A fractal method to distinguish coding and non-coding sequences in a complete genome based on a number sequence representation

A fractal method to distinguish coding and non-coding sequences in a complete genome is proposed, based on different statistical behaviors between these two kinds of sequences. We first propose a number sequence representation of DNA sequences. Multifractal analysis is then performed on the measure representation of the obtained number sequence. The three exponents C-1, C1 and C2 are selected from the result of multifractal analysis. Each DNA may be represented by a point in the three-dimensional space generated by these three-component vectors. It is shown that points corresponding to coding and non-coding sequences in the complete genome of many prokaryotes are roughly distributed in different regions. Fisher's discriminant algorithm can be used to separate these two regions in the spanned space. If the point (C-1,C1,C2) for a DNA sequence is situated in the region corresponding to coding sequences, the sequence is discriminated as a coding sequence; otherwise, the sequence is classified as a non-coding one. For all 51 prokaryotes we considered , the average discriminant accuracies pc,pnc,qc and qnc reach 72.28%, 84.65%, 72.53% and 84.18%, respectively.