Pharmacophores in Chemoinformatics 1 Pharmacophore Patterns Topological Fingerprints

Pharmacophores in Chemoinformatics: 1. Pharmacophore Patterns & Topological Fingerprints Dragos Horvath Laboratoire d’Info. Chimie UMR 7177 CNRS – Université de Strasbourg horvath@chimie. u-strasbg. fr

The Pharmacophore Way of Life – A Medicinal Chemist’s Dream • (Bio)Molecular Recognition is based on ligand-site interactions of extremely complicated nature – Understanding them requires a solid knowledge of statistical physics and, therefore, of higher maths… – But medicinal chemists hate maths… so they developed a simplified rule set to rationalize ligand binding. • Functional groups of similar physicochemical behavior represent pharmacophore types: – Hydrophobic, Aromatic, Hydrogen Bond (HB) donors, Cations, HB Acceptors, Anions. – Now, we just need to know how each of the six types interacts with the site… welcome to the “pharmacophore” paradigm, farewell higher maths (for the moment, at least)

The Interaction Saga: (1) van der Waals Interactions • Atoms are more or less hard spheres – squeezing them against each other causes a sharp rise in energy: – Erep=Aijd-12 • At distances larger than the sum of their « van der Waals spheres » , an attractive term due to dipole-induced dipole interactions (London dispersion term) is predominant… – Eatt= - Bijd-6

The Interaction Saga: (2) Electrostatics & Solvation • Coulomb charge-charge interactions are easy to compute, once the partial charges Qk are assigned on the atoms… – ECoul=Qi. Qj/4 ped • … and the solvent molecules are explicitly modeled – accountig for all the possible solvation shell structures, in order to estimate a solvation free energy. • Alternatively, a continuum solvent model may be employed.

The Interaction Saga: (2 bis) The Hydrophobic Effect • The mysterious force that separates grease and water is not due to grease-grease van der Waals interactions being stronger than grease-water attraction! • It is not of electrostatic nature either, because greasy alkyl chains have no charges! • Actually, it’s not a force at all, but the consequence of the drift towards a more probable state of matter (? !) • For practical purposes, however, it makes sense to believe that hydrophobes « attract » each other – for making hydrophobic contacts significantly improves binding affinity!

Physical Chemistry For Dummies: The Rules • Hydrophobes make favorable contacts with other hydrophobes (we do not want to know why!). Assume strenght proportional to the buried hydrophobic area. • Hydrophobes in close contact to polar groups cause frustration, for they chase away the water molecules favorably solvating the latter and offer no substitute interactions • Hydrogen bond donors seek to pair with acceptors, so that they may reestablish the water hydrogen bonds they lost • Cations seek to pair with anions and avoid hydrophobes. • Shape is of paramount importance: groups of a same kind may replace each other if they are shaped likely

Bio. Iso. Steres – Equivalent Functional Groups • Wikipedia: bioisosteres are substituents or groups with similar physical or chemical properties that impart similar biological properties to a chemical compound

Pharmacophore Patterns • The pharmacophore pattern of a molecule characterizes the relative arrangement of all its pharmacophore types – What pharmacophore types are represented? – How are they arranged (spatially, topologically) with respect to each other ? – How can these aspects be captured numerically to yield molecular descriptors of the pharmacophore pattern? • Note: Pharmacophore patterns are essentially 3 D. Since geometry is determined by connectivity, 2 D “pharmacophore patterns” also make sense!

Exploiting pharmacophore patterns… • N-dimensional vector D(M)=[D 1(M), D 2(M), …, DN(M)]; each Di encodes an element of the pharmacophore pattern – Allows meaningful quantitative definitions of molecular similarity: • Neighborhood Behavior: Similar molecules - characterized by covariant vectors - are likely to display similar biological properties • As chemists do not easily perceive the pharmacophore pattern, such covariance may reveal hidden but real molecular relatedness… – May serve as starting point for searching a binding pharmacophore – the subset of features that really participate in binding to a receptor • Machine learning to select those elements Di that are systematically present in actives, but not in inactives of a molecular learning set!

Some examples of "hidden similarity"

Tricentric Pharmacophore Fingerprints: monitoring feature arrangement • Topological: the distance between two features equals the (minimal) number of chemical bonds between them Cl O N 9 N N 11 4 • Spatial: if stable conformers are known, use the distance in Ǻ between two features

Example: Binary Pharmacophore Triplets Basis Triplets: • all possible feature combinations • at a given series of distances… 3 3 4 3 5 4 0 … … 1 4 3 7 … … 6 … C 6 -P r 4 7 - A Hp … 0 ? … r 5 -A A 5 4 -H Hp … … … 0 5 5 … r 5 -A A 5 3 -H Hp … 0 3 5 4 … p 5 -H p 3 4 -H p 4 Ar -H p 3 4 -H Ar … p 5 -H p 3 3 -H Hp p 4 -H p 3 3 -H p 3 Hp -H p 3 3 -H Hp 0 5 … 0 Pickett, Mason & Mc. Lay, J. Chem. Inf. Comp. Sci. 36: 1214 -1223 (1996) … … 0 …

