Properties of RNA secondary structure matching models

Abstract

RNA secondary structures have been modeled using a variety of matching families. We first explore the intersections of different matching families which are models for likely RNA secondary structures. We then introduce their respective enumeration sequences and prove our proposed equations for enumeration. Next, we prove a formula for the number of matchings with a given crossing number for a variety of matching families. Then we develop a new statistic called the pseudoknot number and find the maximum pseudoknot number on a given set of matchings. We end by providing a comparison between the crossing number, nesting number, and pseudoknot number for three matching families on nine edges.