CTB-MPR is a fusion protein between the B subunit of cholera toxin (CTB) and the membrane-proximal region of gp41 (MPR), the transmembrane envelope protein of Human immunodeficiency virus 1 (HIV-1), and has previously been shown to induce the production of anti-HIV-1 antibodies with antiviral functions. To further improve the design of this candidate vaccine, X-ray crystallography experiments were performed to obtain structural information about this fusion protein. Several variants of CTB-MPR were designed, constructed and recombinantly expressed in Escherichia coli. The first variant contained a flexible GPGP linker between CTB and MPR, and yielded crystals that diffracted to a resolution of 2.3 Å, but only the CTB region was detected in the electron-density map. A second variant, in which the CTB was directly attached to MPR, was shown to destabilize pentamer formation. A third construct containing a polyalanine linker between CTB and MPR proved to stabilize the pentameric form of the protein during purification. The purification procedure was shown to produce a homogeneously pure and monodisperse sample for crystallization. Initial crystallization experiments led to pseudo-crystals which were ordered in only two dimensions and were disordered in the third dimension. Nanocrystals obtained using the same precipitant showed promising X-ray diffraction to 5 Å resolution in femtosecond nanocrystallography experiments at the Linac Coherent Light Source at the SLAC National Accelerator Laboratory. The results demonstrate the utility of femtosecond X-ray crystallography to enable structural analysis based on nano/microcrystals of a protein for which no macroscopic crystals ordered in three dimensions have been observed before.

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