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Reconstruction methods In free electron laser X-ray diffraction

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One of the most important issues in femtosecond free electron laser X-ray diraction is to reconstruct the 3D charge density of molecule from a mass of diraction snapshots. In order

One of the most important issues in femtosecond free electron laser X-ray diraction is to reconstruct the 3D charge density of molecule from a mass of diraction snapshots. In order to determine the orientation of single molecule from diraction patterns, we rst determine the moments and products of inertia of this from 2D experiment data (diraction patterns or EM images to obtain the elements of the inertia tensor. If diraction patterns from uniformly random orientations or some preferred orientations are collected, the principal axes of the molecule can be extracted, together with the Euler angles which relate the principal axes of the molecule to the laboratory frame axes. This is achieved by nding the maximum and minimum values for the measured moments from many single-molecule patterns. Simulations for GroEL protein indicates that the calculation of the autocorrelation help eliminate the Poisson noise in Cryo- EM images and can make correct orientation determination. The eect of water jacket surrounding the protein molecule is studied based on molecular dynamics simulation result. The intensities from water and interference is found to suppress those from protein itself. A method is proposed and applied to the simulation data to show the possibility for it to overcome the water background problem. The scattering between Bragg re ections from nanocrystals is used to aid solution of the phase problem. We describe a method for reconstructing the charge density of a typical molecule within a single unit cell, if suciently nely-sampled diraction data are available from many nanocrystals of dierent sizes lying in the same orientations without knowledge of the distribution of particle size or requiring atomic-resolution data. Triple correlation of the diraction patterns are made use of to reconiii

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Date Created
  • 2011

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Phasing two-dimensional crystal diffraction pattern with iterative projection algorithms

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Phase problem has been long-standing in x-ray diffractive imaging. It is originated from the fact that only the amplitude of the scattered wave can be recorded by the detector, losing

Phase problem has been long-standing in x-ray diffractive imaging. It is originated from the fact that only the amplitude of the scattered wave can be recorded by the detector, losing the phase information. The measurement of amplitude alone is insufficient to solve the structure. Therefore, phase retrieval is essential to structure determination with X-ray diffractive imaging. So far, many experimental as well as algorithmic approaches have been developed to address the phase problem. The experimental phasing methods, such as MAD, SAD etc, exploit the phase relation in vector space. They usually demand a lot of efforts to prepare the samples and require much more data. On the other hand, iterative phasing algorithms make use of the prior knowledge and various constraints in real and reciprocal space. In this thesis, new approaches to the problem of direct digital phasing of X-ray diffraction patterns from two-dimensional organic crystals were presented. The phase problem for Bragg diffraction from two-dimensional (2D) crystalline monolayer in transmission may be solved by imposing a compact support that sets the density to zero outside the monolayer. By iterating between the measured stucture factor magnitudes along reciprocal space rods (starting with random phases) and a density of the correct sign, the complex scattered amplitudes may be found (J. Struct Biol 144, 209 (2003)). However this one-dimensional support function fails to link the rod phases correctly unless a low-resolution real-space map is also available. Minimum prior information required for successful three-dimensional (3D) structure retrieval from a 2D crystal XFEL diffraction dataset were investigated, when using the HIO algorithm. This method provides an alternative way to phase 2D crystal dataset, with less dependence on the high quality model used in the molecular replacement method.

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  • 2016