Statistical approaches to three key challenges in protein structural bioinformatics

. Proteins are the workhorses of all living systems, and protein bioinformatics deals with analysis of protein sequences (one dimensional) and structures (three dimensional). The paper reviews statistical advances in three major active areas of protein structural bioinformatics: structure comparison, Ramachandran plots and structure prediction. These topics play a key role in understanding one of the greatest unsolved problems in biology, how proteins fold from one dimension to three dimensions, and have relevance to protein functionality, drug discovery and evolutionary biology. For each area, we give the biological background and review one of the main bioinformatics solutions to a specific problem in that area. We then present statistical tools recently developed to investigate these problems, consisting of Bayesian alignment, directional distributions and hidden Markov models. We illustrate each problem with a new case-study and describe what statistics can offer to these problems. We highlight challenges facing these areas and conclude with an overall discussion.