Statistical shape analysis with applications in structural bioinformatics

Project description

In statistical shape analysis, objects are often represented by a configuration of landmarks, and in order to compare the shapes of objects, their configurations must first be aligned as closely as possible. When the landmarks are unlabelled (that is, the correspondence between landmarks on different objects is unknown) the problem becomes much more challenging, since both the correspondence and alignment parameters need to be inferred simultaneously.

An example of the unlabelled problem comes from the area of structural bioinformatics, when we wish to compare the 3-d shapes of protein molecules. This is important, since the shape of a protein is vital to its biological function. The landmarks could be, for example, the locations of particular atoms, and the correspondence between atoms on different proteins is unknown. This project will explore methods for unlabelled shape alignment, motivated by the problem of protein structure alignment. Possible topics include development of:

• efficient MCMC methods to explore complicated, high-dimensional distributions, which may be highly multimodal when considering large proteins;
• fast methods for pairwise alignment, needed when a large database of structures is to be searched for matches to a query structure;
• methods for the alignment of multiple structures simultaneously, which greatly exacerbates the difficult problems faced in pairwise alignment.