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.

The superior brightness and ultra short pulse duration of X-ray free electron laser

(XFEL) allows it to outrun radiation damage in coherent diffractive imaging since elastic scattering terminates before photoelectron cascades commences. This “diffract-before-destroy” feature of XFEL opened up new opportunities for biological macromolecule imaging and structure studies by breaking the limit to spatial resolution imposed by the maximum dose that is allowed before radiation damage. However, data collection in serial femto-second crystallography (SFX) using XFEL is affected by a bunch of stochastic factors, which pose great challenges to the data analysis in SFX. These stochastic factors include crystal size, shape, random orientation, X-ray photon flux, position and energy spectrum. Monte-Carlo integration proves effective and successful in extracting the structure factors by merging all diffraction patterns given that the data set is sufficiently large to average out all stochastic factors. However, this approach typically requires hundreds of thousands of patterns collected from experiments. This dissertation explores both experimental and algorithmic methods to eliminate or reduce the effect of stochastic factors in data acquisition and analysis. Coherent convergent X-ray beam diffraction (CCB) is discussed for possibilities of obtaining single-shot angular-integrated rocking curves. It is also shown the interference between Bragg disks helps ab-initio phasing. Two-color diffraction scheme is proposed for time-resolved studies and general data collection strategies are discussed based on error metrics. A new auto-indexing algorithm for sparse patterns is developed and demonstrated for both simulated and experimental data. Statistics show that indexing rate is increased by 3 times for I3C data set collected from beam time LJ69 at Linac coherent light source (LCLS). Finally, dynamical inversion from electron diffraction is explored as an alternative approach for structure determination.

Scientists have used X-rays to study biological molecules for nearly a century. Now with the X-ray free electron laser (XFEL), new methods have been developed to advance structural biology. These new methods include serial femtosecond crystallography, single particle imaging, solution scattering, and time resolved techniques.

The XFEL is characterized by high intensity pulses, which are only about 50 femtoseconds in duration. The intensity allows for scattering from microscopic particles, while the short pulses offer a way to outrun radiation damage. XFELs are powerful enough to obliterate most samples in a single pulse. While this allows for a “diffract and destroy” methodology, it also requires instrumentation that can position microscopic particles into the X-ray beam (which may also be microscopic), continuously renew the sample after each pulse, and maintain sample viability during data collection.

Typically these experiments have used liquid microjets to continuously renew sample. The high flow rate associated with liquid microjets requires large amounts of sample, most of which runs to waste between pulses. An injector designed to stream a viscous gel-like material called lipidic cubic phase (LCP) was developed to address this problem. LCP, commonly used as a growth medium for membrane protein crystals, lends itself to low flow rate jetting and so reduces the amount of sample wasted significantly.

This work discusses sample delivery and injection for XFEL experiments. It reviews the liquid microjet method extensively, and presents the LCP injector as a novel device for serial crystallography, including detailed protocols for the LCP injector and anti-settler operation.

ABSTRACT

X-Ray crystallography and NMR are two major ways of achieving atomic

resolution of structure determination for macro biomolecules such as proteins. Recently, new developments of hard X-ray pulsed free electron laser XFEL opened up new possibilities to break the dilemma of radiation dose and spatial resolution in diffraction imaging by outrunning radiation damage with ultra high brightness femtosecond X-ray pulses, which is so short in time that the pulse terminates before atomic motion starts. A variety of experimental techniques for structure determination of macro biomolecules is now available including imaging of protein nanocrystals, single particles such as viruses, pump-probe experiments for time-resolved nanocrystallography, and snapshot wide- angle x-ray scattering (WAXS) from molecules in solution. However, due to the nature of the "diffract-then-destroy" process, each protein crystal would be destroyed once

probed. Hence a new sample delivery system is required to replenish the target crystal at a high rate. In this dissertation, the sample delivery systems for the application of XFELs to biomolecular imaging will be discussed and the severe challenges related to the delivering of macroscopic protein crystal in a stable controllable way with minimum waste of sample and maximum hit rate will be tackled with several different development of injector designs and approaches. New developments of the sample delivery system such as liquid mixing jet also opens up new experimental methods which gives opportunities to study of the chemical dynamics in biomolecules in a molecular structural level. The design and characterization of the system will be discussed along with future possible developments and applications. Finally, LCP injector will be discussed which is critical for the success in various applications.

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.

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