A sequential folding model predicts length-independent secondary structure properties of long ssRNA

We introduce a simple model for folding random-sequence RNA molecules, arguing that it provides a direct route to predicting and rationalizing several average properties of RNA secondary structures. The first folding step involves identifying the longest possible duplex, thereby dividing the molecule into a pair of daughter loops. Successive steps involve identifying similarly the longest duplex in each new pair of daughter loops, with this process proceeding sequentially until the loops are too small for a viable duplex to form. Approximate analytical solutions are found for the average fraction of paired bases, the average duplex length, and the average loop size, all of which are shown to be independent of sequence length for long enough molecules. Numerical solutions to the model provide estimates for these average secondary structure properties that agree well with those obtained from more sophisticated folding algorithms. We also use the model to derive the asymptotic power law for the dependence of the maximum ladder distance on chain length.