How to describe genes: enlightenment from the quaternary number system

As an open problem, computational gene identification has been widely studied, and many gene finders (software) become available today. However, little attention has been given to the problem of describing the common features of known genes in databanks to transform raw data into human understandable knowledge. In this paper, we draw attention to the task of describing genes and propose a trial implementation by treating DNA sequences as quaternary numbers. Under such a treatment, the common features of genes can be represented by a "position weight function", the core concept for a number system. In principle, the "position weight function" can be any real-valued function. In this paper, by approximating the function using trigonometric functions, some characteristic parameters indicating single nucleotide periodicities were obtained for the bacteria Escherichia coli K12's genome and the eukaryote yeast's genome. As a byproduct of this approach, a single-nucleotide-level measure is derived that complements codon-based indexes in describing the coding quality and expression level of an open reading frame (ORF). The ideas presented here have the potential to become a general methodology for biological sequence analysis.