Program:TutorialOur PDB TutorialConnolly functionAtomic Density functionPDB
One of the most widely used descriptor functions is the Connolly function. For any point x ∈ M (the protein surface in our case), consider the ball Br (x) centered at x with radius r, and let Sr (x) = ∂ Br (x) be the boundary of Br (x), and SI the portion of Sr (x) contained inside the surface. The Connolly function fr : M → R (the real numbers) is defined as : fr (x) = Area(SI )/ r2.
Roughly speaking, the Connolly function can be considered as an analog of the mean curvature within a fixed size neighborhood of each point. A large
function value at x
∈ M means that the surface is concave around x, while
a small one means that it is convex. In particular, it has been shown that in
the limit (when r
→ 0), the critical points of the Connolly function converges
to a subset of those of the mean curvature.
The Connolly function ignores the exact details of the surface contained
in Br (x), as it considers only the intersection between M and Sr (x).
