characterization of chemical libraries using scaffolds and network models

Characteriza*on of Chemical Libraries Using Scaffolds and

Network Models

Dac-‐Trung Nguyen, Rajarshi Guha NIH NCATS

ACS Na:onal Mee:ng, Boston 2015

Outline

OR

Mo*va*ons

•  Library comparison usually driven by a need to construct or expand a library – OLen with constraints on resources

•  Two classes of features to consider – Compound-‐centric (physchem proper:es, bioac:vity, target preferences)

– Library-‐centric (diversity, chemical space coverage) •  Library comparisons generally reduce to – Distribu:ons of compound features (univariate) – Overlap in some chemical space (mul:variate)

Comparing Libraries

•  Most comparisons employ a reduced (numerical) representa:on of the structure – Fingerprints, BCUTs, physicochemical descriptors

•  Perform comparisons in the new space – PCA, SOM, MDS, GTM, …

Schamberger et al, DDT, 2011, 16, 636-‐641; Kireeva et al, Mol. Inf., 2012, 31, 301-‐312

Scaffolds & Networks

•  Scaffolds represent a chemically meaningful reduced representa:on of the structures

•  Can be challenging to define what a (good) scaffold is

•  A network representa:on of the collec:on of structures allows for novel ways to perform library comparisons – How fine grained can such comparisons be?

Scaffold Network Representa*ons

•  Scaffolds are generated by exhaus:ve enumera:on of SSSR

•  Scaffolds are nodes, connected by directed edges •  Nodes are labeled by a hash key of the scaffold

4 compounds 1912 compounds

Scaffold Network Construc*on

•  A scaffold network is a directed graph •  Edges denote sub/super-‐structure rela:onships between scaffolds

•  Each node in the network represents a unique scaffold

•  Singletons are acyclic molecules

Datasets CL1420, 31320 compounds

CL886, 3552 compounds

MIPE, 1920 compounds

Natural Products, 5000 compounds Mathews and Guha et al, PNAS, 2014, 111, 11365; Singh et al, JCIM, 2009, 49, 1010

LOPAC, 1280 compounds

1079 nodes, 115287 edges 69 trees


Approved, inves:ga:onal drugs, constructed for func:onal diversity Diverse library, designed for enrichment of bioac:vity




•  The overall structure of the complete network can characterize the library

•  But distribu:ons of vertex-‐level network metrics may be informa:ve

•  We can also consider approaches to iden:fy “important” scaffolds

Scaffold Network Representa*ons

Metrics for the Complete Network

•  Examined vertex-‐level measures of centrality – Closeness, betweenness, … – High similarity of MIPE & NP and low similarity of LOPAC & NP is surprising (Ertl et al, JCIM, 2008)

0.00

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−10 −9 −8 −7 −6 −5log10(Betweenness)

density

CL1420CL886LOPACMIPENP

0

5000

10000

15000

20000

−8 −7 −6log Closeness (in−degree)

Num

. Sca

ffold


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0.75

1.00

0.00

0.25

0.50

0.75

1.00

0.000

0.025

0.050

0.075

Centralization

CPL

Transitivity

CL1420 CL886 LOPAC MIPE NPLibrary

Value

Metrics for the Complete Network

•  Useful to summarize distribu:ons by scalar metrics

•  Path length metrics are not discriminatory due to many short paths

•  Extent of clustering differs but is quite low overall

Comparing Complete Networks

•  Library overlap is characterized by the set of common scaffolds

•  Scaffolds can be ranked (e.g., PageRank) –  Small fragments have low PR – Large frameworks have high PR –  Interes:ng scaffolds lie in between?

•  Similar libraries will have common scaffolds with similar PageRank values

PageRank vector

PageRank vector

Subset Common

Fragments

Subset Common

Fragments

Normalized Dot Product

Comparing Complete Networks

1 0 0 0 0

0 1 0 0 0

0 0 1 0.2 0.3

0 0 0.2 1 0.3

0 0 0.3 0.3 1

CL1420

CL886

LOPAC

MIPE

NP

CL1420 CL886 LOPAC MIPE NP

Scaffold Recogni*on •  What is a scaffold? •  Can be addressed through the scaffold network – A scaffold is a hub within the scaffold network

•  Provide a prac:cal answer to “What are the missing scaffolds in my library”

•  Examples of unique scaffolds in MIPE but not in NP

Scaffold Comparison

Reduced Network Representa*on

•  The complete network can be reduced to a forest of trees

•  Order nodes by out-‐degree •  From each node, traverse network un:l a terminal node is reached

