Strings, trees, and RNA folding

Date: Wed 29th May 2024

Abstract

Under a suitable abstraction, complex biological problems can reveal surprising mathematical structure. As will be explained, a challenging open problem in molecular biology (i.e. RNA folding) is nicely abstracted to discrete models (e.g. strings and trees). Using combinatorial methods (convex polytopes and their normal fans), we can improve RNA folding prediction accuracy on well-defined families while also illuminating why the general problem is so difficult. We also obtain some new results in the combinatorics of Catalan objects inspired by the branching of RNA secondary structures. This illustrates that the interaction of discrete mathematics and molecular biology can be fruitful for theory while also beneficial for applications.