First key improvement: Fuzzy mapping of atom triplets onto basis triplets in 2 D-FPT 3 3 4 4 … +3 … … … Di(m) = total occupancy of basis triplet i in molecule m. … C 6 -P r 4 7 - A Hp … … +6 … … … 0 7 6 … r 5 -A A 5 4 -H Hp 0 … … 4 5 … r 5 -A A 5 3 -H Hp 0 … p 5 -H p 3 4 -H p 4 Ar -H p 3 4 -H Ar 0 5 3 5 4 … p 5 -H p 3 3 -H Hp p 4 -H p 3 3 -H p 3 Hp -H p 3 3 -H Hp 0 5 … 0 …

Combinatorial enumeration of basis triplets • Example: there are 36796 basis triplets, verifying triangle inequalities, when considering 6 pharmacophore types and 11 edge lenghts between Emin=3 to Emax=13 with an increment of Estep=1: (3, 4, 5, … 13) – Canonical representation: T 1 d 23 -T 2 d 13 -T 3 d 12 with T 3≥T 2≥T 1 (alphabetically). Hp 7 -Ar 4 -PC 6 4 7 Ar 4 -Hp 7 -PC 6 6 – Out of two corners of a same type, priority is given to the one opposed to the shorter edge. Ar 4 -Hp 7 -Hp 6 4 7 6 Ar 5 -Hp 6 -Hp 7

Triplet matching procedure • The triplet matching score represents the optimal degree of pharmacophore field overlap: – if corner k of the triplet is of pharmacophore type T, e. g. F(k, T)=1, then it contributes to the total pharmacophore field of type T, observed at a point P of the plane: Horvath, D. Com. Pharm pp. 395 -439; in "QSPR /QSAR Studies by Molecular Descriptors", Diudea, M. , Editor, Nova Science Publishers, Inc. , New York, 2001

Control parameters for triplet enumeration & matching in two 2 D-FPT versions.

Second key improvement: Proteolytic equilibrium dependence of 2 D-FPT 88% Ar 8 NC 8 PC 8 12% Ar 5 NC 5 PC 8 ?

Some ‘activity cliffs’ in rule-based descriptor space are smoothed out in 2 D-FPT-space • N • 7 eutr 0% al Ca tio n • N • 4 eutr 0% al Ca tio n al r t u l • Ne utra • Ne tral • Neu Cation • 50% al r t u • Ne ion • An tral • Neu Cation • 90% tral • Neu n io • Cat al r t u • Ne ion • An

Pharmacophore Pattern-Based Similarity Queries: Lead Hopping! Pharmacophore Hypothesis Nearest Neighbors Reference Fingerprint ? Superposition-based Similarity Scoring Automated Fingerprint Matching. . . Potential Pharmacophore Fingerprint Library Best Matching Candidates Docking

Some examples of "hidden similarity"

Successful Virtual Screening Simulations D 2 TK

Successful QSAR model construction with 2 DFPT: predicting c-Met TK activity 25 variables entering nonlinear model 153 molecules for training: RMSE=0. 4 (log units), R 2=0. 82 40 molecules for validation: RMSE=0. 8 (log units), R 2=0. 53 8 validation molecules out of 40 mispredicted by more than 1 log

What more could be done? • 3 D FPT version under study – does it pay off to generate conformers? How many would you need to get better results than with 2 D-FPT? What’s the best conformational sampler to use? • Accessibility-weighted fingerprints? – class to return (topological and/or 3 D) estimate of the solventaccessible fraction of an atom? • Tautomer-dependent fingerprints? – if tautomers and their percentage were enumerated like any other microspecies…

THE END

Pharmacophore Hypotheses (A): From individual Active Leads: 2 D/3 D • ALL features in the Lead assumed relevant for binding (B): Consensus hypotheses from set of Leads: 2 D/3 D • Ignore features that can be deleted without losing activity (C): Site-Ligand interaction models: 3 D* • Select Ligand features shown to interact with the site in the 3 D X-ray structure of the site-ligand complex. (D): Active Site filling models: 3 D* • Design a pharmacophoric feature distribution complementary to the groups available in the active site * In these cases, docking may be performed starting from pharmacophore –based overlays

Com. Pharm Overlay… - chosen conformer of the reference - chosen conformer of the candidate - pair of matching atoms - 3 Euler angles - mirroring toggle GA-controlled overlay optimization

Reference Atoms Com. Pharmacophoric Fields 1 Pharmacophoric Features Alk. Aro. HBA HDB (+) (-) X 11 X 12 X 13 X 14 X 15 X 16 2 X 21 X 22 X 23 X 24 X 25 X 26 3 X 31 X 32 X 33 X 34 X 35 X 36 4 X 41 X 42 X 43 X 44 X 45 X 46 5 X 51 X 52 X 53 X 54 X 55 X 56 • A descriptor of the nature of the molecule’s pharmacophoric neighborhood “seen” by every reference atom, assuming an optimal overlay of the molecule on the reference. . .