1 Methodology 1. Calculating spherical harmonic shapes Surface - - PDF document

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ESCUELA TÉCNICA SUPERIOR

Gaussian ensemble screening (GES): A new Gaussian ensemble screening (GES): A new approach to approach to polypharmacology polypharmacology and virtual and virtual screening screening

Violeta I. Pérez-Nueno, Vishwesh Venkatraman, Lazaros Mavridis, David W. Ritchie

Orpailleur Team, INRIA Nancy - Grand Est

LORIA (Laboratoire Lorrain de Recherche en Informatique et ses Applications), INRIA Nancy – Grand Est, 615 rue du Jardin Botanique, 54506 Vandoeuvre-lès-Nancy, France

D gi (x) gj (x) σ σ σ σi σ σ σ σj xi xj

CM CM

Lj : Androgen Li : Estrogen x-xi x-xj

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Polypharmacology

Polypharmacology (Drug selectivity)

Promiscuous Target Promiscuous Ligand

Multiple drugs bind to a given target (promiscuous targets) A given drug binds to more than

• ne target (promiscuous ligands)

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Previous work

Relate receptors to each

• ther

quantitatively based

• n

the similarity in the:

• Keiser et al. Nature Biotechnol. 2007, 25, 197-206. Similarity Ensemble Approach (SEA) relates proteins based
• n the set-wise chemical similarity among their ligands.
• 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. Sequence space Ligand space (chemical fingerprints) Binding pocket space (pharmacophoric descriptors)

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Our approach

Gaussian Ensemble Screening (GES): 3D spherical harmonic (SH) shape-based approach which compares molecular surfaces and predicts quantitatively the relationships between drug classes very fast and efficiently.

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• 1. Calculating

SH consensus shapes and center molecules

• 2. Ligand set representations
• 3. Gaussian ligand set comparisons
• 4. Finding the best clustering threshold
• 5. Gaussian p-values
• 6. MDDR polypharmacology interaction matrix
• 7. Examples of strongly related targets

Methodology

C M C M

s p-value

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• Real SHs:
• Coefficients:
• Encode radial distances

from origin as SH series…

• Solve coefficients by

numerical integration… Surface shapes are represented as radial distance expansions of the molecular surface with respect to the center of the molecule.

• 1. Calculating spherical harmonic shapes

Ritchie, D.W. and Kemp, G.J.L. J. Comp. Chem. 1999, 20, 383–395.

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• 2. Calculating SH consensus shapes and

center molecules

“Consensus” shape r θ,ϕ ( ) = 1 N a

lm k ylm θ,ϕ

( )

m=−l l

∑

l=0 L

∑

k=1 N

∑

Pérez-Nueno et al. J. Chem. Inf. Model. 2008, 48, 2146–2165.

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x-xi

CM

Li : Estrogen

gi x

( ) =

1 2πσ i

2 ⋅e x−xi ( )

2

2σi

2

An illustration of a Gaussian ligand set cluster. σ σ σ σi xi gi (x)

• 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 gi(x) σ : SD of the member distances

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By considering the SD of the member distances as the Gaussian width of a distribution, we calculate a “distance” (D) between two clusters, i and j, and normalizing the distance term we can write it as a Hodgkin-like similarity score Sij between two distributions.

CM CM

D Lj : Thrombin Li : Estrogen σ σ σ σi xi σ σ σ σj xj gj (x) gi (x)

S

ij =1.33! 10″ 41 x-xi x-xj

Illustration of the very small Gaussian overlap between the estrogen and thrombin ligand sets.

• 4. Gaussian ligand set comparisons

S

ij =

2 g

i x

( )⋅ gj x ( )dx

−∞ +∞

∫

g

i x

( )

2 dx+

gj x ( )

2 dx −∞ +∞

∫

−∞ +∞

∫

S

ij =

2

32 ⋅ a⋅b

a+b      

12

⋅e

− a⋅b a+b      ⋅xij

2

a

12 + b 12

( )

a=1/2σi2 b=1/2σj2 xij: distance between the CMs of clusters i and j

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CM CM

Lj : Androgen Li : Estrogen x-xi x-xj D gi (x) gj (x) σ σ σ σi σ σ σ σj xi xj

S

ij = 0.57

Illustration of the large Gaussian overlap between the estrogen and androgen ligand sets.

The similarity between drug classes can be calculated rapidly and reliably by calculating the Gaussian overlap between pairs of such clusters.

Thus, it is straight-forward to calculate all-against-all cluster comparisons. It is worth noting that our cluster similarity score depends only on the similarity of pairs of centre molecules and the SDs of their respective clusters. It does not depend on the number of members of each cluster .

• 4. Gaussian ligand set comparisons

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• 1. MDDR ANNOTATION FAMILIES SPACE

L2 : Estrogen L1 : Thrombin L3 : Androgen L4 : Gaba α α α α subunit L5 : δ δ δ δ opioid agonist L6 : 5HT2A antagonist L7 : Dopamine D3 antagonist L8: Muscarinic M2 antagonist L270: Histamine H3 antagonist L8: Cytocrome P450 Oxidase Inhibitor

. . .

