Investigation of the Bernoulli model for RNA secondary structures

Abstract

Within this paper we investigate the Bernoulli model for random secondary structures of ribonucleic acid (RNA) molecules. Assuming that two random bases can form a hydrogen bond with probability p we prove asymptotic equivalents for the averaged number of hairpins and bulges, the averaged loop length, the expected order, the expected number of secondary structures of size n and order k and further parameters all depending on p. In this way we get an insight into the change of shape of a random structure during the process 1 → p 0 . Afterwards we compare the computed parameters for random structures in the Bernoulli model to the corresponding quantities for real existing secondary structures of large subunit rRNA molecules found in the database of Wuyts et al. That is how it becomes possible to identify those parameters which behave (almost) randomly and those which do not and thus should be considered as interesting, e.g., with respect to the biological functions or the algorithmic prediction of RNA secondary structures.