Using a staged multi-objective optimization approach to find selective pharmacophore models.

It is often difficult to differentiate effectively between related G-protein coupled receptors and their subtypes when doing ligand-based drug design. GALAHAD uses a multi-objective scoring system to generate multiple alignments involving alternative trade-offs between the conflicting desires to minimize internal strain while maximizing pharmacophoric and steric (pharmacomorphic) concordance between ligands. The various overlays obtained can be associated with different subtypes by examination, even when the ligands available do not discriminate completely between receptors and when no specificity information has been used to bias the alignment process. This makes GALAHAD a potentially powerful tool for identifying discriminating models, as is illustrated here using a set of dopaminergic agonists that vary in their D1 vs. D2 receptor selectivity.

Parameterization and conformational sampling effects in pharmacophore multiplet searching.

Pharmacophore patterns in ligands can be effectively characterized in terms of their constituent pharmacophore multiplets. Bitsets (fingerprints) encoding which particular multiplets are found in a given ligand have been and continue to be used as molecular descriptors in a range of molecular modeling applications, from ligand alignment and diversity analysis to pharmacophore-based flexible searching. Being able to create, store, and manipulate multiplets in compressed form - as bitmaps - has made it possible to integrate them into high-throughput technologies. A number of key parameters affect how well multiplets perform, including the granularity of edge length binning; how different multiplets are weighted in creating hypotheses from multiple ligands; and the number of bits that should be included in a pharmacophore hypothesis. The similarity metric employed for bitmap comparisons also affects search performance, as does the conformational sampling regime used for characterizing flexible molecules. In this report we explore the effect of parameter variation on within- and between-class similarity across seven different pharmacological classes and introduce a new measure of molecular similarity - the asymmetric stochastic cosine - uniquely suited to searching a database for matches to query hypotheses deduced from multiple ligands. Surprisingly, it turns out that the most discriminating bitmaps are obtained using relatively few conformers. The extreme discrimination power seen for single conformers, however, seems to reflect consistent effects of 2D connectivity on the 3D structure obtained. Conformational sampling by systematic search reinforces such circumstantial discrimination and should be avoided. The potential for systematic bias becomes clear when the behavior of otherwise similar conformational ensembles created by local energy minimization or by random sampling is considered. Consolidating information from multiple known actives or establishing single "bioactive" conformations a priori are safer ways to improve discrimination in pharmacophoric multiplet searching.

GALAHAD: 1. pharmacophore identification by hypermolecular alignment of ligands in 3D.

Alignment of multiple ligands based on shared pharmacophoric and pharmacosteric features is a long-recognized challenge in drug discovery and development. This is particularly true when the spatial overlap between structures is incomplete, in which case no good template molecule is likely to exist. Pair-wise rigid ligand alignment based on linear assignment (the LAMDA algorithm) has the potential to address this problem (Richmond et al. in J Mol Graph Model 23:199-209, 2004). Here we present the version of LAMDA embodied in the GALAHAD program, which carries out multi-way alignments by iterative construction of hypermolecules that retain the aggregate as well as the individual attributes of the ligands. We have also generalized the cost function from being purely atom-based to being one that operates on ionic, hydrogen bonding, hydrophobic and steric features. Finally, we have added the ability to generate useful partial-match 3D search queries from the hypermolecules obtained. By running frozen conformations through the GALAHAD program, one can utilize the extended version of LAMDA to generate pharmacophores and pharmacosteres that agree well with crystal structure alignments for a range of literature datasets, with minor adjustments of the default parameters generating even better models. Allowing for inclusion of partial match constraints in the queries yields pharmacophores that are consistently a superset of full-match pharmacophores identified in previous analyses, with the additional features representing points of potentially beneficial interaction with the target.

The effects of biasing torsional mutations in a conformational GA.

This paper describes the effects of incorporating torsional bias into a conformational Genetic Algorithm (GA) such as that found in the GASP program. Several major conclusions can be drawn. Biasing torsional angles toward values associated with local energy minima increases the rate of convergence of the fitness function (consisting of energy, steric, and pharmacophoric compatibility terms) for a set of molecules, but a definite tradeoff exists between total model energy and the steric and pharmacophoric compatibility terms in the fitness score. Biasing torsions in favor of sets of angles drawn from low-energy conformations does not guarantee low total energy, but biased torsional sampling does generally produce less strained models than does the uniform torsional sampling in classical GASP. Overall, torsionally biased sampling produces good models comprised of energetically favorable ligand conformations.

Efficient generation, storage, and manipulation of fully flexible pharmacophore multiplets and their use in 3-D similarity searching.

Pharmacophore triplets and quartets have been used by many groups in recent years, primarily as a tool for molecular diversity analysis. In most cases, slow processing speeds and the very large size of the bitsets generated have forced researchers to compromise in terms of how such multiplets were stored, manipulated, and compared, e.g., by using simple unions to represent multiplets for sets of molecules. Here we report using bitmaps in place of bitsets to reduce storage demands and to improve processing speed. Here, a bitset is taken to mean a fully enumerated string of zeros and ones, from which a compressed bitmap is obtained by replacing uniform blocks ("runs") of digits in the bitset with a pair of values identifying the content and length of the block (run-length encoding compression). High-resolution multiplets involving four features are enabled by using 64 bit executables to create and manipulate bitmaps, which "connect" to the 32 bit executables used for database access and feature identification via an extensible mark-up language (XML) data stream. The encoding system used supports simple pairs, triplets, and quartets; multiplets in which a privileged substructure is used as an anchor point; and augmented multiplets in which an additional vertex is added to represent a contingent feature such as a hydrogen bond extension point linked to a complementary feature (e.g., a donor or an acceptor atom) in a base pair or triplet. It can readily be extended to larger, more complex multiplets as well. Database searching is one particular potential application for this technology. Consensus bitmaps built up from active ligands identified in preliminary screening can be used to generate hypothesis bitmaps, a process which includes allowance for differential weighting to allow greater emphasis to be placed on bits arising from multiplets expected to be particularly discriminating. Such hypothesis bitmaps are shown to be useful queries for database searching, successfully retrieving active compounds across a range of structural classes from a corporate database. The current implementation allows multiconformer bitmaps to be obtained from pregenerated conformations or by random perturbation on-the-fly. The latter application involves random sampling of the full range of conformations not precluded by steric clashes, which limits the usefulness of classical fingerprint similarity measures. A new measure of similarity, The Stochastic Cosine, is introduced here to address this need. This new similarity measure uses the average number of bits common to independently drawn conformer sets to normalize the cosine coefficient. Its use frees the user from having to ensure strict comparability of starting conformations and having to use fixed torsional increments, thereby allowing fully flexible characterization of pharmacophoric patterns.