Section: New Results

Applications

Design of interferometric telescopes

Participants : Jean-Daniel Boissonnat, Trung Nguyen.

In collaboration with P. Blanc and F. Falzon (Alcatel Alenia Space)

Given a disk O in the plane called the objective, we want to find n small disks P₁, ..., P_n called the pupils such that , where denotes the Minkowski difference operator, while minimizing the number of pupils, the sum of the radii or the total area of the pupils. This problem is motivated by the construction of very large telescopes from several smaller ones by so-called Optical Aperture Synthesis. In this paper [42] , we provide exact, approximation and heuristic solutions to several variations of the problem.

Revisiting the Voronoi description of protein-protein interfaces

Participant : Frédéric Cazals.

In collaboration with F. Proust, R. Bahadur(CNRS, Orsay) and J. Janin (CNRS, Orsay).

This paper [23] develops a model of macromolecular interfaces based on the Voronoi diagram and the related alpha-complex, and we test its properties on a set of 96 protein-protein complexes taken from the Protein Data Bank. The Voronoi model provides a natural definition of the interfaces, and it yields values of the number of interface atoms and of the interface area that have excellent correlation coefficients with those of the classical model based on solvent accessibility. Nevertheless, some atoms that do not loose solvent accessibility are part of the interface defined by the Voronoi model. The Voronoi model provides robust definitions of the curvature and of the connectivity of the interfaces, and leads to estimates of these features that generally agree with other approaches. Our implementation of the model allows an analysis of protein-water contacts that highlights the contacts of structural water molecules at protein-protein interfaces.

Geometric, topological and contact analysis of interfaces in macro-molecular complexes

Participant : Frédéric Cazals.

Understanding the sociology of interactions between the proteins encoded in a genome is a central question of structural biology, and interface models between molecules forming a complex are instrumental in this perspective. Qualifying interface atoms as atoms loosing solvent accessibility in the complex, or pairs of atoms within a distance threshold, several interface models have been proposed. Yet, until recently, no interface model existed to answer coherently (if at all) the following questions: can one bridge the gap from atoms loosing solvent accessibility to interface pairs? is the interface flat or curvy? is it connected or not (does it have a multi-patch structure)? is a connected component of the interface simply connected or not (does it have a hole)? what is precisely the role played by interface structural water?

Using the -complex of the Van der Waals balls, a construction derived from the Voronoi diagram, we designed such an interface model, and validated it on the usual database of co-crystallized protein-protein complexes. This paper [56] is a methodological contribution aiming at easing the access of the interface model to structural biologists. As such, the following topics are covered: (i) the geometric principles underlying the interface model (ii) the definitions of the interface and its extension to accommodate structural water (iii) the statistics one can compute from the interface model (iv) the Software Intervor and the associated web site. These presentations are accompanied by illustrations and insights on protein - protein complexes.