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.