# Properties of a Two Dimensional Model of RNA Folding

## TL;DR

This paper investigates a 2D RNA folding model, proving properties about unique optimal foldings, computational complexity, and providing an approximation algorithm, advancing understanding of RNA structure prediction.

## Contribution

It introduces a 2D RNA folding model, proves key properties, establishes NP-hardness, and offers a constant-factor approximation algorithm.

## Key findings

- Existence of an infinite family of sequences with unique optimal foldings
- Identification of two ideal foldings for even-length sequences
- NP-hardness of finding optimal foldings in this model

## Abstract

Ribonucleic Acid (RNA) can fold into shapes that perform functions in the cell. These foldings are governed by Watson-Crick base pairing, namely Adenine to Uracil and Cytosine to Guanine (A-U and G-C). The properties of the H-P (hydrophobic-hydrophilic) model of protein folding has been well studied in the two dimensional orthogonal case, and we attempt to achieve similar results. We prove that (1) there is an infinite family of even-length sequences with unique optimal foldings, (2) there are two ideal foldings for an even length sequence and given a sequence is is quickly verifiable if both, one, or neither are optimal, (3) finding an optimal foldings under this model is NP-hard, and (4) we give a constant-factor approximation algorithm for optimally folding RNA sequences.