Computational protocol: AlphaSpace: Fragment-Centric Topographical MappingTo Target Protein–Protein Interaction Interfaces

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[…] The central geometric construct employed by AlphaSpace is alpha sphere, a geometric feature derived from the Voronoi diagram of a set of points in three-dimensional space. The Voronoi diagram is a tessellation of the space containing the points into a set of Voronoi cells, or polyhedrons, formed from planes that bisect adjacent points from the set. The alpha sphere centers are defined at the vertices of this tessellation. Each alpha sphere center will be an intersection of six bisecting planes and equidistant to exactly four points from the set. The concept of applying Voronoi tessellation to protein structure was first introduced by Richards in 1974, along with the “weighted” Voronoi tessellation, a variation in the calculation to account for different atomic radii that was later implemented by Liang et al. in CAST. AlphaSpace employs the “classical” Voronoi tessellation, also used by fpocket, for which all atoms are treated as equivalent points. In this case, the alpha sphere makes contact with the centers of exactly four atoms but is otherwise empty of other atomic centers. Its radius is measured from alpha sphere center to atom center. Alpha spheres centered outside the protein surface mark concave surface regions and can be used to represent potential interaction space. A illustrates how a Voronoi diagram can be used to map the concave interaction space in a two-dimensional schematic model of shallow pockets in a surface.With AlphaSpace, we introduce two additional alpha sphere-related geometric features: alpha-atom and alpha-space (B,C). An alpha-atom shares a center with its associated alpha sphere but with a reduced radius set to 1.8 Å. An alpha-atom can be thought of as a theoretical ligand atom at a discrete interaction point, positioned to make approximate contact with the small region of protein surface associated with the set of four alpha sphere contact atoms. The alpha-space is the volume of the tetrahedron defined by the centers of the four alpha sphere contact atoms. Every alpha-atom has an associated alpha-space, the volume of which captures information about the relative positions of the four contact atoms, which is related to the structure of the surface region associated with these four atoms. The set of all alpha-spaces for a set of points is equivalent to its Delaunay triangulation, the dual graph of the Voronoi diagram.AlphaSpace fragment-centric topographical mapping (FCTM) is performed in two stages: pocket identification and pocket evaluation, as shown in . [...] Selected pockets from the first stage are quantitatively characterized in Stage 2 of AlphaSpace FCTM. The analysis includes Pocket ranking, Pocket-fragment complementarity, Pocket matching, and Pocket communities, as illustrated in . Pocket evaluation is facilitated by the alpha-atom and alpha-space features and provides a high-resolution map of underutilized and targetable pocket space at a PPI interface.We use alpha-space as a geometric feature related to the size and shape of a localized region of protein surface. The size of an individual alpha-space reflects the surface area and curvature of the small surface region associated with the set of four alpha sphere “contact” atoms (). While the set of alpha spheres in an alpha-cluster will overlap, the corresponding set of alpha-spaces will fit face-to-face to form a contiguous volume. This allows for the sum over all alpha-spaces within a pocket to serve as a single metric that approximates the surface area and curvature of the complete pocket. Figure S5 illustrates the geometric relationship between the alpha-atom and the alpha-space in the context of an alpha-cluster (the Trp92 pocket from Mdm2/p53).The alpha-atom construct can be used to calculate the alpha-cluster contact surface area (ACSA) for each individual pocket. When alpha spheres are clustered to define a pocket, the corresponding alpha-atoms form an overlapping alpha-cluster, the outline of which represents the approximate shape and size of that pocket’s complementary pseudofragment (). To calculate the atomistic ACSAs for an individual pocket, we use Naccess to calculate the atomistic accessible surface areas for the protein structure alone and then for the same protein in complex with that pocket’s single alpha-cluster. Subtracting the atomistic values associated with the alpha-cluster complex from the corresponding atomistic values associated with the protein alone will yield non-zero (and positive) values only for the set of atoms in direct contact with the alpha-cluster. These differences are taken as the atomistic surface areas associated with that individual pocket. The sum of these atomistic values provides the total ACSA for that pocket. […]

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