A combinatorial algorithm for calculating ligand binding

We consider the problem of predicting the mode of binding of a small molecule to a receptor site on a protein. One plausible approach, given a rigid molecule and its geometry, is to search directly for the orientation in space that maximizes the degree of contact. The computation time required for such a naive procedure is proportional to n3m3, where n is the number of points in the site where binding can occur, and m is the number of atoms in the ligand. We give an alternative, combinatorial approach, in which only “contact–no‐contact” criteria are considered. We relate this problem to the well‐known combinatorial problem of finding cliques in a graph and show that we can use a solution to the clique problem not only to solve our original problem, but also the problem of avoiding energetically unfavorable matches. Our experience with this method indicates that the computation time required is proportional to nm2.8, with a lower constant of proportionality than that of the naive procedure.