schulz J., DePonte D. P., Weierstall U. et al., “Femtosecond X-ray protein nanocrystallography”, Nature, 470 (2011), 73–78 | DOI

[3] Boutet S., Lomb L., Williams G. J., Barends T. R. M., Aquila A., Doak R. B., Weierstall U., DePonte D. P., Steinbrener J., Shoeman R. L. et al., “High resolution protein structure determination by serial femtosecond crystallography”, Science, 337 (2012), 362–364 | DOI

[4] Krupyanskii Yu. F., Balabaev N. K., Grum-Grzhimailo A. N., Lunin V. Yu., Petrova T. E., Sinitsyn D. O., Gryzlova E. V., Tereshkina K. B., Abdulnasyrov E. G., Stepanov A. S., “Femtosekundnye rentgenovskie lazery na svobodnykh elektronakh: novyi metod izucheniya nanokristallov i odinochnykh makromolekul”, Khimicheskaya fizika, 32:4 (2013) (to appear)

[5] Kern J., Alonso-Mori R., Hellmich J., Tran R., Hattne J., Laksmono H., Glöckner C., Echols N., Sierra R. G., Sellberg J. et al., “Room temperature femtosecond X-ray diffraction of photosystem II microcrystals”, Proc. Natl Acad. Sci. USA, 109 (2012), 9721–9726 | DOI

[6] Johansson L. C., Arnlund D., White T. A., Katona G., DePonte D. P., Weierstall U., Doak R. B., Shoeman R. L., Lomb L., Malmerberg E. et al., “Lipidic phase membrane protein serial femtosecond crystallography”, Nature Methods, 9 (2012), 263–265 | DOI

[7] Redecke L., Nass K., DePonte D. P., White T. A., Rehders D., Barty A., Stellato F., Liang M., Barends T. R. M., Boutet S. et al., “Natively Inhibited Trypanosoma brucei Cathepsin B Structure Determined by Using an X-ray Laser”, Science, 339 (2013), 227–230 | DOI

[8] Shapiro D., Thibault P., Beetz T., Elser V., Howells M., Jacobsen C., Kirz J., Lima E., Miao H., Neiman A. M., Sayre D., “Biological imaging by soft x-ray diffraction microscopy”, Proc. Natl. Acad. Sci. USA, 102 (2005), 15343–15346 | DOI

[9] Seibert M. M., Ekeberg T., Maia F. R. N. C., Svenda M., Andreasson J., Jönsson O., Odic D., Iwan B., Rocker A., Westphal D. et al., “Single mimivirus particles intercepted and imaged with an x-ray laser”, Nature, 470 (2011), 79–81 | DOI

[10] Martin A. V., Andreasson J., Aquila A., Bajt S., Barends T. R. M., Barthelmess M., Barty A., Benner W. H., Bostedt C., Bozek J. D. et al., “Single particle imaging with soft X-rays at the Linac Coherent Light source”, Proc. SPIE, 8078 (2011), 807809(1)–807809(9) | DOI

[11] Neutze R., Wouts R., van der Spoel D., Weckert E., Hajdu J., “Potential for biomolecular imaging with femtosecond X-ray pulses”, Nature, 406 (2000), 752–757 | DOI

[12] Harker D., Kasper J. S., “Phases of Fourier coefficients directly from crystal diffraction data”, Acta Crystallographica, 1 (1948), 70–75 | DOI | MR

[13] 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 Res., 28 (2000), 235–242 | DOI

[14] Urzhumtsev A. G., Afonine P. V., Adams P. D., “On the use of logarithmic scales for analysis of diffraction data”, Acta Crystallographica. Sec. D, 65 (2009), 1283–1291

[15] Landau L. D., Lifshits E. M., Teoreticheskaya fizika, v. I, Mekhanika, Nauka, M., 1973, 208 pp. | MR

[16] Landau L. D., Lifshits E. M., Teoreticheskaya fizika, v. II, Teoriya polya, Nauka, M., 1973, 504 pp. | MR

[17] Slater J. C., “A Simplification of the Hartree-Fock Method”, Phys. Rev., 81 (1951), 385–390 | DOI | Zbl

[18] Brown P. J., Fox A. G., Maslen E. N., O'Keefe M. A., Willis B. T. M., “Intensity of diffracted intensities”, International Tables for Crystallography, Volume C, ed. Prince E., 2006, 554–595 (data obrascheniya: 07.03.2013) http://it.iucr.org/C/ | DOI

[19] Coppens P., X-ray Charge Densities Chemical Bonding, Oxford University Press, New York, 1997

[20] Coppens P., Su Z., Becker P. G., “Analysis of charge and spin densities”, International Tables for Crystallography, Volume C, ed. Prince E., 2006, 713–734 (data obrascheniya: 07.03.2013) http://it.iucr.org/C/ | DOI

[21] Housset D., Benabicha F., Pichon-Pesme V., Jelsch C., Maierhofer A., David S., Fontecilla-Camps J. C., Lecomte C., “Towards the charge-density study of proteins: a room-temperature scorpion-toxin structure at 0.96Å resolution as a first test case”, Acta Crystallographica. Sec. D, 56 (2000), 151–160

