Protein Engineering vol.7 no.l pp.39-46, 1994 Molecular surface recognition by a computer vision-based technique Raquel Norel 1 , Daniel Fischer 1 * 2 , Haim J.Wolfson 1 - 3 and Ruth Nussinov 2 ' 4 * 5 'Computer Science Department, School of Mathematical Sciences, 2 Saclder Institute of Molecular Medicine, Faculty of Medicine, Tel Aviv University, Tel Aviv 69978, Israel, 'Robotics Research Laboratory, Courant Institute of Mathematical Sciences, New York University, 715 Broadway, 12th Floor, New York, NY 10003 and 4 Laboratory of Mathematical Biology, PRI/Dynacorp, NCI-FCRF, Building 469, Room 151, Frederick, MD 21712, USA 'To whom correspondence should be addressed at NCI-FCRF Correct docking of a ligand onto a receptor surface is a complex problem, involving geometry and chemistry. Geometrically acceptable solutions require close contact between corresponding patches of surfaces of the receptor and of the ligand and no overlap between the van der Waals spheres of the remainder of the receptor and ligand atoms. In the quest for favorable chemical interactions, the next step involves minimization of the energy between the docked molecules. This work addresses the geometrical aspect of the problem. It is assumed that we have the atomic coordinates of each of the molecules. In principle, since optimally matching surfaces are sought, the entire conformational space needs to be considered. As the number of atoms residing on molecular surfaces can be several hundred, sampling of all rotations and translations of every patch of a surface of one molecule with respect to the other can reach immense propor- tions. The problem we are faced with here is reminiscent of object recognition problems in computer vision. Here we borrow and adapt the geometric hashing paradigm developed in computer vision to a central problem in molecular biology. Using an indexing approach based on a transformation invariant representation, the algorithm efficiently scans groups of surface dots (or atoms) and detects optimally matched surfaces. Potential solutions displaying receptor-ligand atomic overlaps are discarded. Our tech- nique has been applied successfully to seven cases involving docking of small molecules, where the structures of the receptor -ligand complexes are available in the crystallo- graphk database and to three cases where the receptors and ligands have been crystallized separately. In two of these three latter tests, the correct transformations have been obtained. Key words: computer vision-based technique/molecular surface recognition/receptor-ligand interaction Introduction The problem of receptor-ligand recognition and interaction has two major aspects: the first involves the 3-D geometrical fitting of the molecules and the second requires that the chemical interactions be optimized. Of these two aspects, the first is more fundamental: two atoms simply cannot be at the same spatial location. Geometrical fitting of the surfaces of two molecules is closely related to object recognition and assembly problems in computer vision and robotics. There one is frequently faced with questions such as the automatic assembly of fitting parts by a robot [a challenging application is an assembly of a jigsaw puzzles; Burdea and Wolfson (1989)], or the detection of a known part in a cluttered scene by fitting the surfaces of the known parts to the surface of the observed scene [for surveys, see Besl and Jain (1985) and Chin and Dyer (1986)]. Only a partial match can be required here, since the parts may partially occlude each other. The close analogy between the types of problems addressed, brought about this interdisciplinary research endeavor, developing and adapting techniques borrowed from the computer vision discipline (Lamdan and Wolfson, 1988, 1991; Larndan etal., 1988, 1990) and applying them to central problems in molecular biology (Nussinov and Wolfson, 1991; Fischer et al., 1992, 1993b, Bachar et al., 1993). Here, we further develop the technique and adapt and apply it to the problem of receptor-ligand recognition arid docking. The application of these computer-vision tools brought about a reduction in the complexity of the proposed algorithm compared to previously reported results (Kuntz et al., 1982; Connolly, 1986; Jiang and Kim 1991; Shoichet and Kuntz, 1991). Our worst case of complexity is of the order n 2 , where n is the number of surface atoms considered and in practice the results are even better. In addition, our algorithm allows simultaneous matching of many ligands to one receptor (or many receptors to one ligand) with only a sublinear increase in the time required. There have been several geometrically-based approaches to docking (Kuntz et al., 1982; Connolly, 1986; Jiang and Kim, 1991; Shoichet and Kuntz, 1991; Katchalski-Katzir et al., 1992; Shoichet et al., 1992). In a seminal and elegant work Kuntz and his colleageus introduced, more than 10 years ago (Kuntz et al., 1982), two basic concepts. First, they suggested a convenient way for representing the negative image of the receptor surface and the positive image of the ligand. The second concept involved matching of distances between the receptor negative image 'spheres' and the ligand positive image, either atoms or spheres. Other geometrical methods have placed the atoms of the molecules' surfaces on a regular 3-D grid and matched them by rotating and translating one of the grids, so that the best fit to the other molecules' grid is obtained (e.g. Jiang and Kim, 1991). The accuracy of these methods depends on the tesselation of the space and the number of orientations explored. A better accuracy, however, requires a significant increase in complexity. A faster, grid-based method which utilizes die fast Fourier transform has recently been suggested (Katchalski-Katzir et al., 1992). A major problem in docking is the representation of the molecular surface. Lee and Richards (1971) estimated the accessible molecular surface. For the docking problem Connolly's (1993,a,b) method, which is based on the Richards' (1977) definition, is often used. A water molecule is rolled over the van der Waals atomic surfaces. Narrow crevices are bridged and the molecular surface is described in terms of concave, convex and saddle regions. Most methods use the sampled dot representation of this surface with different densities. To improve the efficiency of the docking algorithms one may consider matching only small 39 at Columbia University Libraries on February 28, 2013 http://peds.oxfordjournals.org/ Downloaded from