Section: New Results

RNA structures

RNA structure alignment

It is widely accepted that, for a large number of RNA families, the structure is more conserved than the sequence. Therefore, any reasonable notion of homology should consider the similarity in the secondary structure, i.e. how well the base-pairing positions in two structures can be put in correspondence, or aligned. In collaboration with a significant part of the French bioinformatics community, an assessment of the quality of existing algorithms for the problem was proposed [6] . Furthermore, a review of the state-of-the-art in RNA comparison algorithms is to be published [11] , and a chapter in a forthcoming book on RNA computational biology was written in collaboration with Robert Giegerich (University Bielefeld) during his stay.

Most existing alignment tools rely on the assumption that the RNA structure is free of pseudoknots, i.e. free of crossing interactions. This condition naturally arises from the intractability of the unconstrained version of the problem. In a joint work, A. Denise, Ph. Rinaudo and Y. Ponty worked around this issue by proposing a parameterized complexity algorithmic solution for the unconstrained version of the problem. One of the key feature of this algorithm is that, although exponential in the worst-case scenario, it naturally adapts its complexity to the level of intricacy of the aligned structures, and remains polynomial for large classes of pseudoknots. Preliminary results of this work were presented at the WABI'12 conference [35] .

Energy-weighted RNA algorithmics

We complemented previous studies led within Amib on RNA structures with restricted classes of pseudoknots by showing, in a collaboration with Rolf Backofen (Freiburg University), that the computational hardness of RNA folding with general pseudoknots is extremely robust to the choice of a precise energy model. It was shown that the problem is completely unapproximable when expressive – yet realistic – energy models are taken into consideration. These results were presented at CPM'12  [37] (Helsinki, Finland).

Moreover, using an interpolation technique introduced at the RECOMB'11 conference, we were able to improve both the sequential and parallel complexities of the RNAbor algorithm developed within P. Clote's lab. The resulting algorithm and its application to the detection of conformational switches in sequence lengths that were previously unreachable by the algorithm, are described in a manuscript accepted in Plos One.

RNA knowledge-based potentials and 3D studies

The building of an RNA potential proved much harder and interesting than we initially expected. A non-redundant dataset had first to be extracted from the literature as the available dataset were not suitable for our study even the very recent ones. From the collected distance data, the building of a knowledge-based potential was usually done using histograms; and the histogram interval size and data fitting was an issue. In our 2012 study, we showed that the best solution to build potentials with no interval issue is by using Dirichlet Process Mixture Models (DPMs) [24] . We also benefited of the group experience in modeling the dynamics of RNA and normal-mode experiments to obtain two good decoy sets which complemented the well-known Farna study. We also showed that in many case our high-resolution predictions were better than the Farna/Rosetta standard.

RNA 3D structure prediction

In collaboration with Prism at Versailles and Westhof's group at Strasbourg, we addressed the problem of ab initio prediction of RNA three-dimensional structure. We developed an algorithm for automatically predicting the topological family of any RNA three-way junction, an thus its coarse-grained local geometry, given only the information from the secondary structure: the sequence and the Watson–Crick pairings. Additionally, we showed that the results are noticeably improved if homology information is used [14] . The resulting software, Cartaj , is available online and downloadable at http://cartaj.lri.fr . Then we investigated a new approach for the global prediction of the coarse-grain 3D structure of RNA molecules. We model a molecule as being made of helices and junctions. Using our results above, we are able to classify junctions into topological families that determine their preferred 3D shapes. All the parts of the molecule are then allowed to establish long-distance contacts that induce a threedimensional folding of the molecule. An algorithm relying on game-theory was proposed to discover such long-distance contacts that allow the molecule to reach a Nash equilibrium. As reported by our experiments, this approach allows one to predict the global shape of large molecules of several hundreds of nucleotides that are out of reach of the state-of-the-art methods [15] .

A graph-theoretic approach has been successfully used for classification and structure prediction of transmembrane beta-barrel proteins[23] , [25] .