Understanding the specificity of protein interactions is a central question in structural biology, whence the importance of models for protein binding patches---a patch refers to the collection of atoms of a given partner accounting for the interaction. To improve our understanding of the structure-function relationship, we present a patch model decoupling the topological and geometric properties. While the geometry is classically encoded by the atomic positions, the topology is recorded in a graph encoding the relative position of concentric shells partitioning the interface atoms. The topological - geometric duality provides the basis of a generic dynamic programming based algorithm comparing patches at the shell level, which may favor topological or geometric features.

On the biological side, we make three contributions using 249 co-crystallized heterodimers organized in biological sub-families.

First, we show that Nature enjoyed the topological and geometric degrees of freedom independently while retaining a finite set of qualitatively distinct topological signatures, and show that isotropic patch models fall short from capturing the diversity of patches.
Second, we argue that our shell-based comparison is effective to perform atomic-level comparisons, and show that topological similarity is a less stringent than geometric similarity. We also use the topological versus geometric duality to exhibit topo-rigid patches, whose topology (but not geometry) remains stable upon docking. Third, we show that complexes related to the same biological function can encompass geometrically distinct shapes.
To conclude, we believe that the topological - geometric duality paves the way to new classifications, in particular in the context of flexible docking.

The software Vorpatch and Compatch developed in this presentation are made available from http://cgal.inria.fr/abs/vorpatch-compatch/