Introduction to Abstract Shape Analysis
Looking Deeper into the RNA Folding SpaceAccording to the rules of base pairing, an RNA molecule can fold into a very large number of structures. RNA secondary structure prediction is often based on a thermodynamic model. Established tools such as Mfold or RNAfold can predict the structure with minimum free energy (MFE). This is also the most likely individual structure for the given molecule, but tells us little about all its competing folding alternatives. Yet often, there is good reason not to rely on one predicted structure, albeit of minimal free energy. Inaccuracy of energy parameters, varied physiological conditions or temperature, unconsidered base modifications, interaction with RNA binding proteins or with another RNA molecule, and many other circumstances may cause the functional structure to be different from the MFE structure. But still -in these cases, the functional structure is hidden among the near-optimal foldings of our molecule, and we seek means to analyze this folding space more completely.Abstract shape analysis is a systematic way to extract comprehensive information about the folding possibilities of an RNA molecule. Shape abstraction is a mathematical version of what humans do when they communicate about RNA structure: We speak of a hairpin structure for miRNA precursors, a cloverleaf structure for tRNAs, two adjacent hairpins for oxyS RNA, and, for lack of a compact name, ''the arrangement of helices P3-P9 typical of a group I intron.'' The number and arrangement of helices can characterize a particular structure quite comprehensively, while abstracting from details such as loop sizes or length of stems. (If, however, a precise size or distance of structural features or a sequence motif is characteristic for a class of RNA, then this characteristic is lost and shape abstraction is not useful.)Postponing formal definitions to Section 27.1.3, we see that the idea of shape abstraction partitions the folding space into different classes of structures, each class characterized by an abstract shape. This idea can, in principle, be added to Handbook of RNA Biochemistry, Second Edition. Edited