RNA Sequence to Structure Mapping

Motivated by the observation, that RNA folding gives rise to extended neutral networks in sequence space, concepts of random graph theory are applied to build a model of RNA sequence to structure mappings. This model allows to investigate generic properties of sequence-structure relations as well as the effect of neutrality. The random mapping construction is based on two tunable parameters. These parameters pu and pp resemble the average degree of neutrality for unpaired and paired part of the RNA secondary structure, respectively. In the model a set of secondary structures must be given. The mapping is performed by building the preimage of the structures. For this purpose, the set of sequences C is constructed which are compatible with a given structure s. From this set, sequences are chosen with a probability determined by pu and pp, and finally assigned to the structure s, if (and only if) this sequence has not been mapped to another structure. The properties we are focusing on are the existence of extended neutral nets in sequence space, the connectivity of these nets and their denseness in C. The mathematical theory for our model claims the existence of a threshold value for connectivity and denseness properties of neutral nets. The theorems hold in the limit of infinite chain length and determine the threshold value to be p = 1− κ−1 √ 1/κ in both cases. Here, κ is the size of the alphabet used to encode the unpaired or paired parts of the sequences, respectively. Below this threshold the nets are neither connected not dense in C, whereas above the threshold almost all nets are connected and dense in C. Computer experiments indicate that a threshold exists also for finite chain length, although it is not sharp anymore. However, within the accuracy of the simulations the threshold value is identical with the theoretically predicted one. Furthermore, it is identical for both properties. We investigate the influence of the tertiary contacts on generic properties of sequence-structure mappings. Instead of trying to predict tertiary structures of sequences we determine the tertiary contacts. Compatible sequences are then constructed according to an arbitrary base-pairing rule. This model also contains a tunable parameter determining the frequency of tertiary contacts in a structure. We show that in this model large neutral networks exist for tertiary structures even in the case where the structures contain a relatively high number of tertiary contacts.