Exploring the multifractal behavior of the human genome T2T-CHM13v2.0: Graphical representations and cytogenetics

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 individual chromosomes, including mitochondrial DNA, to characterize the fractal structure and multifractal spectra of the genome.

Multifractal spectra were determined using box-counting coverage. We compared two representations - the Binary Genomic Representation (BGR) and the Markov Chain (MC) representation - using the complete assembly as a reference. The effect of the assigned length parameter was evaluated, and the optimal fit was achieved using MC for twelve-base chains.

Although the geometric support was consistent across chromosomes, distinct distribution patterns emerged. Chromosomes 9 and Y exhibited the greatest differences in singularity (Hölder exponent), with only minor variations in fractal support. The CGR distributions segregated coding and non-coding regions, as well as CpG/GpC islands, and detected tandemly repeated short DNA sequences at centromeres and heterochromatic regions, thereby characterizing related polymorphisms. In comparing representations, BGR aligned more closely with high-frequency components, while MC better captured low-frequency regions. The optimal MC fit for twelve-base chains yielded an average error of 2% relative to the complete assembly.

Our findings demonstrate that CGR is a powerful tool for structural DNA analysis, offering valuable insights into genomic architecture and polymorphism characterization. Moreover, the complementary use of BGR and MC enhances our ability to resolve distinct frequency components within the genome. This approach shows promise for further genomic functional studies and potential medical applications, as illustrated by our example on chromosomes 9 and Y.