Iterative projection algorithms and applications in x-ray crystallography

Type of content
Theses / Dissertations
Publisher's DOI/URI
Thesis discipline
Electrical Engineering
Degree name
Doctor of Philosophy
Publisher
University of Canterbury. Electrical and Computer Engineering
Journal Title
Journal ISSN
Volume Title
Language
Date
2011
Authors
Lo, Victor Lai-Xin
Abstract

X-ray crystallography is a technique for determining the structure (positions of atoms in space) of molecules. It is a well developed technique, and is applied routinely to both small inorganic and large organic molecules. However, the determination of the structures of large biological molecules by x-ray crystallography can still be an experimentally and computationally expensive task. The data in an x-ray experiment are the amplitudes of the Fourier transform of the electron density in the crystalline specimen. The structure determination problem in x-ray crystallography is therefore identical to a phase retrieval problem in image reconstruction, for which iterative transform algorithms are a common solution method.

This thesis is concerned with iterative projection algorithms, a generalized and more powerful version of iterative transform algorithms, and their application to macromolecular x-ray crystallography. A detailed study is made of iterative projection algorithms, including their properties, convergence, and implementations. Two applications to macromolecular crystallography are then investigated. The first concerns reconstruction of binary image and the application of iterative projection algorithms to determining molecular envelopes from x-ray solvent contrast variation data. An effective method for determining molecular envelopes is developed. The second concerns the use of symmetry constraints and the application of iterative projection algorithms to ab initio determination of macromolecular structures from crystal diffraction data. The algorithm is tested on an icosahedral virus and a protein tetramer. The results indicate that ab initio phasing is feasible for structures containing 4-fold or 5-fold non-crystallographic symmetry using these algorithms if an estimate of the molecular envelope is available.

Description
Citation
Keywords
iterative projection algorithms, inverse problems, image reconstruction, phase retrieval, macromolecular crystallography
Ngā upoko tukutuku/Māori subject headings
ANZSRC fields of research
Rights
Copyright Victor Lai-Xin Lo