Bayesian Hierarchical Models and Flexible Proteins with biomedical applications

If the last century belongs to Physical Sciences, then this century must belong to Life Sciences. Many breakthroughs have been seen, starting from DNA and proteins. Their applications in drug discovery are well known but still there are many diseases needing new drug developments. A recent review of the statistical importance in this area is given in Mardia (2013 Journal of the Royal Statistical Society) .

It is well known that proteins are the work-horses of all living systems. A protein is a sequence of amino acids, of which there are twenty types. The sequence folds into a 3-dimensional structure. This three-dimensional shape of a protein plays a key role in determining its function, so proteins in which particular atoms have very similar configurations in space often have similar functions. There is therefore a need for efficient methodology to align the proteins after allowing for rigid transformations.

Real problems in Protein Bioinformatics can be very complex, such as their flexibility. This problem fits in statistical shape analysis where one assumes that the points in two or more configurations (atoms here) are labelled and these configurations are to be matched after filtering out some transformation such as a rigid transformation. Green, P.J. and Mardia, K.V. (2006, Biometrika, 93) have developed a new Bayesian hierarchical method to align unlabelled configurations under rigid transformation. This project will extend the methodology to allow for various different types of transformations, mostly motivated by problems of protein flexibility. Several medical data sets are already available to test the adequacy of the tools developed under this project.