Classification of RNA Secondary Structures Using the Techniques of Cluster Analysis

An RNA molecule has a lot of suboptimal secondary structures. Some of these suboptimal structures are very similar and some are entirely different. In some cases, the free energy of these suboptimal structures does not differ much from that of the optimal structure. In order to characterize this relationship more clearly, we defined a metric among the secondary structures by the unweighted pair group method, using the arithmetic average and extended this metric to the sets of secondary structures. We report two applications of this metric. First, we developed a method for the classification of these suboptimal secondary structures of a given RNA sequence. Results of classification are presented with the secondary structures of cadang-cadang coconut viroid, potato spindle tuber viroid and polio virus as examples. Second, we applied this metric to the classification of the secondary structures derived from a set of mutant RNA sequences. We discuss that the mutation of a given RNA sequence changes not only the optimal secondary structure, but also the population of the cluster of the secondary structures.