Frequency Chaos Game Method and Fractals Show Evolutionary Relationships of the PRKN Gene in Primates

Year 2025, Volume: 7 Issue: 2, 146 - 153, 31.07.2025

Rodrigo Pérez-gala Yordy S. Cangrejo-useda Camila V. Castillo-lopez Maria J. Sanchez-manjarrez Cristian E. Cadena-caballero Francisco Martinez-perez Fernando Ramirez-alatriste

https://doi.org/10.51537/chaos.1643191

Cited By: 1

Abstract

The Chaos Game Representation (CGR) algorithm and its frequency-based optimization, the Frequency Chaos Game Representation (FCGR), offer alignment-free methods for analyzing DNA sequences through fractal geometry. This study investigates the evolutionary relationships of the PRKN gene in primates using FCGR, exploring his capacity to reveal phylogenetic signals. We applied FCGR to PRKN gene sequences from 16 primate species, calculating nucleotide frequencies and generating fractal representations. Phylogenetic relationships were inferred from fractal similarity and compared to established phylogenies and Shannon entropy was employed to correlate sequence organization with fractal patterns. Results demonstrate that FCGR effectively captures evolutionary relationships of the PRKN gene, yielding phylogenetic clustering consistent with conventional methods. The fractal patterns and their relation to Shannon entropy reveal structural organization within the PRKN gene sequence, independent of sequence length. This alignmentfree, fractal-based approach offers a rapid and informative tool for studying genetic evolution, with potential applications in understanding primate phylogeny and neurodegenerative disorders linked to PRKN.

Keywords

Chaos Game Representation , Frequency chaos game representation , Fractals , Phylogeny , PRKN gene , Primates , Evolutionary relationships

Thanks

This work was supported by Maestria en Ciencas de la Complejidad from the Universidad Autonoma de la Ciudad de Mexico, Campus Colonia del Valle, Mexico; by the Complexity Science Group: Chaos, Fractals, Nature Applications from the Universidad Autonoma de la Ciudad de Mexico. Moreover, by a research stay granted by the Universidad Industrial de Santander by resolution 558 of October 20, 2023, and for the Grupo de Investigación en Computo Avanzado y a Gran Escala (CAGE) from Centro de Supercomputacion y Calculo Cientifico of the Universidad Industrial de Santander.

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