B B Goldman | PubMed Health

PubMed2000

QSD quadratic shape descriptors. 2. Molecular docking using quadratic shape descriptors (QSDock).

We present a new shape-based polynomial time algorithm for the rapid docking of rigid ligands into their macromolecular receptors. The method exploits molecular surface complementarity existing between a putative ligand and its receptor protein. Molecular shapes are represented by using a new shape descriptor that is based on local quadratic approximations to the molecular surface. The quadratic shape descriptor is capable of representing a plethora of molecular shapes and is not limited to describing convex or concave regions of molecular surface. A single pair of complementary descriptors is sufficient for computing the transformation matrix that positions a ligand into the receptor site. We demonstrate the capabilities of our algorithm by successfully reproducing the crystallographically determined orientation for a test set of 20 ligand-protein complexes.

Algorithms↗

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Quadratic shape descriptors. 1. Rapid superposition of dissimilar molecules using geometrically invariant surface descriptors.

In this paper, we present a novel approach to shape-based molecular similarity searching. The method that we introduce is able to superimpose dissimilar molecules by using geometrically invariant molecular surface descriptors. The shape descriptors are calculated by least-squares fitting of a quadratic function to small sections of the molecular surface of a ligand. Invariant geometric properties of the approximated surface patch are then extracted from the fitted quadratic function. The extracted properties are used to quantify the shape and to obtain a canonical orientation for this section of surface. The superimposition algorithm uses these geometric invariants to recognize similar regions of surface shape existing on two molecules and to bring these regions (and consequently the molecules) into registration. Because these geometric descriptors are based upon local surface shape, the superimposing algorithm is insensitive to the connectivity and the relative sizes of the molecules being matched. The capabilities of our algorithm are demonstrated by superimposing dissimilar ligands known to inhibit the same enzyme system. In all cases examined the algorithm generates superpositions that are in agreement with crystallographic results. The algorithm is also applied to align the two different proteins on the basis of the shape of their active sites.

Models, Molecular↗