Some Comments on Mathematical Descriptors of Biomolecular Sequences and their Characteristics

The advent of techniques of graphical representation and mathematical characterization of biomolecular sequences has seen the growth of a genre of non-alignment methods for analyses of their similarities/dissimilarities. The new descriptors are important and convenient to provide a  quantitative measure of the composition and distribution of the basic units, allow discrimination amongst members of a family of similar sequences with a low computational overhead and hold promise for discovery of new systematics. These opportunities led to a plethora of models for graphical representation and numerical characterisations, but the question is how far the various sequence descriptors derived by these different mathematical approaches encode non-redundant information. We briefly consider the issues that when comparative studies of biomolecular sequences are undertaken, it is important to consider which properties are being considered and choose models that allow for computational closure and non-redundancy. We believe graphical representation and numerical characterization models have a significant role to play in non-alignment similarity/dissimilarity analysis of bio-molecular sequences, but the issues have to be approached with an eye to specific properties being investigated.