Barrier heights between ground states in a model of RNA secondary structure

Secondary structure formation is an important factor influencing the behaviour of many types of naturally occurring RNA molecules. RNA secondary structure also provides an example of a disordered system showing frustration and a rugged energy landscape with many alternative ground states. We use a numerical method to estimate energy barrier heights between a set of alternative ground-state structures of a given sequence. Both the mean barrier height and the maximum barrier height for a given sequence scale with a sequence length N approximately as . The matrix h of barriers is exactly ultrametric, which means that structures form an exactly hierarchical set of clusters based on barrier heights. The matrix of distances d between structures is correlated with h, but with large fluctuations. Hence, the d matrix is approximately ultrametric, but the clustering of structures based on distances is not perfectly hierarchical. Certain base pairs are observed to be present in every ground-state structure. These `frozen' pairs divide the molecule up into mutually inaccessible pieces. All of the separate pieces contribute to determining the distance between structures, but only the largest piece will contribute to the barrier height. The length of the largest piece varies between sequences, and scales in proportion to N on average. We compare these results with studies of other disordered systems, and discuss the consequences for the folding of naturally occurring RNAs.