The Use of Connected Masks for Reconstructing the Single Particle Image from X-Ray Diffraction Data

V. Yu. Lunin ; N. L. Lunina ; T. E. Petrova

Matematičeskaâ biologiâ i bioinformatika, Tome 9 (2014) no. 2, pp. 543-562.

Résumé

The task of reconstructing the image of a single macromolecular object from X-ray diffraction data can be formulated as a task of the reconstruction of the 3D electron density distribution from the magnitudes of its Fourier transform. This task can be reduced to a series of standard X-ray crystallography tasks, namely, the recovery of a periodic function from its Fourier transform magnitudes (structure factors), which are determined in an X-ray diffraction experiment. In this work, a new approach to the solution of these tasks is suggested which is based on the use of connected binary masks as an approximation of the required electron density distribution. The approach includes the random generation of a great number of connected masks, the selection of the masks that are in agreement with an experimental and a prior information about the object, and the alignment and the averaging of the phase sets of the structure factors that correspond to the selected masks. The averaged phase values together with the experimentally determined magnitudes are used for the calculation of the Fourier synthesis, which is applied for the visualization of the object under study. The approach can be used in studies of both single particles and crystalline species; however, it holds the greatest promise for investigations of single objects. The results of testing the approach are presented.

Bibliographie

[1] Krupyanskii Yu. F., Balabaev N. K., Petrova T. E., Sinitsyn D. O., Gryzlova E. V., Tereshkina K. B., Abdulnasyrov E. G., Stepanov A. S., Lunin V. Yu., Grum-Grzhimailo A. N., “Femtosekundnye rentgenovskie lazery na svobodnykh elektronakh: novyi metod izucheniya nanokristallov i odinochnykh makromolekul”, Khimicheskaya fizika, 33:7 (2014), 7–20 | DOI

[2] Sinitsyn D. O., Lunin V. Yu., Grum-Grzhimailo A. N., Gryzlova E. V., Balabaev N. K., Lunina N. L., Petrova T. E., Tereshkina K. B., Abdulnasyrov E. G., Stepanov A. S., Krupyanskii Yu. F., “Novye vozmozhnosti rentgenovskoi nanokristallografii biologicheskikh makromolekul s ispolzovaniem rentgenovskikh lazerov na svobodnykh elektronakh”, Khimicheskaya fizika, 33:7 (2014), 21–28 | DOI

[3] Lunin V. Y., Lunina N. L., Petrova T. E., Skovoroda T. P., Urzhumtsev A. G., Podjarny A. D., “Low-resolution ab initio phasing: problems and advances”, Acta Crystallographica Section D: Biological Crystallography, 56 (2000), 1223–1232 | DOI

[4] Lunin V. Y., Urzhumtsev A. G., Podjarny A., “Ab initio phasing of low-resolution Fourier syntheses”, International Tables for Crysallography, v. F, Second Edition, eds. Arnold E., Himmel D. M., Rossmann M. G., John Wiley Sons, 2011, 437–442

[5] Lunin V. Y., Lunina N. L., Urzhumtsev A. G., “Connectivity properties of high-density regions and ab initio phasing at low resolution”, Acta Crystallographica Section D: Biological Crystallography, 56 (2000), 375–382 | DOI

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

[7] Fienup J. R., “Reconstruction of an object from the modulus of its Fourier transform”, Optics Letters, 3:1 (1978), 27–29 | DOI

[8] Elser V., “Solution of the crystallographic phase problem by iterated projections”, Acta Crystallographica Section A: Foundations of Crystallography, 59 (2003), 201–209 | DOI

[9] Baker D., Krukowski A. E., Agard D. A., “Uniqueness and the ab initio phase problem in macromolecular crystallography”, Acta Crystallographica Section D: Biological Crystallography, 49 (1993), 186–192 | DOI

[10] Lunin V. Y., Urzhumtsev A. G., Skovoroda T. P., “Direct low-resolution phasing from electron-density histograms in protein crystallography”, Acta Crystallographica Section A: Foundations of Crystallography, 46 (1990), 540–544 | DOI

[11] Lunin V. Y., Lunina N. L., “The map correlation coefficient for optimally superposed maps”, Acta Crystallographica Section A: Foundations of Crystallography, 52 (1996), 365–368 | DOI

[12] Lunin V. Y., Urzhumtsev A., Bockmayr A., “Direct phasing by binary integer programming”, Acta Crystallographica Section A: Foundations of Crystallography, 58 (2002), 283–291 | DOI

[13] Murakami S., Nakashima R., Yamashita E., Yamaguchi A., “Crystal structure of bacterial multidrug efflux transporter AcrB”, Nature, 419 (2002), 587–593 | DOI

[14] Urzhumtsev A., Afonine P. V., Lunin V. Y., Terwilliger T. C., Adams P. D., “Metrics for comparison of crystallographic maps”, Acta Crystallographica Section D: Biological Crystallography, 70 (2014), 2593–2606 | DOI

[15] Lunin V. Y., Woolfson M. M., “Mean phase error and the map correlation coefficient”, Acta Crystallographica Section D: Biological Crystallography, 49 (1993), 530–533 | DOI

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