Combinatorics of locally optimal RNA secondary structures

Area of Science:

• Computational Biology
• Bioinformatics
• RNA Structure Prediction

Background:

• The asymptotic number of RNA secondary structures is a classical result.
• Locally optimal structures are relevant to RNA folding kinetics.
• Previous work established counts for saturated structures in the Nussinov model.

Purpose of the Study:

• To determine the asymptotic number of locally optimal RNA secondary structures under a base stacking energy model.
• To extend combinatorial methods for counting RNA structures.
• To investigate structures with annotated single-stranded nucleotides (dangles).

Main Methods:

• Application of enumerative combinatorics.
• Analysis of secondary structures with non-extendable stems.
• Adaptation of dynamic programming algorithms for enumeration.

Main Results:

• Derived the asymptotic count for locally optimal structures under the base stacking model.
• Established a connection between locally optimal structures and non-extendable stems.
• Extended combinatorial analysis to include dangles.

Conclusions:

• The base stacking energy model yields a distinct asymptotic count for locally optimal RNA structures.
• Enumerative combinatorics provides powerful tools for RNA structure counting.
• Further research can explore the impact of dangles on structure enumeration.