Polypharmacology Polypharmacology (Drug selectivity) Gaussian ensemble screening (GES): A new Gaussian ensemble screening (GES): A new approach to approach to polypharmacology polypharmacology and virtual and virtual Multiple drugs bind to a given target A given drug binds to more than screening screening (promiscuous targets) one target (promiscuous ligands) Violeta I. Pérez-Nueno, Vishwesh Venkatraman, Lazaros Mavridis, David W. Ritchie Orpailleur Team, INRIA Nancy - Grand Est Promiscuous Ligand L i : Estrogen L j : Androgen D g i (x) g j (x) CM σ σ σ σ i σ σ σ σ j CM x-x j x-x i x i x j LORIA (Laboratoire Lorrain de Recherche en Informatique et ses Applications), Promiscuous Target ESCUELA TÉCNICA SUPERIOR INRIA Nancy – Grand Est, 615 rue du Jardin Botanique, 54506 Vandoeuvre-lès-Nancy, France 1/31 1 /31 2/31 2 2 /31 Previous work Our approach Relate receptors to each other quantitatively based on the Gaussian Ensemble Screening (GES): 3D spherical harmonic (SH) similarity in the: shape-based approach which compares molecular surfaces and predicts quantitatively the relationships between drug classes very fast and efficiently. !"# $% & ' (& )& *+, % ! - . /% & ' ( & )& *+, % !"# $% & ' (& )& *+, % - . /% & ' (& )& *+, % ! ! ! ! ! ! ! ! Sequence space Ligand space 0123 # 4% 2' *56+' & 7*% "89: +*, & 8' 8% ; <' *( 87 & 7 % !' ( & )& *+, % 0123 # 4% 2' *56+' & 7*% Binding pocket space ! "89: +*, & 8' 8% ; <' *(87 & 7 % !' (& ) & *+, % ! (chemical fingerprints) (pharmacophoric descriptors) ! ! ! ! •Keiser et al . Nature Biotechnol. 2007 , 25 , 197-206. Similarity Ensemble Approach (SEA) relates proteins based ! ! 15, )5=8>( 8? % 18>(5@ +7>+, & ' % 15, )5=8>( 8? % on the set-wise chemical similarity among their ligands. ! 18>(5@ +7>+, & ' % •Vidal & Mestres. Mol. Inf. 2010 , 29, 543. PHRAG, FPD, SHED molecular descriptors. ! ! •Weskamp et al. Proteins 2009 , 76 , 317-330. Similarity amongst binding pockets extracted by LIGSITE algorithm. ! ! ! •Milletti, F.; Vulpetti, A. J. Chem. Inf. Model., 2010 , 50 , 1418–143. Binding pocket comparison using four-point ! pharmacophoric descriptors based on GRID. B ! ! % 2' *& 5' A, +68' % ; *8, +& A% B ! ! ! ! % , 8A9=*57 8% ; *8, +& A% ! ! , 8A9=*578% 2' *& 5' A, +68' % ! 3/31 3 /31 4 4 4/31 /31 1
Methodology 1. Calculating spherical harmonic shapes Surface shapes are represented as radial distance expansions of the 1. Calculating SH consensus shapes and molecular surface with respect to the center of the molecule. center molecules • Real SHs: 2. Ligand set representations • Coefficients: • Encode radial distances 3. Gaussian ligand set comparisons from origin as SH series… C C M M • Solve coefficients by numerical integration… 4. Finding the best clustering threshold 5. Gaussian p-values p-value s 6. MDDR polypharmacology interaction matrix 7. Examples of strongly related targets Ritchie, D.W. and Kemp, G.J.L. J. Comp. Chem. 1999 , 20, 383–395. 5/31 5 /31 6/31 6 6 /31 2. Calculating SH consensus shapes and center molecules 3. Ligand set representations The idea is to represent a cluster of molecules as a Gaussian distribution with respect to a selected centre molecule (CM). - Calculate SH molecular surfaces of each ligand in each ligand set and superpose them. - Calculate the center molecule (CM) of the ligand set and the normalised SH distance (1-Similarity Score) between that of the CM and each cluster member. - Assuming that these distances follow a Gaussian distribution, each cluster may be represented as a probability density function g i (x) L i : Estrogen ( ) 2 g i (x) x − x i ) = 1 N L l 1 k y lm θ , ϕ ( ∑ ∑ ∑ ( ) r θ , ϕ a ( ) = 2 g i x 2 ⋅ e 2 σ i lm N 2 πσ i k = 1 l = 0 m =− l CM σ i σ σ σ σ : SD of the member distances “Consensus” shape x-x i x i Pérez-Nueno et al . J. Chem. Inf. Model. 2008 , 48 , 2146–2165. An illustration of a Gaussian ligand set cluster. 7/31 7 /31 8 8 8/31 /31 2
