SNR of DNA sequences mapped by general affine transformations of the indicator sequences

The identification of gene coding regions of DNA sequences through digital signal processing techniques based on the so-called 3-base periodicity has been an emerging problem in bioinformatics. The signal to noise ratio (SNR) of a DNA sequence is computed after mapping the DNA symbolic sequence into numerical sequences. Typical mapping schemes include the Voss, Z-curve and tetrahedron representations and the like, which have been used to construct gene coding region detecting algorithms. In this paper, an extended definition of SNR is proposed, which has less computational cost and wider applicability than its original ones. Furthermore, we analyze the SNRs of different mapping schemes and derive the general relationship between Voss based SNR and that of its general affine transformations. We conclude that the SNRs of Z-curve and tetrahedron map are also linearly proportional to that of Voss map. Not only is our conclusion instructional for the design of other affine transformations, but it is also of much significance in understanding the role of the symbolic-to-numerical mapping in the detection of gene coding regions.