Topological Sequence Analysis of Genomes: Category Approaches

Area of Science:

• Bioinformatics
• Computational Biology
• Genomics

Background:

• Sequence data (DNA, RNA, protein) possess complex, multi-scale structures challenging traditional analysis methods like alignment or statistical approaches.
• Existing alignment-free methods often lack structured mathematical formalisms for capturing intricate sequence topology.

Purpose of the Study:

• To introduce Category-Based Topological Sequence Analysis (CTSA) for modeling genomic sequences.
• To develop a framework that extracts multi-scale topological features from sequences using categorical constructions and persistent homology.
• To demonstrate the efficacy of CTSA in biological sequence analysis tasks.

Main Methods:

• Modeling sequences as resolution categories to capture hierarchical structure.
• Deriving substructure complexes from categorical representations.
• Computing persistent homology to extract multi-scale topological features.
• Applying CTSA to phylogenetic analysis of SARS-CoV-2 variants and protein-nucleic acid binding affinity prediction.

Main Results:

• CTSA generates informative topological signatures for biological sequences.
• The method achieves excellent and consistent performance in phylogenetic analysis and binding affinity prediction tasks.
• Comparative studies show CTSA outperforms six state-of-the-art methods.

Conclusions:

• CTSA provides a robust and generally applicable framework for biological sequence analysis.
• The approach integrates categorical and homological theories, opening new research directions.
• CTSA offers a powerful alternative to traditional sequence analysis methods.