Combinatorial analysis of interacting RNA molecules

► We present enumerative results biological relevant to interaction structures. ► Our framework is based on refined shapes which allow elegant derivation of the generating function. ► This theoretical foundation for a class of interaction structures is the target of several MFE folding algorithm. ► Our results allow simple asymptotic formulas for numbers of interaction structures for large number of nucleotides. ► A novel folding algorithm into these structures, in particular the derivation of approximation algorithm, is implied.