Asymptotic enumeration of some RNA secondary structures

AbstractIn this paper, we derive recursions of some RNA secondary structures with certain properties under two new representations. Furthermore, by making use of methods of asymptotic analysis and generating functions we present asymptotic enumeration of these RNA secondary structures

Inverse folding of RNA pseudoknot structures

Background: RNA exhibits a variety of structural configurations. Here we consider a structure to be tantamount to the noncrossing Watson-Crick and \pairGU-base pairings (secondary structure) and additional cross-serial base pairs. These interactions are called pseudoknots and are observed across the whole spectrum of RNA functionalities. In the context of studying natural RNA structures, searching for new ribozymes and designing artificial RNA, it is of interest to find RNA sequences folding into a specific structure and to analyze their induced neutral networks. Since the established inverse folding algorithms, {\tt RNAinverse}, {\tt RNA-SSD} as well as {\tt INFO-RNA} are limited to RNA secondary structures, we present in this paper the inverse folding algorithm {\tt Inv} which can deal with 3-noncrossing, canonical pseudoknot structures. Results: In this paper we present the inverse folding algorithm {\tt Inv}. We give a detailed analysis of {\tt Inv}, including pseudocodes. We show that {\tt Inv} allows to design in particular 3-noncrossing nonplanar RNA pseudoknot 3-noncrossing RNA structures-a class which is difficult to construct via dynamic programming routines. {\tt Inv} is freely available at \url{http://www.combinatorics.cn/cbpc/inv.html}. Conclusions: The algorithm {\tt Inv} extends inverse folding capabilities to RNA pseudoknot structures. In comparison with {\tt RNAinverse} it uses new ideas, for instance by considering sets of competing structures. As a result, {\tt Inv} is not only able to find novel sequences even for RNA secondary structures, it does so in the context of competing structures that potentially exhibit cross-serial interactions.Comment: 20 pages, 26 figure

Topology of RNA-RNA interaction structures

The topological filtration of interacting RNA complexes is studied and the role is analyzed of certain diagrams called irreducible shadows, which form suitable building blocks for more general structures. We prove that for two interacting RNAs, called interaction structures, there exist for fixed genus only finitely many irreducible shadows. This implies that for fixed genus there are only finitely many classes of interaction structures. In particular the simplest case of genus zero already provides the formalism for certain types of structures that occur in nature and are not covered by other filtrations. This case of genus zero interaction structures is already of practical interest, is studied here in detail and found to be expressed by a multiple context-free grammar extending the usual one for RNA secondary structures. We show that in $O(n^6)$ time and $O(n^4)$ space complexity, this grammar for genus zero interaction structures provides not only minimum free energy solutions but also the complete partition function and base pairing probabilities.Comment: 40 pages 15 figure

In silico modelling of RNA-RNA dimer and its application for rational siRNA design and ncRNA target search

Non-protein coding region, which constitutes 98.5% of the human genome, were long depreciated as evolutive relict. It is only recently that the biological relevance of\ud the non-coding RNAs associated with these non-coding regions was recognized. The development of experimental and bioinformatical methods aimed at detecting these non-coding RNAs (ncRNAs) lead to the discovery of more than 29,000,000 sequences, grouped into more than 1300 families. More often than not these ncRNAs function by binding to other RNAs, either pro- tein coding or non-protein coding. Compared to the number of tools to detect and classify ncRNAs, the number of tools to search for putative RNA binding partners is negligible. This leads to the actual situation where the function of the majority of the annotated ncRNAs genes is completely unknown. The aim of this work is to assess the function of different families of ncRNAs by developing new algorithms and methods to study RNA-RNA interactions. These new methods are extensions of RNA-folding algorithms applied to the problem of RNA- RNA interactions. Depending on the class of ncRNA studied, different methods were developed and tested. This work shows that the development of RNA-folding algorithms to study RNA- RNA interactions is a promising way to functionally annotate ncRNAs. Still other factors like RNA-proteins interaction, RNA-concentration or RNA-expression, play an important role in the process of RNA hybridization and will have to be taken into account in future works in order to achieve reliable prediction of RNA binding partners.Non-protein coding region, which constitutes 98.5% of the human genome, were long depreciated as evolutive relict. It is only recently that the biological relevance of the non-coding RNAs associated with these non-coding regions was recognized. The development of experimental and bioinformatical methods aimed at detecting these non-coding RNAs (ncRNAs) lead to the discovery of more than 29,000,000 sequences, grouped into more than 1300 families. More often than not these ncRNAs function by binding to other RNAs, either pro- tein coding or non-protein coding. Compared to the number of tools to detect and classify ncRNAs, the number of tools to search for putative RNA binding partners is negligible. This leads to the actual situation where the function of the majority of the annotated ncRNAs genes is completely unknown. The aim of this work is to assess the function of different families of ncRNAs by developing new algorithms and methods to study RNA-RNA interactions. These new methods are extensions of RNA-folding algorithms applied to the problem of RNA- RNA interactions. Depending on the class of ncRNA studied, different methods were developed and tested. This work shows that the development of RNA-folding algorithms to study RNA- RNA interactions is a promising way to functionally annotate ncRNAs. Still other factors like RNA-proteins interaction, RNA-concentration or RNA-expression, play an important role in the process of RNA hybridization and will have to be taken into account in future works in order to achieve reliable prediction of RNA binding partners