Folding biopolymer sequences into molecular structures of minimal free energy is a standard problem in biophysics. The corresponding inverse problem: To find sequences for given structures can be approached by suitable algorithms only in very few cases, inverse folding of RNA secondary structures is one example. The inverse folding algorithm will be presented together with exact results on counting structural elements by combinatorial statistics.
The relation between RNA sequences and structures is visualized as a mapping from a metric space of RNA sequences into a space of RNA structures. Commonly such a mapping is non-invertible because many sequences fold into the same structure. The nature of the pre-image of a structure in sequence space is important in RNA evolution and will be discussed in detail.
Minimum free energy structures are only one issue in understanding biopolymer structures. Other relevant problems are related to the set of suboptimal structures as well as to folding at time resolution.
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