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Although functional RNA molecules are known to be biased in overall composition, the effects of background composition on the probability of finding a particular active site by chance has received little attention. The probability of finding a particular motif has important implications both for understanding the distribution of functional RNAs in ancient and modern organisms with varying genome compositions and for tuning SELEX pools to optimize the chance of finding specific functions. Here we develop a new method for calculating the probability of finding a modular motif containing base-paired regions, and use a computational grid to fold several hundred million random RNA sequences containing the core elements of the isoleucine aptamer and the hammerhead ribozyme to estimate the probability that a sequence containing these structural elements will fold correctly when isolated from background sequences of different compositions. We find that the two motifs are most likely to be found in distinct regions of compositional space, and that the regions of greatest abundance are influenced by the probability of finding the conserved bases, finding the flanking helices, and folding, in that order of importance. Additionally, we can refine our estimates of the number of random sequences required for a 50% probability of finding an example of each site in unbiased random pools of length 100 to 4.1 x 10(9) for the isoleucine aptamer and 1.6 x 10(10) for the hammerhead ribozyme. These figures are consistent with the facile recovery of these motifs from SELEX experiments.

Abundance of correctly folded RNA motifs in sequence space, calculated on computational grids