Section: New Results

RNA algorithms

• A universal framework for RNA algorithms. We have proposed a new generic specification framework, called inverted coupled rewrite systems that can deal with optimization problems on strings, trees, and arc-annotated sequences. It is specifically well-suited to handle RNA algorithms, such as alignment or folding algorithms. It is based on the following ideas. The solutions of combinatorial optimization problems are the inverse image of a term rewrite relation that reduces problem solutions to problem inputs. A tree grammar is used to further refine the search space, and optimization objectives are specified as interpretations of these terms. All these constituents provide a mathematically precise and complete problem specification, leading to concise yet translucent specifications of dynamic programming algorithms. This work is a collaborative project with R. Giegerich from Universität Bielefeld, and has been published in [4] .

• RNA multistructures. In many RNA families, the signature of the family cannot be characterized by a single consensus structure, and is mainly described by a set of alternate secondary structures. For example, certain classes of RNAs adopt at least two distinct stable folding states to carry out their function. This is the case of riboswitches, that undergo structural changes upon binding with other molecules, and recently some other RNA regulators were proven to show evolutionary evidence for alternative structure. The necessity to take into account multiple structures also arises when modeling an RNA family with some structural variation across species, or when it comes to work with a set of predicted suboptimal foldings. In this perspective, we have introduced the concept of RNA multistructures, that is a formal grammar based framework specifically designed to model a set of alternate RNA secondary structures. We provide several motivating examples and propose an efficient algorithm to search for RNA multistructures within a genomic sequence. This work was published in [8] .