Anze Bozic (Inst. Jožef Stefan, Ljubljana)

Formation of base pairs between the nucleotides of an RNA sequence gives rise to a complex
and often highly branched RNA structure. While numerous studies have demonstrated the
functional importance of the high degree of RNA branching—for instance, for its spatial
compactness or interaction with other biological macromolecules—RNA branching topology
remains largely unexplored. We use the theory of randomly branching polymers to explore the
scaling properties of RNAs by mapping their secondary structures onto planar tree graphs.
Focusing on random RNA sequences of varying lengths, we determine the two scaling
exponents related to their topology of branching. Our results indicate that ensembles of RNA
secondary structures are characterized by annealed random branching and scale similarly to
self-avoiding trees in three dimensions. We further show that the obtained scaling exponents
are robust upon changes in nucleotide composition, tree topology, and folding energy
parameters. Finally, in order to apply the theory of branching polymers to biological RNAs,
whose length cannot be arbitrarily varied, we demonstrate how both scaling exponents can be
obtained from the distributions of the related topological quantities of individual RNA
molecules with fixed length. In this way, we establish a framework to study the branching
properties of RNA and compare them to other known classes of branched polymers. By
understanding the scaling properties of RNA related to its branching structure we aim to
improve our understanding of the underlying principles and open up the possibility to design
RNA sequences with desired topological properties.