Properties of a Two Dimensional Model of RNA Folding

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.