Wavelet-based multifractal analysis of DNA sequences by using chaos-game representation

Chaos game representation (CGR) is proposed as ascale-independent representation for DNA sequences and providesinformation about the statistical distribution of oligonucleotidesin a DNA sequence. CGR images of DNA sequences represent some kinds offractal patterns, but the common multifractal analysis based on thebox counting method cannot deal with CGR images perfectly. Here, thewavelet transform modulus maxima (WTMM) method is applied to themultifractal analysis of CGR images. The results show that thescale-invariance range of CGR edge images can be extended to threeorders of magnitude, and complete singularity spectra can becalculated. Spectrum parameters such as the singularity spectrumspan are extracted to describe the statistical character of DNAsequences. Compared with the singularity spectrum span, exonsequences with a minimal spectrum span have the most uniformfractal structure. Also, the singularity spectrum parameters arerelated to oligonucleotide length, sequence component and species,thereby providing a method of studying the length polymorphism ofrepeat oligonucleotides.