Multifractal analysis of DNA sequences using a novel chaos-game representation

We present a generalization of the standard chaos-game representation method introduced by Jeffrey. To this aim, a DNA symbolic sequence is mapped onto a singular measure on the attractor of a particular IFS model, which is a perfect statistical representation of the sequence. A multifractal analysis of the resulting measure is introduced and an interpretation of singularities in terms of mutual information and redundancy (statistical dependence) among subsequence symbols within the DNA sequence is provided. The multifractal spectrum is also shown to be more sensitive for detecting dependence structures within the DNA sequence than the averaged contribution given by redundancy. This method presents several advantages with respect to other representations such as walks or interfaces, which may introduce spurious effects. In contrast with the results obtained by other standard methods, here we note that no general statement can be made on the influence of coding and non-coding content on the correlation length of a given sequence.