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Atom assignment onto 3D molecular graphs is a combinatoric problem in discrete space. If atoms are to be placed efficiently on molecular graphs produced in drug binding sites, the assignment must be optimized. An algorithm, based on simulated annealing, is presented for efficient optimization of fragment placement. Extensive tests of the method have been performed on five ligands taken from the Protein Data Bank. The algorithm is presented with the ligand graph and the electrostatic potential as input. Self placement of molecular fragments was monitored as an objective test. A hydrogen-bond option was also included, to enable the user to highlight specific needs. The algorithm performed well in the optimization, with successful replications. In some cases, a modification was necessary to reduce the tendency to give multiple halogenated structures. This optimization procedure should prove useful for automated de novo drug design.

If atom assignment onto 3D molecular graphs is to be optimized, an efficient scheme for placement must be developed. The strategy adopted in this paper is to analyze the molecular graphs in terms of cyclical and non-cyclical nodes; the latter are further divided into terminal and non-terminal nodes. Molecular fragments, from a fragments database, are described in a similar way. A canonical numbering scheme for the fragments and the local subgraph of the molecular graph enables fragments to be placed efficiently onto the molecular graph. Further optimization is achieved by placing similar fragments into bins using a hashing scheme based on the canonical numbering. The graph perception algorithm is illustrated in detail.

This paper considers some of the landscape problems encountered in matching molecules by simulated annealing. Although the method is in theory ergodic, the global minimum in the objective function is not always encountered. Factors inherent in the molecular data that lead the trajectory of the minimization away from its optimal route are analysed. Segments comprised of the C alpha atoms of dihydrofolate reductase are used as test data. The evolution of a reverse ordering landscape problem is examined in detail. Where such patterns in the data could lead to incorrect matches, the problem can in part be circumvented by assigning an initial random ordering to the molecules.

Three previous papers in this series have outlined an optimization method for atom assignment in drug design using fragment placement. In this paper the procedure is rigorously tested on a selection of five ligand-protein co-crystals. The algorithm is presented with the molecular graph of the ligand, and the electrostatic/hydrophobic potential of the site, with the aim of creating a placement on the molecular graph which is as electrostatically complementary or hydrophobically similar to the site as possible. Various designer options were tested, including, where appropriate, hydrogen bonding and a restricted number of halogens. In most cases, the placement obtained was at least as good as the native ligand, if not significantly better.

This paper extends an application of the method of simulated annealing for molecular matching so that the best common subsets of atom positions can be identified. Null correspondences are introduced into the difference distance matrix to enable poorly matched positions to be ignored in minimizing the objective function. The efficiency of the algorithm in finding correct subsets is rigorously tested.

This paper outlines an application of the theory of simulated annealing to molecular matching problems. Three cooling schedules are examined: linear, exponential and dynamic cooling. The objective function is the sum of the elements of the difference distance matrix between the two molecules generated by continual reordering of one molecule. Extensive tests of the algorithms have been performed on random coordinate data together with two related protein structures. Combinatorial problems, inherent in the assignment of atom correspondences, are effectively overcome by simulated annealing. The algorithms outlined here can readily optimize molecular matching problems with 150 atoms.