Date of Award

August 2017

Degree Type


Degree Name

Doctor of Philosophy



First Advisor

George Hanson

Committee Members

George Hanson, Dilano Saldin, Wilfred Tysoe, Zeyun Yu, Yi Hu


There is a remarkable shortage of the detailed knowledge of membrane proteins at atomic resolution despite the fact that they are the targets of many of today's drugs. The reason is that membrane proteins tend to have large hydrophobic surfaces which ensure their correct positioning in a membrane. However, this seems to make crystallization difficult, and this makes traditional methods of structure determination by X-ray crystallography difficult. In this thesis, we take advantage of this very fact to suggest an alternative method for structure determination by X-ray scattering of the projected structures of membrane proteins in their natural environments. Although in such environments the proteins are not perfectly aligned as in a crystal, we find that the algorithm suggested by Kurta and Pedrini appears to promise structure determination, perhaps down to atomic resolution.

We also suggest and develop how the method may be extended to obtain general (non-symmetric) 3D structures by exploiting the curved nature of Ewald spheres at lower energy. The extension of the 2D idea into 3D is straightforward, since a curved Ewald sphere also consists of a set of rings (one expects the different rings have different q_z components). We can get the intensities in 3D reciprocal space as that is exactly what we need for 3D structure recovery via a phasing program. Of course, the construction of intensity data on a uniform grid in 3D reciprocal space (required by a typical phasing program) requires a girdding program. The registry between the I_m(q)'s on different q's can be found as before if one knows B_m(q_1,q_2) from the experiment, as can be found from a set of diffraction patterns of the same energy. Of course, varying the energy then gives us the 3D reciprocal space for a range of q_z's, just what we need for getting info about the 3D structure.

In the second part of this thesis, we have reconstructed icosahedral images of the Coliphage PR772 and Rice Dwarf (RDV) viruses from the angular correlations of experimental data. We calculate the correlations using the standard method that Hanbury, Brown and Twiss developed in astronomy. The pattern of dominant icosahedral angular momentum quantum numbers that results is a strong indication of the icosahedral nature of the capsid. Having first determined by objective means that the structure of the capsid has icosahedral symmetry, we then recover a dodecahedral diffraction volume from which we correctly reconstruct an icosahedral structure using our phasing algorithm. We quantify the quality of the reconstructed image using the Fourier shell correlation curve of two independent datasets. For PR772, the FSC curve stays above 0.5 throughout the range of experimental data, which suggests that the resolution is still determined by the limitations of the experimental data rather than by the reconstruction method. For RDV, the resolution is around 200A. We also calculated an R_spllit quantity that compares two randomly split diffraction patterns for PR772 and RDV data and, as expected, they remained low.

In a nutshell, three most important things to come out of this work are:

1-We recover the 2D structure of an individual membrane proteins up to atomic resolution using our suggested 2D phasing algorithm.

2-We develop an idea for producing 3D images using 2D diffraction patterns by combining multi-wavelength data from a soft X-ray fluctuation scattering experiment on membrane proteins partially oriented in a membrane, for the first time.

3- We also determine the the three-dimensional structure of PR772 and RDV viruses from experimental data, using our new 3D method.