Mathematical evaluation of the formation and evolution of hierarchical structures of repetitive DNA sequences

Ziyan Hao; Xiaochang Xu; Xiyin Wang; Ziyan Hao; Xiaochang Xu; Xiyin Wang

doi:10.3934/mbe.2026095

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 9: 2634-2654. doi: 10.3934/mbe.2026095

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Research article

Mathematical evaluation of the formation and evolution of hierarchical structures of repetitive DNA sequences

1.
College of Mathematics and Science, North China University of Science and Technology, Tangshan, China
2.
School of Life Science, North China University of Science and Technology, Tangshan, China
3.
School of Public Health and Protective Medicine, North China University of Science and Technology, Tangshan, China

Received: 05 December 2025 Revised: 21 January 2026 Accepted: 26 January 2026 Published: 03 September 2026

With the advancement of genome sequencing technologies, telomere-to-telomere (T2T) genome assemblies provide valuable opportunities to understand the formation and evolution of centromeric regions, which are enriched in highly repetitive DNA sequences. In this study, we applied a well-established alignment-free approach using k-mer frequency vectors and Euclidean distance to quantify the similarities among hierarchical repetitive units. By introducing point, insertion, and deletion mutations at varying rates, we systematically assessed their effects on the repeat unit similarity at different hierarchical levels. All analyses were based on the averages of 30 independent simulation runs, with standard deviations used to quantify the stochastic variability. Point mutations generally led to monotonic increases in the Euclidean distance, reflecting progressively reduced sequence similarities, whereas insertion and deletion mutations produced more variable patterns, highlighting the complex effects of length-altering mutations on the hierarchical structure evolution. To further evaluate the biological relevance of our simulations, representative centromeric regions from rice, Arabidopsis, and human genomes were analyzed, showing hierarchical patterns consistent with the simulated sequences. Overall, this study provides a reproducible and interpretable computational framework for quantitatively assessing how different mutation types influence on the formation and evolution of multi-layered repetitive sequences, thereby explicitly linking simulation results to biologically observed patterns while acknowledging the established nature of the methods.
- DNA repetitive sequences,
- mutation,
- frequency vector,
- Euclidean distance
Citation: Ziyan Hao, Xiaochang Xu, Xiyin Wang. Mathematical evaluation of the formation and evolution of hierarchical structures of repetitive DNA sequences[J]. Mathematical Biosciences and Engineering, 2026, 23(9): 2634-2654. doi: 10.3934/mbe.2026095

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Abstract

With the advancement of genome sequencing technologies, telomere-to-telomere (T2T) genome assemblies provide valuable opportunities to understand the formation and evolution of centromeric regions, which are enriched in highly repetitive DNA sequences. In this study, we applied a well-established alignment-free approach using k-mer frequency vectors and Euclidean distance to quantify the similarities among hierarchical repetitive units. By introducing point, insertion, and deletion mutations at varying rates, we systematically assessed their effects on the repeat unit similarity at different hierarchical levels. All analyses were based on the averages of 30 independent simulation runs, with standard deviations used to quantify the stochastic variability. Point mutations generally led to monotonic increases in the Euclidean distance, reflecting progressively reduced sequence similarities, whereas insertion and deletion mutations produced more variable patterns, highlighting the complex effects of length-altering mutations on the hierarchical structure evolution. To further evaluate the biological relevance of our simulations, representative centromeric regions from rice, Arabidopsis, and human genomes were analyzed, showing hierarchical patterns consistent with the simulated sequences. Overall, this study provides a reproducible and interpretable computational framework for quantitatively assessing how different mutation types influence on the formation and evolution of multi-layered repetitive sequences, thereby explicitly linking simulation results to biologically observed patterns while acknowledging the established nature of the methods.

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