Exploring the Multifractal Behavior of the Human Genome T2T-CHM13v2.0: Graphical Representations and Cytogenetics

Abstract: In this work, we applied the Chaos Game Representation (CGR) to the complete human genomic sequence T2T-CHM13v2.0, analyzing the entire chromosome assembly and each chromosome separately, including mitochondrial DNA. Multifractal spectra were determined using two types of box-counting coverage, revealing slight variations across most chromosomes. While the geometric support remained consistent, distinct distributions were observed for each chromosome. Chromosomes 9 and Y exhibited the greatest differences in singularity (H\"older exponent), with minor variations in their fractal support. The CGR distributions generally demonstrated an approximate separation between coding and non-coding sections, as well as CpG or GpC islands. A base-by-base analysis of the fractal support of the CGR uncovered characteristic structural bands in chromosome sequences, which align with patterns identified in cytogenetic studies. Using the complete assembly as a reference, we compared two alternative representations: the Binary Genomic Representation (RGB) and the Markov Chain (MC) representation. Both methods tended toward the same fractal support but displayed differing distributions based on the assigned length parameter. Multifractal analysis highlighted quantitative differences between these representations: RGB aligned more closely with high-frequency components, while MC showed better correspondence with low frequencies. The optimal fit was achieved using MC for twelve-base chains, yielding an average percentage error of 2% relative to the full genomic assembly.