The arithmetic topology of genetic alignments
Christopher Barrett1,2, Andrei Bura1, Qijun He1
1Biocomplexity Institute, University of Virginia, 994 Research Park Boulevard, Charlottesville, VA, 22911, USA.
Journal of Mathematical Biology
|January 25, 2023
Summary
This study introduces a new mathematical framework for analyzing genetic variation by generalizing pairwise comparisons to k-ary dissimilarity. This approach effectively models viral evolution dynamics, as demonstrated with SARS-CoV-2 and H1N1 flu genomic data.
Area of Science:
- Computational Biology
- Mathematical Biology
- Genomics
Background:
- Current genetic variation analysis relies on pairwise relations.
- A need exists for more comprehensive methods to capture complex genetic interdependencies.
Purpose of the Study:
- To introduce a novel mathematical paradigm for studying genetic variation in sequence alignments.
- To extend the concept of pairwise dissimilarity to k-ary dissimilarity.
Main Methods:
- Developed a generalization of simplicial complexes with weighted simplices.
- Introduced the concept of k-stances and dissimilarity complexes.
- Analyzed mathematical properties of dissimilarity complexes.
Main Results:
- The proposed framework captures arithmetic and topological structures of k-ary relations.
- Demonstrated the framework's ability to identify key events in viral evolution.
- Applied the method to genomic data from SARS-CoV-2 and H1N1 influenza.
Conclusions:
- The k-ary dissimilarity approach offers a powerful new tool for genetic variation analysis.
- This framework provides insights into viral dynamics and evolutionary patterns.
- The dissimilarity complex is a robust structure for understanding complex biological sequence data.
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