Associate Professor of Mathematics Jose Ceniceros and Josef Komissar ’22 are co-authors of a paper published recently in the journal Communications of the Korean Mathematical Society. “RNA foldings and stuck knots” presents findings from a study of the folding of RNA molecules in which they analyzed the molecules’ structural characteristics through the application of knot theory and embedded rigid vertex graphs. Researchers from the University of South Florida also participated in this work.
Ceniceros said that although traditional knot theory has proven advantageous in representing biomolecules, it tends to concentrate on the entanglement aspect, overlooking interactions within the molecular chain. In this study, they employed stuck knots and links, thereby accentuating both the entanglement and intrachain interactions.
“In our initial exploration,” Ceniceros said, “we present a set of oriented stuck Reidemeister moves for oriented stuck links.” He noted that while demonstrating that this set of moves constitutes a generating set, the group plans to identify a minimal generating set of moves in an upcoming project.
Next, they defined an algebraic structure to formalize the stuck Reidemeister moves, allowing them to develop a coloring counting invariant for stuck links. Ceniceros said the efficacy of this invariant, specifically its effectiveness in classifying RNA foldings, is shown in the detailed computations included in the paper. “A noteworthy advancement in our study is the demonstration of the superiority of our invariant over the previously defined signed sticking number,” he said.
Komissar collaborated on this work while a participant in Ceniceros’ senior seminar on knot theory, where he expressed an interest in research. “It's worth noting that this project was not specifically a senior project; rather, it originated from Josef's curiosity,” Ceniceros said. Komissar is currently pursuing a Ph.D. in mathematics at Syracuse University.
Ceniceros will be offering his senior seminar on knot theory next fall.
