For example, aptamers that bind to ATP, chloramphenicol, neomycin B, and streptomycin all have simple, linear stem–loop structures ( Laserson et al. That is, linear or slightly branched structures occur far more often than highly compact structures. However, an analysis of existing aptamers has shown that RNA sequences isolated from selection experiments tend to have simple topologies ( Bae et al. Indeed, in vitro selection experiments have revealed novel functional RNAs from random sequence pools, including a wide range of RNA aptamers that bind to particular compounds, such as ATP, antibiotics or proteins, and catalytic RNAs ( Wilson and Szostak 1999 Hodgson and Suga 2004) see the collection of several hundred aptamers in the Aptamer Database ( ). RNA in vitro selection technology has greatly advanced the field of RNA structure and function. Specifically, the optimal RNA sequence pool length to identify a structure with x stems is 20 x. These analyses show not only that random pools do not lead to a uniform distribution of possible RNA secondary topologies they point to avenues for designing pools with specific simple and complex structures in equal abundance in the goal of broadening the range of functional RNAs discovered by in vitro selection. Moreover, we quantify the rise of structural complexity with sequence length and report the dominant class of tree motifs (characterized by vertex number) for each pool. Our results show that such random pools heavily favor simple topological structures: For example, linear stem–loop and low-branching motifs are favored rather than complex structures with high-order junctions, as confirmed by known aptamers. Toward this goal, we have generated by computer five random pools of RNA sequences of length up to 100 nt to mimic experiments and characterized the distribution of associated secondary structural motifs using sets of possible RNA tree structures derived from graph theory techniques. Such an understanding is a prerequisite for designing sequence pools to increase the probability of finding complex functional RNA by in vitro selection techniques. However, the structural diversity in random pools is not well understood. In vitro selection of functional RNAs from large random sequence pools has led to the identification of many ligand-binding and catalytic RNAs.
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