Pseudoknots are essential for the functioning of many small RNA molecules. In addition, viral RNAs often exhibit pseudoknots that are required at various stages of the viral life-cycle. Techniques for detecting evolutionarily conserved, and hence most likely functional RNA pseudoknots, are therefore of interest. Here we present an extension of the alidot approach that extracts conserved secondary structures from a multiple sequence alignment and predicted secondary structures of the individual sequences. In contrast to purely phylogenetic methods, this approach yields good results already for small samples of 10 sequences or even less.

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.

Aligner des macromolécules telles que des protéines, des ADN et des ARN afin de révéler ou exploiter, leur homologie fonctionnelle est un défi classique en bioinformatique, qui offre de nombreuses applications, notamment dans la modélisation de structures et l'annotation des génomes. Un certain nombre d'algorithmes et d'outils ont été proposés pour le problème d'alignement structure-séquence d'ARN. Cependant, en ce qui concerne les ARN complexes, comportant des pseudo-noeuds, des interactions multiples et des paires de bases non canoniques, de tels outils sont rarement utilisés dans la pratique, en partie à cause de leurs grandes exigences de calcul, et de leur incapacité à supporter des types généraux de structures. Récemment, Rinaudo et al. ont donné un algorithme paramétré général pour la comparaison structure-séquence d'ARN, qui est capable de prendre en entrée n'importe quel type de structures comportant des pseudo-noeuds. L'algorithme paramétré est un algorithme de programmation dynamique basée sur la décomposition arborescente. Nous avons développé plusieurs variantes et extensions de cet algorithme. Afin de l'accélérer sans perte sensible de précision, nous avons introduit une approche de programmation dynamique par bandes. De plus, trois algorithmes ont été développés pour obtenir des alignements sous-optimaux. De plus, nous introduisons dans ce contexte la notion de MEA (Maximum-expected Structure-Alignment) pour calculer un alignement avec la précision maximale attendue sur un ensemble d'alignements. Tous ces algorithmes ont été implémentés dans un logiciel nommé LiCoRNA (aLignment of Complex RNAs). Les performances de LiCoRNA ont été évaluées d'abord sur l'alignement des graines des familles de de la base de données RFAM qui comportent des pseudo-noeuds. Comparé aux autres algorithmes de l'état de l'art, LiCoRNA obtient généralement des résultats équivalents ou meilleurs que ses concurrents. Grâce à la grande précision démontrée par LiCoRNA, nous montrons que cet outil peut être utilisé pour améliorer les alignements de certaines familles de RFAM qui comportent des pseudo-noeuds. / Aligning macromolecules such as proteins, DNAs and RNAs in order to reveal, or conversely exploit, their functional homology is a classic challenge in bioinformatics, with far-reaching applications in structure modelling and genome annotation. In the specific context of complex RNAs, featuring pseudoknots, multiple interactions and non-canonical base pairs, multiple algorithmic solutions and tools have been proposed for the structure sequence alignment problem. However, such tools are seldom used in practice, due in part to their extreme computational demands, and because of their inability to support general types of structures. Recently, Rinaudo et al. gave a fully general parameterised algorithm for structure-sequence comparison, which is able to take as input any type of pseudoknotted structures. The parameterised algorithm is a tree decomposition based dynamic programming. To accelerate the dynamic programming algorithm without losing two much accuracy, we introduced a banded dynamic programming. Then three algorithms are introduced to get the suboptimal structure-sequence alignments. Furthermore, we introduce the notation Maximum Expected structure-sequence Alignment (MEA) to compute an alignment with maximum expected accuracy over a set of alignments. The Boltzmann match probability are computed based on the inside-outside algorithm. The algorithms are implemented in a software named LiCoRNA (aLignment of Complex RNAs). We first evaluate the performance of LiCoRNA on the seed alignment in the pseudoknotted RFAM families. Compared to the state-of-the-art algorithms, LiCoRNA shows generally equivalent or better results than its competitors. With the high accuracy showed by LiCoRNA, we further curate RFAM full pseudoknotted alignment. The reason why we realign full alignments is that covariance model does not support pseudoknot which may lead to misalign when building the full alignment.