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Femtosecond x-ray protein nanocrystallography and correlated fluctuation small-angle x-ray scattering

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With the advent of the X-ray free-electron laser (XFEL), an opportunity has arisen to break the nexus between radiation dose and spatial resolution in diffractive imaging, by outrunning radiation damage

With the advent of the X-ray free-electron laser (XFEL), an opportunity has arisen to break the nexus between radiation dose and spatial resolution in diffractive imaging, by outrunning radiation damage altogether when using single X-ray pulses so brief that they terminate before atomic motion commences. This dissertation concerns the application of XFELs to biomolecular imaging in an effort to overcome the severe challenges associated with radiation damage and macroscopic protein crystal growth. The method of femtosecond protein nanocrystallography (fsPNX) is investigated, and a new method for extracting crystallographic structure factors is demonstrated on simulated data and on the first experimental fsPNX data obtained at an XFEL. Errors are assessed based on standard metrics familiar to the crystallography community. It is shown that resulting structure factors match the quality of those measured conventionally, at least to 9 angstrom resolution. A new method for ab-initio phasing of coherently-illuminated nanocrystals is then demonstrated on simulated data. The method of correlated fluctuation small-angle X-ray scattering (CFSAXS) is also investigated as an alternative route to biomolecular structure determination, without the use of crystals. It is demonstrated that, for a constrained two-dimensional geometry, a projection image of a single particle can be formed, ab-initio and without modeling parameters, from measured diffracted intensity correlations arising from disordered ensembles of identical particles illuminated simultaneously. The method is demonstrated experimentally, based on soft X-ray diffraction from disordered but identical nanoparticles, providing the first experimental proof-of-principle result. Finally, the fundamental limitations of CFSAXS is investigated through both theory and simulations. It is found that the signal-to-noise ratio (SNR) for CFSAXS data is essentially independent of the number of particles exposed in each diffraction pattern. The dependence of SNR on particle size and resolution is considered, and realistic estimates are made (with the inclusion of solvent scatter) of the SNR for protein solution scattering experiments utilizing an XFEL source.

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Date Created
  • 2011

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Reconstruction methods In free electron laser X-ray diffraction

Description

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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  • 2011

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Phasing two-dimensional crystal diffraction pattern with iterative projection algorithms

Description

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

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Investigating beta-sheet nanocrystal ordering and correlation with small-angle X-ray scattering

Description

In disordered soft matter system, amorphous and crystalline components might be coexisted. The interaction between the two distinct structures and the correlation within the crystalline components are crucial to the

In disordered soft matter system, amorphous and crystalline components might be coexisted. The interaction between the two distinct structures and the correlation within the crystalline components are crucial to the macroscopic property of the such material. The spider dragline silk biopolymer, is one of such soft matter material that exhibits exceptional mechanical strength though its mass density is considerably small compare to structural metal. Through wide-angle X-ray scattering (WAXS), the research community learned that the silk fiber is mainly composed of amorphous backbone and $\beta$-sheet nano-crystals. However, the morphology of the crystalline system within the fiber is still not clear. Therefore, a combination of small-angle X-ray scattering experiments and stochastic simulation is designed here to reveal the nano-crystalline ordering in spider silk biopolymer. In addition, several density functional theory (DFT) calculations were performed to help understanding the interaction between amorphous backbone and the crystalline $\beta$-sheets.

By taking advantage of the prior information obtained from WAXS, a rather crude nano-crystalline model was initialized for further numerical reconstruction. Using Markov-Chain stochastic method, a hundreds of nanometer size $\beta$-sheet distribution model was reconstructed from experimental SAXS data, including silk fiber sampled from \textit{Latrodectus hesperus}, \textit{Nephila clavipes}, \textit{Argiope aurantia} and \textit{Araneus gemmoides}. The reconstruction method was implemented using MATLAB and C++ programming language and can be extended to study a broad range of disordered material systems.

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Date Created
  • 2015