Applied DNA visibility graphs: Understanding DNA structure-function relationship in genomics

Abstract

DNA sequences have a complex structure that reflects their evolutionary history, such as functional elements, gene modifications, and repetitive segments. To study this structure, mathematical models like DNA walks can be used. DNA walks assign opposite movements to pyrimidines (C, T) and purines (A, G), allowing the application of nonlinear dynamics and complex systems theory. These methods can reveal long-range correlations and genome signatures that are useful for metagenomics. We combined DNA walks and visibility graphs to create DNA visibility graphs (Kosmidis and Hütt, 2023), which can capture correlations in DNA regions and artificial sequences.

We applied these methods to E. coli genes and found patterns that suggest gene grouping into classes. We also found that the degree distribution of visibility graphs in different organisms follows a power-law, indicating universal scaling. Importantly, we find that genes of the same organism i.e. E. coli exhibit vast differences in their visibility graph characteristics while complete-genome visibility graphs from different organisms have remarkable similarities. Our results offer new ways to visualize the relationship between DNA structure and function and have implications for genomics, bioinformatics, and systems biology.