Multi-Objective Genetic Algorithm for Pseudoknotted RNA Sequence Design

RNA inverse folding is a computational technology for designing RNA sequences which fold into a user-specified secondary structure. Although pseudoknots are functionally important motifs in RNA structures, less reports concerning the inverse folding of pseudoknotted RNAs have been done compared to those for pseudoknot-free RNA design. In this paper, we present a new version of our multi-objective genetic algorithm (MOGA), MODENA, which we have previously proposed for pseudoknot-free RNA inverse folding. In the new version of MODENA, (i) a new crossover operator is implemented and (ii) pseudoknot prediction methods, IPknot and HotKnots, are used to evaluate the designed RNA sequences, allowing us to perform the inverse folding of pseudoknotted RNAs. The new version of MODENA with the new crossover operator was benchmarked with a dataset composed of natural pseudoknotted RNA secondary structures, and we found that MODENA can successfully design more pseudoknotted RNAs compared to the other pseudoknot design algorithm. In addition, a sequence constraint function newly implemented in the new version of MODENA was tested by designing RNA sequences which fold into the pseudoknotted structure of a hepatitis delta virus ribozyme; as a result, we successfully designed eight RNA sequences. The new version of MODENA is downloadable from http://rna.eit.hirosaki-u.ac.jp/modena/

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

McGenus: A Monte Carlo algorithm to predict RNA secondary structures with pseudoknots

We present McGenus, an algorithm to predict RNA secondary structures with pseudoknots. The method is based on a classification of RNA structures according to their topological genus. McGenus can treat sequences of up to 1000 bases and performs an advanced stochastic search of their minimum free energy structure allowing for non trivial pseudoknot topologies. Specifically, McGenus employs a multiple Markov chain scheme for minimizing a general scoring function which includes not only free energy contributions for pair stacking, loop penalties, etc. but also a phenomenological penalty for the genus of the pairing graph. The good performance of the stochastic search strategy was successfully validated against TT2NE which uses the same free energy parametrization and performs exhaustive or partially exhaustive structure search, albeit for much shorter sequences (up to 200 bases). Next, the method was applied to other RNA sets, including an extensive tmRNA database, yielding results that are competitive with existing algorithms. Finally, it is shown that McGenus highlights possible limitations in the free energy scoring function. The algorithm is available as a web-server at http://ipht.cea.fr/rna/mcgenus.php .Comment: 6 pages, 1 figur

A steepest descent calculation of RNA pseudoknots

We enumerate possible topologies of pseudoknots in single-stranded RNA molecules. We use a steepest-descent approximation in the large N matrix field theory, and a Feynman diagram formalism to describe the resulting pseudoknot structure

Shapes of topological RNA structures

A topological RNA structure is derived from a diagram and its shape is obtained by collapsing the stacks of the structure into single arcs and by removing any arcs of length one. Shapes contain key topological, information and for fixed topological genus there exist only finitely many such shapes. We shall express topological RNA structures as unicellular maps, i.e. graphs together with a cyclic ordering of their half-edges. In this paper we prove a bijection of shapes of topological RNA structures. We furthermore derive a linear time algorithm generating shapes of fixed topological genus. We derive explicit expressions for the coefficients of the generating polynomial of these shapes and the generating function of RNA structures of genus $g$. Furthermore we outline how shapes can be used in order to extract essential information of RNA structure databases.Comment: 27 pages, 11 figures, 2 tables. arXiv admin note: text overlap with arXiv:1304.739

A bijection between unicellular and bicellular maps

In this paper we present a combinatorial proof of a relation between the generating functions of unicellular and bicellular maps. This relation is a consequence of the Schwinger-Dyson equation of matrix theory. Alternatively it can be proved using representation theory of the symmetric group. Here we give a bijective proof by rewiring unicellular maps of topological genus $(g+1)$ into bicellular maps of genus $g$ and pairs of unicellular maps of lower topological genera. Our result has immediate consequences for the folding of RNA interaction structures, since the time complexity of folding the transformed structure is $O((n+m)^5)$, where $n,m$ are the lengths of the respective backbones, while the folding of the original structure has $O(n^6)$ time complexity, where $n$ is the length of the longer sequence.Comment: 18 pages, 13 figure

From RNA folding to inverse folding: a computational study: Folding and design of RNA molecules

Since the discovery of the structure of DNA in the early 1953s and its double-chained complement of information hinting at its means of replication, biologists have recognized the strong connection between molecular structure and function. In the past two decades, there has been a surge of research on an ever-growing class of RNA molecules that are non-coding but whose various folded structures allow a diverse array of vital functions. From the well-known splicing and modification of ribosomal RNA, non-coding RNAs (ncRNAs) are now known to be intimately involved in possibly every stage of DNA translation and protein transcription, as well as RNA signalling and gene regulation processes. Despite the rapid development and declining cost of modern molecular methods, they typically can only describe ncRNA's structural conformations in vitro, which differ from their in vivo counterparts. Moreover, it is estimated that only a tiny fraction of known ncRNAs has been documented experimentally, often at a high cost. There is thus a growing realization that computational methods must play a central role in the analysis of ncRNAs. Not only do computational approaches hold the promise of rapidly characterizing many ncRNAs yet to be described, but there is also the hope that by understanding the rules that determine their structure, we will gain better insight into their function and design. Many studies revealed that the ncRNA functions are performed by high-level structures that often depend on their low-level structures, such as the secondary structure. This thesis studies the computational folding mechanism and inverse folding of ncRNAs at the secondary level. In this thesis, we describe the development of two bioinformatic tools that have the potential to improve our understanding of RNA secondary structure. These tools are as follows: (1) RAFFT for efficient prediction of pseudoknot-free RNA folding pathways using the fast Fourier transform (FFT)}; (2) aRNAque, an evolutionary algorithm inspired by Lévy flights for RNA inverse folding with or without pseudoknot (A secondary structure that often poses difficulties for bio-computational detection). The first tool, RAFFT, implements a novel heuristic to predict RNA secondary structure formation pathways that has two components: (i) a folding algorithm and (ii) a kinetic ansatz. When considering the best prediction in the ensemble of 50 secondary structures predicted by RAFFT, its performance matches the recent deep-learning-based structure prediction methods. RAFFT also acts as a folding kinetic ansatz, which we tested on two RNAs: the CFSE and a classic bi-stable sequence. In both test cases, fewer structures were required to reproduce the full kinetics, whereas known methods (such as Treekin) required a sample of 20,000 structures and more. The second tool, aRNAque, implements an evolutionary algorithm (EA) inspired by the Lévy flight, allowing both local global search and which supports pseudoknotted target structures. The number of point mutations at every step of aRNAque's EA is drawn from a Zipf distribution. Therefore, our proposed method increases the diversity of designed RNA sequences and reduces the average number of evaluations of the evolutionary algorithm. The overall performance showed improved empirical results compared to existing tools through intensive benchmarks on both pseudoknotted and pseudoknot-free datasets. In conclusion, we highlight some promising extensions of the versatile RAFFT method to RNA-RNA interaction studies. We also provide an outlook on both tools' implications in studying evolutionary dynamics