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

N. L. Lunina ; T. E. Petrova ; A. G. Urzhumtsev ; V. Yu. Lunin

Matematičeskaâ biologiâ i bioinformatika, Tome 10 (2015) no. 2, pp. 508-525.

Résumé

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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