Modeling Macromolecular Complexes: A Journey Across Scales - Modeling in Computational Biology and Biomedicine - page 18

1.2.4 Modeling Interfaces

Consider a binary complex involving three molecular species, say A and B for
the two partners, and W for the water molecules. As mentioned in Sect. 1.2.1.1 ,
a typical PDB entry lists the coordinates of the atoms making up these species. To
model a binary complex, one wishes to identify the interface atoms, including water
molecules that may be present between the two partners, and to describe the geom-
etry and the topology of the interface in a manner best accounting for biological
and biophysical properties. An interface model is therefore of phenomenological
nature, and the rest of this section presents our Voronoı based model [ 14 ], whose
implementation is available from http://cgal.inria.fr/abs/Intervor .

Interface atoms. Identifying interface atoms can be done resorting to a distance
threshold, typically in the range 4-7 A. But such a strategy tends to overcount atoms
in the inner regions of the interface, as seen from Fig. 1.5 a. A common alternative
consists of selecting as interface atoms those losing solvent accessibility in the
complex, as illustrated in Fig. 1.4 b. However, interface atoms will be missed if they
have zero solvent accessibility [ 16 ].
To avoid these drawbacks, we define a threshold-independent interface model
using the Voronoı diagram of the atoms of the three species A, B, W of the complex
in the SAS model. The construction is based on pairs of adjacent restrictions, which,
by the definition of the α -complex, correspond to edges in the α -complex of the SAS
model for α =0.
Let an interface water molecule be a water molecule whose restriction has
neighboring restrictions of type A and B . As opposed to bulk water molecules,
such molecules are exactly sandwiched between the partners. As illustrated on
Fig. 1.5 b, our Voronoı interface model involves the pairs of neighboring restrictions
of type [ A ; B ] or [ A ; W ] or [ B ; W ], with W interface water molecules. Note that
in addition to the two atoms in contact, each pair also defines the Voronoı facet,
also called tile , separating the Voronoı regions of these two atoms. Tiles of a given
type define the eponymous interface, namely the AB ( AW and BW ) interface
for tiles of type AB ( AW and BW ). Tiles AB define direct contacts between the
partners, while tiles AW and BW tiles define contacts between A and B mediated
by interface water molecules. Moreover, the union of tiles AW and BW defines the
AW − BW interface, and the union of the AW − BW and AB interfaces defines
the ABW interface. The latter separates the partners and gives a global overview of
the interaction area, regardless of the role played by water molecules. These notions
are illustrated on Fig. 1.6 , the role of water molecules being illustrated by Fig. 1.6 c.
A key property of this interface model is to precisely encode the geometry and the
topology of the interface.

Topology of the interface. The connectivity between the tiles allows one to define
the number of connected components or patches of the interface. Of particular
interest are the number of connected components of the AB interface, and if more
than one, the role of water molecules (possibly) sealing these connected components