4. Gaussian ligand set comparisons 4. Gaussian ligand set comparisons By considering the SD of the member distances as the Gaussian width of a distribution, The similarity between drug classes can be calculated rapidly and reliably we calculate a “distance” ( D ) between two clusters, i and j , and normalizing the distance by calculating the Gaussian overlap between pairs of such clusters. term we can write it as a Hodgkin-like similarity score Sij between two distributions. Thus, it is straight-forward to calculate all-against-all cluster comparisons. It is worth +∞ 12 − a ⋅ b 32 ⋅ a ⋅ b noting that our cluster similarity score depends only on the similarity of pairs of centre ∫ ( ) ⋅ g j x ( ) dx ⋅ x ij 2 2 g i x 2 ⋅ e a + b a + b molecules and the SDs of their respective clusters. It does not depend on the number of a=1/2 σ i2 S ij = −∞ S ij = ( ) b=1/2 σ j2 +∞ 2 dx + +∞ 2 dx members of each cluster . ∫ ∫ 12 + b 12 g i x ( ) g j x ( ) a x ij : distance between the CMs of clusters i and j −∞ −∞ L i : Estrogen L j : Androgen L i : Estrogen L j : Thrombin D g i (x) g j (x) D g i (x) g j (x) σ σ i σ σ σ j σ σ σ σ σ σ σ j σ σ σ σ i CM CM CM CM x i x j x-x j x-x j x i x j x-x i x-x i S ij = 0.57 S ij = 1.33 ! 10 ″ 41 Illustration of the very small Gaussian overlap between Illustration of the large Gaussian overlap between the the estrogen and thrombin ligand sets. estrogen and androgen ligand sets. 9/31 9 /31 10 10 10/31 10 /31 4. Gaussian ligand set comparisons 4. Gaussian ligand set comparisons 1. MDDR ANNOTATION FAMILIES SPACE 2. MDDR ANNOTATION SHAPE CLUSTERS THERAPEUTIC ANNOTATION L 5 : δ δ opioid agonist L 1 C3 δ δ L 7 C1 L 1 C2 L 5 C1 L 267 C1 L 7 : Dopamine L 1 : Thrombin L 270 : Histamine D3 antagonist L 1 C1 L 267 C2 H3 antagonist CM C3 L 5 C2 CM C2 L 7 C2 L 2 : Estrogen L 2 C1 . . . . . . C M L 6 : 5HT2A C L 4 : Gaba α α subunit L 8 C1 α α L 8 : Cytocrome P450 1 L 6 C1 antagonist L 4 C1 L 8 : Muscarinic Oxidase Inhibitor L 6 C2 L 3 C1 L 3 : Androgen L 8 C1 L 8 C2 L 8 C3 M2 antagonist L 6 C3 L 6 C4 L 8 C4 L 8 C5 L 8 C6 ANNOTATION CLUSTER In order to eliminate outliers, we used the CAST clustering algorithm to cluster the We applied the approach to 270 specific therapeutic annotations in MDDR. Ligands which share an annotation define a set of functionally related molecules members of each annotation using their PARAFIT Tanimoto similarity scores. We which we call a “ligand set”. MDDR annotations are quite general and were then calculated the consensus shape and the center molecule for each cluster, and primarily derived from the patent literature. A given annotation may thus contain a we eliminated any cluster members beyond 1.5 standard deviations (SDs) from the corresponding CM. diverse set of compounds with a wide range of affinities. 11/31 11 11 11 /31 12 12 12/31 12 /31 3
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