**Computer Simulation of Diffraction of X-ray Pulses by Nanocrystals of Biological Macromolecules Using Unitary Approximation of Nonstationary Atomic Scattering Factors**
**Lunin V.Y., Grum-Grzhimailo A.N., Gryzlova E.V., Sinitsyn D.O., Balabaev N.K., Lunina N.L., Petrova T.E., Tereshkina K.B., Abdulnasyrov E.G., Stepanov A.S., Krupyanskii Y.F.**
*Institute of Mathematical Problems of Biology, Russian academy of sciences, Pushchino, 142290, Russia *

Skobeltsyn Institute of Nuclear Physics Lomonosov Moscow state university, Moscow, 119991, Russia

Semenov Institute of Chemical Physiscs, Russian Academy of Sciences, Moscow 119991, Russia

lunin@impb.psn.ru

algrgr1492@yahoo.com

yufk@chph.ras.ru

**Abstract**. 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.

**Key words**: *X-ray free electron lasers, femtosecond X-ray pulses, X-ray scattering, diffraction, nanocrystals, biomacromolecules.*