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

Summary

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.

Appendix: Assigning features to partial match sets

Suppose that clusters of query features have been sorted in decreasing order of how many features they contain—i.e., of how many of the n ligands in a hypermolecule they “hit.” Suppose further that one wishes to distribute the features in such a way that features hitting the same number of ligands fall under the same partial match constraint. Then the feature centroids q _i representing the clusters i = 1,2,... can be allocated among partial match constraints in the query by applying the following method:

• 1. Let k(q _i) be the number features in the cluster represented by q _i—i.e., the number of ligands that hit query feature q _i;

• 2. Drop any q _i for which k(q _i) < t _min, where t _min is the minimum number of ligands that each query feature must “hit.”

• 3. Initialize the partial match sets q ₂ and q ₁as empty sets;

• 4. If the number of features |q _i| < 5, set q ₁ = {q _i} and go to Step 15;

• 5. Set t = max(k(q _i));

• 6. If k(q _i) = t, add q _i to q ₁;

• 7. Set t = t − 1;

• 8. If t < min(t _min, 0.75n), go to step 15;

• 9. If the cardinality |q ₁| < 3 and some features q _i have not been assigned, go to step 6:

• 10. If k(q _i) = t, add q _i to q ₂;

• 11. Set t = t − 1;

• 12. If t < t _min, go to step 14;

• 13. If |q ₁ | + |q ₂| < 8, go to step 10;

• 14. If |q ₂| = 1 and |q ₁| = 3, set q ₁ = q ₁ ∪ q ₂ and set q ₂ equal to the empty set;

• 15. If |q ₁| ≤ 3, mark all q _i in q ₁ as required matches and go to step 18;

• 16. if |q ₁| = 4:

  • a. If k(q _i) = n for any q _i in q ₁, mark all q _i in q ₁ as required matches and go to step 18; else

  • b. Set the minimum partial match for q ₁ (min ₁) to 3 and go to step 18;

• 17. If |q ₁| > 4, set min ₁ = 4;

• 18. Set min ₂ as follows:

  • a. min ₂ = 0 if |q ₂| = 1;

  • b. min ₂ = 1 if |q ₂| = 2;

  • c. min ₂ = 2 if |q ₂| = 3;

  • d. min ₂ = 5 − min ₁ or to 2, whichever is greater, if |q ₂| > 3.