•  Result is a set of spanning trees

Reduced Network Representa*on

MIPE, 1912 compounds

Network Structure

•  A scaffold forest is characterized by – Disconnected components

•  structurally related scaffolds, scaffolds diversity – Singletons

•  scaffolds with no superstructure – Branching within connected components

•  scaffold complexity

Forest Size vs Library Size

•  A large libraries doesn’t imply a large forest •  Forest size is a func:on of scaffold diversity

CL1420, 31K combinatorial library MIPE, 1912 (target) diverse library

Summarizing Forests

•  A key feature is the nature of branching in individual trees

•  Characterized by ID -‐ informa:on theore:c descriptor of branching derived from the distance matrix

Bonchev & Trinajis:c, IJQC, 1978, 14, 293-‐303

ID = 978 ID = 90794 ID = 3456 ID = 979252

Summarizing Forests

•  Distribu:on of ID dis:nguishes datasets primarily in the tails

•  Aggrega:ng by mean ID s:ll discriminates well – Driven by the tails

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1.00

2 4 6log10(ID)

Density


0

1

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CL1420 CL886 LOPAC MIPE NP

Mea

n lo

g10(

I D)

Exploring the Forest

•  The metric also allows us to drill down – Select scaffolds of given branching complexity –  Iden:fy scaffolds of given complexity range across different libraries (equivalent to finding holes in scaffold coverage)

≈

LOPAC, ID = 10214 MIPE, ID = 10197

Library Comparison via Merging

•  … reduces to comparing networks •  We compute a graph union and construct new edges between nodes with the same hash

•  How does the network structure of the union differ from the original networks?

•  Can be extended to merge more than two networks

Source Forests

•  Structurally similar networks

•  2659 iden:cal nodes

•  Construct union by connec:ng nodes with iden:cal hash

LOPAC MIPE

Merged Network

•  Green edges “bridge” the two networks

•  Trees can now have two types of nodes

•  How can we characterize the – Contrac:on? – Degree of mixing?

Contrac*on to Measure Overlap

•  Merging very similar libraries should generate a smaller forest compared to the original forests

•  But this doesn’t really describe how the individual trees become (more) connected

Cnorm =F12

F1 + F2

where Fi = G1i,G2i,!,Gni{ }

0.00

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Cl886/CL1420 MIPE/CL886 MIPE/LOPAC MIPE/NP

Cnorm

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Cl886/CL1420 MIPE/CL886 MIPE/LOPAC MIPE/NP

% o

f tre

es

Assortive Not Assortive

Assorta*vity to Measure Overlap

•  Quan:fies the no:on that “like connects to like”

•  Undefined for trees that only have one type of vertex (i.e., only from a single library)

•  The number of trees that are assorta:ve is a global indicator of library similarity

Newman, Phys. Rev. E., 2003, 026126

0

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0.4 0.6 0.8 1.0Assortativity

density

Cl886/CL1420

MIPE/CL886

MIPE/LOPAC

MIPE/NP


•  We then examine the distribu:on of assorta:vity across assorta:ve trees

•  Dissimilar libraries have few assorta:ve trees – But they have high values of assorta:vity

•  However, high assorta:vity doesn’t imply high overlap


Assorta:vity = 0.85 (MIPE & NP)

Assorta:vity = 0.95 (CL886 & CL1420)

Overlap via Tree Complexity

•  Similar libraries lead to fewer trees in the merged network, but also denser trees

•  Change in density (branching) across the forest can also measure the extent of overlap

MIPE LOPAC Merged

Summarizing via Tree Complexity

•  Distribu:ons of ID before and aLer merging don’t differ very much, visually

•  However a KS test does discriminate them

0.0

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0.8

1 2 3 4log10(ID)

density

IndividualMerged

CL886 / CL1420 MIPE / NP

0.0

0.1

0.2

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2.5 5.0 7.5log10(ID)

density

IndividualMerged

D = 0.0173, p = 1 D = 0.0582, p = .0008

Summary

•  Scaffold networks are a rela:vely objec:ve way to characterize & compare libraries – Supports fast comparisons between libraries

•  The approach supports mul:plexing informa:on in to a single data structure – Physchem proper:es, bioac:vi:es, …

•  “What is a good comparison?” quickly becomes a philosophical ques:on

characterization of chemical libraries using scaffolds and network models

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