Mathematics Colloquia and Seminars

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Description

Advancements in sequencing technologies have produced a wealth of genomic data. In parallel, the development of artificial intelligence has enabled powerful folding models that accurately predict molecular structures from sequences. These advancements have resulted in a myriad of biomolecular structure data. Analytics of structure data offers more accurate approaches to genotype-to-phenotype analyses, as biomolecular structures are more evolutionarily conserved than sequences and more directly linked to biological functions. A major challenge of structure data analytics is the lack of efficient and accurate structure encodings. In this talk, we introduce encodings of RNA secondary structures using polynomial invariants of graphs, which are a fundamental object in algebraic combinatorics. We show that the tree-polynomial encodings enable efficient, accurate and interpretable RNA secondary structure analyses using modern data analytics tools. We demonstrate their applications in predicting and understanding R-loop formation, as well as in analyzing similarity and diversity of RNA structures in the genomes of single-stranded RNA viruses.