Wavelet-based multifractal analysis of C.elegans sequences based on FCGS signal

Abstract

The frequency chaos game signal (FCGS) is a new mapping technique of DNA sequences inspired by the Chaos Game theory. It has the particularity of exploiting the statistical properties of the genomic sequences composition which may serve in detecting interesting structures within the DNA sequences. Unlike the classical DNA sequences coding techniques, where the nucleotides are assigned numerical values depending on their chemical and structural characteristics, the advantage of the FCGS coding method is its invariance concerning the assignment of nucleotides to their numerical values. Mapping nucleotide sequences by the FCGS technique produces a multifractal landscape that can be studied quantitatively by applying the so-called wavelet transform modulus maxima method (WTMM). This method provides a natural generalization of the classical box-counting techniques for the multifractal signal analysis. In fact, the wavelets are playing the role of generalized oscillating boxes. In this paper, we use the WTMM method to perform a multifractal analysis of the C.elegans genome using FCGS signal with order two. First, we generate the FCGS signal of particulars C.elegans genome regions like exon, intron, Helitron, CERP3, and CEREP55. Next, we apply the WTMM to calculate the singularity spectrum. Finally, we prove, with the obtained results, the multifractal nature of this genome and the variability of this multifractal characteristic according to the region studied. We also discover that this variability was mainly dependent on differences in the contents of repetitive DNA in each DNA sequence. This approach will be used to characterize sequences to allow their automatic classification. The technique aims to characterize structural and functional regions of chromosomes in genomes and will help later to explore automatically and study unidentified sequences.