THERAPEUTIC ANNOTATION We applied the approach to 270 specific therapeutic annotations in MDDR. Ligands which share an annotation define a set of functionally related molecules which we call a “ligand set”. MDDR annotations are quite general and were primarily derived from the patent literature. A given annotation may thus contain a diverse set of compounds with a wide range of affinities.

• 4. Gaussian ligand set comparisons

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• 2. MDDR ANNOTATION SHAPE CLUSTERS

L3 C1 L4 C1 L5 C1 L6 C1 L7 C1 L8 C1 L8 C2 L8 C3 L267 C1 L8 C1

. . .

ANNOTATION CLUSTER In order to eliminate outliers, we used the CAST clustering algorithm to cluster the members of each annotation using their PARAFIT Tanimoto similarity scores. We then calculated the consensus shape and the center molecule for each cluster, and we eliminated any cluster members beyond 1.5 standard deviations (SDs) from the corresponding CM.

L8 C4 L8 C5 L8 C6 L6 C2 L6 C3 L6 C4 L5 C2 L7 C2 L267 C2

• 4. Gaussian ligand set comparisons

L2 C1 L1 C1 L1 C2 L1 C3

C M

C 1

CM C2 CM C3

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4

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• 2. MDDR ANNOTATION SHAPE CLUSTERS

L2 C1 L1 C1 L3 C1 L4 C1 L5 C1 L6 C1 L7 C1 L8 C1 L8 C2 L8 C3 L267 C1 L8 C1

. . .

ANNOTATION CLUSTER

L1 C2

We clustered each annotation according to Parafit Shape Tanimoto using different similarity thresholds: 0.6, 0.65, 0.675, 0.7, 0.8, 0.85.

L1 C1 A L1 C1 B L1 C3 L8 C4 L8 C5 L8 C6 L6 C2 L6 C3 L6 C4 L5 C2 L7 C2 L267 C2

Each ligand set was randomly split into two almost equally sub-clusters, and all- vs- all clustering was performed with the aim of split and reassemble the split clusters correctly.

• 5. Finding the best clustering threshold

CM C1 B CM C1 A CM C2 A CM C2 B CM C3 A CM C3 B

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L2 C1 (Estrogen) L1 C1 (Thrombin) L3 C1 (Androgen)

L1 C1 B L1 C1 A L2 C1 B L2 C1 A L3 C1 B L3 C1 A

x-xi

I.e. here are shown the C1 of different annotations split in two groups to obtain the distribution of scores for the true cases, where annotations are related to each other (L1 C1 A vs L1 C1 B , L2 C1 A vs L2 C1 B ...) , and the false cases, where the annotations are not related (L1 C1 A vs L2 C1 A, L1 C1 A vs L3 C1 A ...). CM C1 A CM C1 B

x-xj

CMC1 B

x-xi

CM C1 A

x-xj L4 C1 (Gaba a subunit)

L4 C1 B L4 C1 A

. . .

CM C1 B

x-xj

X-Xi

x-xi x-xj

CM C1 A CM C1 B CM C1

A

3. SPLIT ANNOTATION SHAPE CLUSTERS + GAUSSIAN SCORING

• 5. Finding the best clustering threshold

If we can split and reassemble clusters of molecules that we know they are related, then we can identify interesting relationships between clusters of molecules that we don’t know they are related

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L1 C1 A L1 C1 B L1 C2 A L1 C2 B L1 C3 A L1 C3 B

. . .

L1 C1 A L1 C1 B L1 C2 A L1 C2 B L1 C3 A L1 C3 B SC1A ,C1B TRUE REST SC1A, C2A SC1A ,C2B SC1A ,C3A SC1A ,C3B SC1B ,C1A SC1B, C2A SC1B, C2B SC1B, C3A SC1B, C3B SC2A, C1A SC2A ,C1B SC2A, C2B SC2A, C2B SC2A, C3B L2 C1 A L2 C1 B L2 C1 A L2 C1 B

We produce a matrix of Gaussian Overlap Scores for true target classes (members

• f the same annotation cluster) and the rest (members supposed not to be related).

L3 C1 A L3 C1 A L3 C1 B

. . . C M

C 1 A

C M

C 1 B

• 4. GAUSSIAN SCORES ALL VS ALL

RANK & ROC

. . .

L3 C1 B

SCORE LIGAND SET 1 LIGAND SET 2 SL1C1A ,L1C1B 0.999 L1 C1 A L1 C1 B T 1 SL1C2A , L1C2B 0.998 L1 C2 A L1 C2 B T 1 SL2C1A ,L3C1A 0.854 L2 C1 A L3 C1 A F SL1C1B ,L4C1B 0.153 L1 C1 B L4 C1 B F

• 5. Finding the best clustering threshold

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ROC curves obtained for the range of similarity thresholds of 0.6, 0.65, 0.675, 0.7, 0.8, 0.85. Using a PARAFIT shape Tanimoto value of 0.65 gave the best early performance AUC(5%,10%). Hence, 0.65 was chosen as the appropriate for shape-based clustering. .

