DNA walk of specific fused oncogenes exhibit distinct fractal geometric characteristics in nucleotide patterns

Symmetry and symmetry-breaking in distinct biological cell features or components have been examined in cancer investigations. However, there can be possible limitations in directly interpreting the symmetry-based approach from a physical viewpoint due to the lack of understanding of physical laws governing symmetry in complex systems like cancer. To overcome this, herein, fractal geometry and DNA walk representation were employed to investigate the geometric features i.e., self-similarity and heterogeneity in DNA nucleotide coding sequences of wild-type and mutated oncogenes, tumour-suppressor, and other unclassified genes. The mutation-facilitated self-similar and heterogenous features were quantified by the fractal dimension and lacunarity measures, respectively. Additionally, the geometrical orderedness and disorderedness in the analyzed sequences were interpreted from the combination of the fractal measures. The findings showed distinct fractal features in the case of specific fusion mutations. They also highlight the possible interpretation of the fractal features as geometric analogues concerning explicit observations corresponding to specific cancer types. The two-dimensional multi-fractal analysis highlighted the prominence of mono-fractal scaling in the self-similarity of the analyzed sequences though asymmetric multi-fractal characteristics were vaguely observed. This study highlights the potential of integrating fractal geometry into cancer genomics to bridge the gap between molecular complexity and heterogeneity and translational cancer research.