[22] Grosse-Kunstleve R. W., Sauter N. K., Adams P. D., “Cctbx news”, Newsletter of the IUCr Commission on Crystallographic Computing, 3 (2004), 22–31 (data obrascheniya: 18.02.2013) http://www.iucr.org/iucr-top/comm/ccom/newsletters/

[23] Trueblood K. N., Bürgi H.-B., Burzlaff H., Dunitz J. D., Gramaccioli C. M., Schulz H. H., Schmueli U., Abrahams S. C., “Atomic Displacement Parameter Nomenclature. Report of a Subcommitee on Atomic Displacement Parameter Nomenclature”, Acta Crystallographica, A52 (1996), 770–781

[24] Grosse-Kunstleve R. W., Adams P. D., “On the handling of atomic anisotropic displacement parameters”, J. of Applied Crystallography, 35 (2002), 477–480 | DOI

[25] Afonine P. V., Urzhumtsev A., Grosse-Kunstleve R. W., Adams P. D., “Atomic Displacement Parameters (ADPs), their parameterization and refinement in PHENIX”, Computational Crystallography Newsletter, 1 (2010), 24–31 (data obrascheniya: 18.02.2013) http://www.phenix-online.org/newsletter/CCN_2010_07.pdf

[26] Phillips S. E. V., “Structure and refinement of oxymyoglobin at $1\cdot6$ Å resolution”, J. Mol. Biol., 142 (1980), 531–554 | DOI

[27] Jiang J.-S., Brünger A. T., “Protein Hydration Observed by X-ray Diffraction: Solvation Properties of Penicillopepsin and Neuraminidase Crystal Structures”, J. Mol. Biol., 243 (1994), 100–115 | DOI

[28] Fokine A., Urzhumtsev A., “Flat bulk-solvent model: obtaining optimal parameters”, Acta Crystallographica Sec. D, 58 (2002), 1387–1392

[29] Fenn T. D., Schnieders M. J., Brunger A. T., “A smooth and differentiable bulk-solvent model for macromolecular diffraction”, Acta Crystallographica Sec. D, 66 (2010), 1024–1031

[30] Blandel T., Dzhonson L., Kristallografiya belka, Mir, M., 1979, 620 pp.

[31] Lunin V. Y., Urzhumtsev A. G., “Improvement of protein phases by coarse model modification”, Acta Crystallographica Sec. A, 40 (1984), 269–277 | DOI

[32] Read R. J., “Improved Fourier Coefficients for Maps Using Phases from partial Structures with Errors”, Acta Crystallographica Sec. A, 42 (1986), 140–149 | DOI

[33] Pannu N. S., Read R. J., “Improved Structure Refinement Through Maximum Likelihood”, Acta Crystallographica Sec. A, 52 (1996), 659–668 | DOI

[34] Bricogne G., Irwin J., “Maximum-Likelihood Refinement of incomplete models with BUSTER+TNT”, Proceedings of the CCP4 Study Weekend. Macromolecular Refinement, Daresbury Laboratory, Warrington, 1996, 85–92

[35] Murshudov G. N., Vagin A. A., Dodson E. J., “Refinement of Macromolecular Structures by the Maximum-Likelihood Method”, Acta Crystallographica Sec. D, 53 (1997), 240–255

[36] Lunin V. Y., Afonine P. V., Urzhumtsev A. G., “Likelihood-based refinement. I: Irremovable model errors”, Acta Crystallographica Sec. A, 58 (2002), 270–282 | DOI

[37] Wang J., Dauter M., Alkire R., Joachimiak A., Dauter Z., “Triclinic lysozyme at 0.65Å resolution”, Acta Crystallographica Sec. D, 63 (2007), 1254–1268

[38] Afonine P. V., Grosse-Kunstleve R. W., Echols N., Headd J. J., Moriarty N. W., Mustyakimov M., Terwilliger T. C., Urzhumtsev A., Zwart P. H., Adams P. D., “Towards automated crystallographic structure refinement with phenix.refine”, Acta Crystallographica Sec. D, 68 (2012), 352–367 | DOI

[39] Sheldrick G. M., “Phase annealing in SHELX-90: direct methods for larger structures”, Acta Crystallographica Sec. A, 46 (1990), 467–473 | DOI

[40] Morris R. J., Bricogne G., “Sheldrick's 1.2Å rule and beyond”, Acta Crystallographica Sec. D, 59 (2003), 615–617

[41] Sobolev O. V., Lunin V. Y., “Detection of alternative conformations by unrestrained refinement”, Acta Crystallographica Sec. D, 68 (2012), 1118–1127

[42] Young L., Kanter E. P., Krassig B., Li Y., March A. M., Pratt S. T., Santra R., Southworth S. H., Rohringer N., DiMauro L. F. et al., “Femtosecond electronic response of atoms to ultra-intense X-rays”, Nature, 466 (2010), 56–62 | DOI

[43] Herman F., Skillman S., Atomic Structure Calculations, Prentice-Hall Inc., Englewood Cliffs, 1963

[44] Son S.-K., Young L., Santra R., “Impact of hollow-atom formation on coherent x-ray scattering at high intensity”, Phys. Rev. A, 83 (2011), 033402(1)–033402(11) | DOI

[45] Lorenz U., Kabachnik N. M., Weckert E., Vartanyants I. A., “Impact of ultrafast electronic damage in single-particle x-ray imaging experiments”, Phys. Rev. E, 86 (2012), 051911(1)–051911(7) | DOI