Section: New Results

Protein structures

Participants : Rumen Andonov, Guillaume Chapuis, Dominique Lavenier, Mathilde Le Boudic-Jamin, Antonio Mucherino.

• Comparison of pairwise protein structure alignments. The method provides either optimal, top-scoring alignments or heuristic alignments with quality guarantee for some inter-residue distance-based measures. Alignments are compared using a number of quality measures and intuitive visualizations. The methodology brings new insight into the structural relationship of the protein pairs and is a valuable tool for studying structural similarities. [23]

• Alignment graph. This object is the main input to find similarities between biomolecules (ARN, proteins). This kind of graph has to model physical and/or chemical properties of the biomolecules and need to take into account constraints dictated by the type of applications (3D comparison, docking, etc.). Our research aims to provide a strategy to automate the building of alignment graphs. A prototype software, called MAGE, is currently under test to validate our approach.

• Mathematical model and exact algorithm for optimally aligning protein structures. The algorithm proposes for the first time, to evaluate the popular DALI heuristic in sound mathematical terms. The results indicate that DALI usually computes optimal or close to optimal alignments. However, we detect a subset of small proteins for which DALI fails to generate any significant alignment, although such alignments do exist [22] .

• Modeling the protein flexibility by distance geometry. We suggest a strategy for modeling protein flexibility that is based on the discretization of the space of possible molecular conformations for a protein. The same discretization process was previously employed for discretizing Molecular Distance Geometry Problems (MDGPs) [30] .

• NMR problems. We introduce formally the Discretizable Molecular Distance Geometry Problem (DMDGP) for solving the 3D structure of a protein based on Nuclear Magnetic Resonance data together with an algorithm, which we named the "Branch & Prune" (BP), for the solution of DMDGPs [16] .We also provide surveys on these recent works about DMDGPs [15] , [27] .

• Improvements and variants of the DMDGP. We exploit symmetries in DMGP trees. We consider similar or related problems (re-ordering of the vertices, relaxing vertices consecutivity assumtion, including side chains and finding low energy homopolymer conformations). Parallelism has also been investigated. [17] , [14] , [18] , [28] , [26] , [29]