Information, probability, and the abundance of the simplest RNA active sites

The abundance of simple but functional RNA sites in random-sequence pools is critical for understanding emergence of RNA functions in nature and in the laboratory today. The complexity of a site is typically measured in terms of information, i.e. the Shannon entropy of the positions in a multiple sequence alignment. However, this calculation can be incorrect by many orders of magnitude. Here we compare several methods for estimating the abundance of RNA active-site patterns in the context of in vitro selection (SELEX), highlighting the strengths and weaknesses of each. We include in these methods a new approach that yields confidence bounds for the exact probability of finding specific kinds of RNA active sites. We show that all of the methods that take modularity into account provide far more accurate estimates of this probability than the informational methods, and that fast approximate methods are suitable for a wide range of RNA motifs.