Mathematical characterization of DNA sequences - Towards new directions

Extracting information from the rapidly growing sequence data in DNA databases poses formidable computational problems. Over the last few years a number of approaches have been formulated to mathematically characterize the base distribution and composition characteristics of DNA sequences with a view to aiding biologists in their quest for rapidly identifying sequence segments of interest and make comparative studies of genes and genomes. Methods based on graphical representations have been found to be intuitively appealing and potentially highly informative and have led to several interesting applications. In this paper we briefly review the motivations and major methods of graphical representation and mathematical characterization of DNA sequences, analyze the strengths and weaknesses of current techniques and consider some of the important applications that have been made using these techniques. We finally discuss some of the new developments and applications areas that are likely to be of much importance in bringing the usefulness of this approach to the notice of the wider scientific community.