Threshold FPR 0.0 0.2 0.4 0.6 0.8 1.0

0.6 0.65 0.675 0.7 0.8 0.85 RANDOM

• 5. Finding the best clustering threshold

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In order to transform a list of cluster similarity scores into a more meaningful list of probabilities, a statistical model was developed.

Each Gaussian similarity score was transformed into a probability value, or “p-value”, from the observed distribution of scores. For a Gaussian distribution, it can be shown that the probability of finding at random from the distribution some value X greater than a given value x is given by: where f(t) is the standard normalized Gaussian probability density function and erfc(x) is the complementary error function. For a normalized distribution of scores, we obtain p (S > s)

A “p-value” for a given score, s, is the probability of finding at random from the distribution some other score, S, which is greater than s.

p X > x

( ) =

f t

( )dt = erfc x ( )

x ∞

∫

p S> s

( ) = erfc

S 2σ 2      

Very un-likely

• bservations

s p-value Very un-likely

• bservations

Most likely observations

Probability Observed scores

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We used the R package to fit the distribution of all pair-wise Gaussian

• verlap scores to a

Gaussian function with σ σ σ σ=0.05274 A p-value was calculated analytically from the scores distribution for any given pair-wise score using the erfc(x)

• 6. Gaussian p-values

In our real data we can see that all the false pairs appear at the beginning and after the score of the true pairs. We are looking at the really top end of the distribution which tell us how statistically significant is the result

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• 7. MDDR polypharmacology interaction matrix

MDDR polypharmacology interaction matrix for the top 50 ligand set relationships found from the all against all comparison of the 270 MDDR specific annotations

p ≤ 5× × × ×10-60 5× × × ×10-60 < p ≤ 5× × × ×10-50 5× × × ×10-50 < p ≤ 5× × × ×10-40 5× × × ×10-40 < p ≤ 5× × × ×10-30 5× × × ×10-30 < p-value ≤ 5× × × ×10-20 5× × × ×10-20 < p ≤ 5× × × ×10-10 p > 5× × × ×10-10 No score for a ligand set and itself

19 19/31 /31 19 19 A subset of the MDDR interaction matrix involving several nuclear hormone receptors. Antiglucocorticoids and progesterone antagonists are identified as promiscuous (orange).

• 8. Nuclear hormone receptors

20 20/31 /31 20 20 A subset of the MDDR interaction matrix involving several serine proteases. Coagulation factors Xa and VIIa inhibitors are identified as promiscuous, as well as trypsin inhibitors (orange).

• 8. Serine proteases

SLIDE 6

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21 21/31 /31 21 21 A subset of the MDDR interaction matrix involving several enzyme inhibitors. Acetylcholinesterase inhibitors and Tyrosine Specific protein kinase inhibitors are identified as promiscuous (orange).

• 8. Enzyme inhibitors

22 22/31 /31 22 22 5HT2A and 5HT2C antagonists, and dopamine D2 agonists and antagonists are identified as promiscuous GPCRs (orange).

• 8. GPCRs

23 23/31 /31 23 23 A subset of the MDDR interaction matrix involving several ion channels. GABA A/Benzodiazepine receptor complex are identified as promiscuous (orange).

• 8. Ions channels

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Examples of SH shape superpositions

• f the CMs of some of the strongly

related targets found in the selected MDDR subset.

• 8. Examples of strongly related targets

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Overall, we find interesting relationships between targets such as GABA A and tyrosine-specific protein kinase, ACE and neutral endopeptidase, thromboxane antagonist and thromboxane synthetase inhibitor, dopamine reuptake inhibitor and norepinephrine uptake inhibitor, ie, whose dual inhibitors have been experimentally confirmed. GES also detects

• ther

relationships previously predicted by SEA and subsequently confirmed in vitro by Keiser et al. such as serotonin reuptake inhibitors acting also as β-blockers, 5 HT re- uptake inhibitors and adrenergic β- blockers.

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• We have presented a new 3D shape-based approach for predicting

and quantifying drug promiscuity by correlating Gaussian clusters

• f ligand SH shapes.
• The method has been validated using drug ligand sets of the

MDDR and has been demonstrated to be effective in identifying drug families which are known to have related MDDR activity classes.

• Our results show that GES provides an efficient way to measure

the similarity between clusters of arbitrary numbers of members.

• The examples shown in this study demonstrate that GES is a

useful way to study polypharmacology relationships, and it could provide a novel way to propose new targets for drug repositioning.

Conclusions

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Acknowledgements

• INRIA Nancy - Grand Est

ParaSurf + ParaFit: http://www.ceposinsilico.de/ Papers: http://www.loria.fr/~pereznue/ http://www.loria.fr/~ritchied/

• FP7 Marie Curie IEF Fellowship (DOVSA 254128)

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Thank you!

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Comparison with SEA approach

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a p-value < 10-80; b E-value < 10-320