Biomedical Engineering Reference
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Fig. 1.4 An example binary protein complex and its interface (PDB id: 1a2k). ( a )Thecomplexis
defined by two components: chains A and B, colored white , and chain C, colored grey .( b )Burial
of Solvent Accessible Surface in the complex (SAS, see definition in Sect. 1.2.3 ). The two
components have been separated, and each is rotated about its vertical axis so as to display the
binding patches. Amino acids are colored from blue to red in order of increasing burial in the
interface, evaluated as their SAS in the separated component minus the SAS in the complex. Blue
indicates zero buried area, corresponding to surface left free in the complex
a
b
Tile dual of pair ( a 1 ,w 1 ): AW interface
Tile dual of pair ( a 1 ,b 1 ): AB interface
a 1
partner A
d
w 1
w 2
b 1
partner B
Tile dual of pair ( b 1 ,w 1 ): BW interface
Fig. 1.5 Modeling interfaces of macro-molecular complexes. ( a ) The distance based definition,
which consists of selecting for a given atom all atoms of the partner within a distance threshold d ,
imposes a bias towards convex regions. ( b )The α -shape based definition consists of selecting pairs
of incident restrictions
together. Another important topological descriptor is the number of boundaries of
the AB interface, since all but the outer boundary correspond to water molecules
trapped in between the partners.
Geometry of the interface. From a geometric standpoint, a simple yet important
parameter of the interface is the surface area of the
and AW − BW interfaces,
defined as the sum of the areas of their constituting tiles. The surface area is a good
descriptor of the specificity of interactions [ 17 ]. Another important parameter is
the curvature of the ABW interface. Since the ABW interface is a cell complex
consisting of Voronoı tiles, its extrinsic , or mean, curvature, is directly encoded in
the dihedral angles defined by incident Voronoı facets—two incident Voronoı facets
define a hinge. From a biological standpoint, curvier interfaces indeed generally
AB
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