Modeling Macromolecular Complexes: A Journey Across Scales - Modeling in Computational Biology and Biomedicine - page 20

Fig. 1.6 The Voronoı interface of complex PDB 2dqa, the color code of Voronoı facets being
the Shelling Order defined in Sect. 1.2.5 .( a ) The two polypeptide chains and the interface atoms
( b ) Top view of the ABW interface ( c )The AB interface and the solvent molecules involved in
the AW − BW interface. ( d )The AW − BW interface and the solvent molecules

correspond to specific interactions—the more curved a surface the more difficult it
is to find a complementary surface.

1.2.5 On the Morphology of Binding Patches and Interfaces

We have so far provided geometric and topological descriptors of interfaces, but
these hardly answer the question of describing the global morphology of the
interface: is the interface isotropic, or does it have a more complex geometry, like a
dumbbell?
Given a Voronoı interface, let us define the binding patch of a partner as the
collection of its interface atoms. In the following, we present a strategy to define
the morphology of interfaces and binding patches. In a nutshell, the idea consists
of partitioning the object of interest (Voronoı interface or binding patch) into

concentric shells.

Shelling order. The ABW Voronoı interface consists of Voronoı tiles. Some of
them are clearly outer tiles as they bound the whole interface, while others are
located in the center, a distinction known as the rim-core model in molecular
modeling [ 18 ]. However, this boolean model does not convey the fact that describing
the position of a tile within the interface is a gradual process. This observation
motivates the definition of the Shelling Order (SO), which we present in abstract
terms as it actually applies to cell complexes in general, and to the Voronoı interface
as well as binding patches in particular.
Consider a cell complex

consisting of d -dimensional cells incident across
( d− 1)-dimensional cells. For the ABW Voronoı interface, the cells are the Voronoı
tiles, and two incident tiles share a Voronoı edge. For the SAS surface, possibly
restricted to a binding patch, the cells are spherical caps of the boundary of the
union, and two such cells share a circle arc. Note that cells and their incidence define
agraph G whose nodes are the cells, and edges correspond to incidences between
cells.

C