Section: New Results

Protein structures

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

• A book on distance geometry problems (DGP). This is a collection of invited papers on the topic "distance geometry" [38] . Among the other contributions, it contains a survey on "distance geometry" and "structural biology", which tries to function as a bridge between two scientific communities: computer science and biology. It presents some recent developments in the field by using a language common to the two communities [37] . In another contribution, the complexity of the DGP is discussed: even if this problem is NP-hard in general, we noticed a polynomial complexity on instances of DGP related to protein conformations (in the case all the available distances are exact)[36] .

• DGP with interval data. In our preliminary works on the discretization of the Distance Geometry Problem (DGP), we considered instances where all distances were supposed to be exactly known. When biological molecules are concerned, however, this is not generally the case. We worked therefore for considering the full-atom representation of the protein backbone, where some of the distances are subject to uncertainty within a given nonnegative interval. We showed that the discretization is still possible in this case, and proposed the iBP algorithm to solve the discretized DGP. [20]

• New pruning device for DGP. After the discretization, DGPs can be solved by a branch-and-prune (BP) algorithm, which is potentially able to enumerate the entire solution set. This solution set, however, can be very large for some instances, while only the most energetically stable conformations are of interest. We worked therefore for integrating the BP algorithm with two new energy-based pruning devices. Our computational experiments showed that the newly added pruning devices were actually able to improve the performance of the algorithm, as well as the quality (in terms of energy) of the conformations in the solution set. [28]

• Discretization orders for the DGP. The main assumption that allows for the discretization of DGPs is strongly based on the order in which the atoms of the molecule are considered. The "natural" order of the atoms in the amino acid chain does not always allow for the discretization. We tried to find discretization orders in several ways, based on different approaches. In [31] , we extended a previously proposed greedy algorithm that is able to deal with interval data (inexact distances). In [27] , we handcrafted some discretization orders for the side chains of the amino acids involved in the protein synthesis. In [29] , we proposed a heuristic, which outperforms, on large instances, the greedy algorithm previously proposed.

• DGP with Clifford Algebra The BP algorithm for the DGP is based on a search on the tree, where nodes of the tree belonging to a common layer provide the possible positions for the same atom of the molecule. When interval data are given, a curve in 3d (containing the possible positions for the atom) can be associated to one of such nodes. Since it is generally not necessary to have protein conformations with a precision higher than 1A, sample points on these curves can be chosen. The way to choose these sample points is not, however, a simple task. This is the reason why we are trying to make this selection process adaptive, by exploiting Clifford Algebra to this purpose. Preliminary studies in this direction were presented in [25]

• Parallel seed-based approach to protein structure similarity detection We have developed a new parallel heuristic-based approach to structural similarity detection between proteins that discovers multiple pairs of similar regions. We prove that returned alignments have RMSDc and RMSDd lower than a given threshold. Computational complexity is addressed by taking advantage of both fine- and coarse-grain parallelism. [26]

• Datamining. The selection of features that describe samples in sets of data is a typical problem in data mining. A crucial issue is to select a maximal set of pertinent features, because the scarce knowledge of the problem under study often leads to consider features which do not provide a good description of the corresponding samples. The concept of consistent biclustering of a set of data has been introduced to identify such a maximal set. The problem can be modeled as a 0–1 linear fractional program, which is NP-hard. We reformulated this optimization problem as a bilevel program, and we proposed a heuristic for its solution [39] .