1Chemical Structure Representation

and Search Systems

Lecture 3. Nov 4, 2003

John Barnard

Barnard Chemical Information LtdChemical Informatics Software & Consultancy Services

Sheffield, UK

2 Lecture 3: Topics to be Covered

More Graph Theory Structure Analysis and Processing

• canonicalisation and symmetry perception• ring perception• functional group identification• structure fingerprints and fragments• structure depiction• principles of structure searching

3 Graph Terminology

degree of a nodenumber of edges

meeting at it

leaf nodea node of degree 1

pathconnected sequence

of edges between two nodes

1

3

2

3

33

2

1

1

1

2

2

2

4 Graph Terminology

cyclepath which returns

to its starting node

treegraph with no cycles

subgraphgraph containing a

subset of the nodes and edges of another graph

5 Graph Terminology

spanning treea tree subgraph that

contains all the nodes(but not necessarilyall the edges) of a graph

6 Graph Terminology

connected graphgraph in which there

is a path between every pair of nodes

fully-connected graphgraph in which there

is an edge between every pair of nodes(all nodes have degree n-1)

7 Graph Terminology

disconnected graphgraph in which some

pairs of nodes have no path betweenthem

componentsubgraph in which all

pairs of nodes are linked by a path, but no node has a path to a node in another component

8 Graph Terminology

forestgraph containing two

or more components that are trees

9 Canonicalisation

a given chemical structure (or graph) can have many valid and unambiguous representations• different order of rows in connection table• different order of atoms in SMILES

for comparison purposes it would be useful to have a single unique or “canonical” representation

process of converting input representation to canonical form is called “canonicalisation” or “canonisation”• process of applying “rules” (i.e. an algorithm)

10 Canonicalisation

an obvious approach:• generate all possible valid SMILES• choose the one that comes first alphabetically

this would be very slow, but effective, and there is a danger of missing one• principle was used for canonicalising

Wiswesser Line Notation

11 Canonicalisation

most methods in use today involve renumbering the atoms in some unique and reproducible way• can be used to number rows in connection table• can determine order of atoms in SMILES

normally involve a node labelling technique called “relaxation”• example is Morgan’s algorithm (1965)

12 Morgan’s algorithm

1. Label each node with its degree

2. Count number ofdifferent values

1

3

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3

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2

1

1

1

2

2

2

3 d iffe re nt v a lu e s{ 1 , 2 , 3 }

13 Morgan’s algorithm

3. Recalculate labelsby summing labelvalues at neighbournodes

4. Count number ofdifferent values

1

3

2

3

33

2

1

1

1

2

2

2

3 d iffe re nt v a lu e s{ 1 , 2 , 3 }

14 Morgan’s algorithm

3. Recalculate labelsby summing labelvalues at neighbournodes

4. Count number ofdifferent values

5. Repeat fromstep 3

3

5

5

6

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5

3

3

3

5

5

6

3 d iffe re nt v a lu e s{ 3 , 5 , 6 }

15 Morgan’s algorithm

3. Recalculate labelsby summing labelvalues at neighbournodes

4. Count number ofdifferent values

5. Repeat fromstep 3

5

13

10

16

1214

11

5

5

6

10

11

12

8 d iffe re nt v a lu e s{ 5 , 6 , 1 0 , 11 , 1 2 , 1 3 , 1 4 , 1 6 }

16 Morgan’s algorithm

3. Recalculate labelsby summing labelvalues at neighbournodes

4. Count number ofdifferent values

5. Repeat fromstep 3

13

25

24

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2418

26

12

12

14

24

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30

9 d iffe re nt v a lu e s{ 1 2 , 1 3 , 1 4 , 1 8 , 2 4 , 2 5 , 2 6 , 3 0 , 3 4 }

17 Morgan’s algorithm

3. Recalculate labelsby summing labelvalues at neighbournodes

4. Count number ofdifferent values

5. Repeat fromstep 3

25

61

51

82

4268

48

24

24

18

51

48

42

9 d iffe re nt v a lu e s{ 1 8 , 2 4 , 2 5 , 4 2 , 4 8 5 1 , 6 1 , 6 8 , 8 2 }

18 Morgan’s algorithm

3. Recalculate labelsby summing labelvalues at neighbournodes

4. Count number ofdifferent values

5. Repeat fromstep 3 until thereis no increase in thenumber of differentvalues

61

127

109

138

116102

133

42

42

68

109

133

150

1 0 d iffe re nt v a lu e s{ 4 2 , 6 1 , 6 8 , 1 0 2 , 1 0 9 , 11 6 , 1 2 7 , 1 3 3 , 1 3 8 , 1 5 0 }

19 Morgan’s algorithm

most nodes nowhave differentlabels

choose node withhighest label asnode 1

number its neighbours in orderof label values

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127

109

138

116102

133

42

42

68

109

133

150

1 0 d iffe re nt v a lu e s{ 4 2 , 6 1 , 6 8 , 1 0 2 , 1 0 9 , 11 6 , 1 2 7 , 1 3 3 , 1 3 8 , 1 5 0 }

20 Morgan’s algorithm

most nodes nowhave differentlabels

choose node withhighest label asnode 1

number its neighbours in orderof label values

61

127

109

138

116102

133

42

42

68

109

133

150

1 0 d iffe re nt v a lu e s{ 4 2 , 6 1 , 6 8 , 1 0 2 , 1 0 9 , 11 6 , 1 2 7 , 1 3 3 , 1 3 8 , 1 5 0 }

1

2

3

21 Morgan’s algorithm

move to node 2 number its remaining

neighbours in orderof label values

• because label valuesare tied, choose one with higher bond order (green) first

move to node 3

61

127

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138

116102

133

42

42

68

109

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1501

2

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45

22 Morgan’s algorithm

continue till all nodesare numbered

we now have a numbering for the rowsof the connection table

“breadth-first” trace• nodes are dealt with

in a “queue” (first in,first out)

61

127

109

138

116102

133

42

42

68

109

133

1501

2

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45

67

89

10

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13

23 Morgan’s algorithm

continue till all nodesare numbered

we now have a numbering for the rowsof the connection table

“breadth-first” trace• nodes are dealt with

in a “queue” (first in,first out)

1

2

45

67

89

10

11

12

13

3

24 Morgan’s algorithm

“depth-first” trace isalso possible

• nodes are dealt with ina “stack” (last in, first out)

more suitable for assigningatom numbers in SMILES where we want consecutivenumbers to form a path

OC(=O)C(N)CC1C=CC(O)=CC=1

61

127

109

138

116102

133

42

42

68

109

133

1506

7

4

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25

129

3

1

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11

25 Symmetry perception

if ties between label values cannot beresolved on basis of atom/bond types, the atoms are symmetrically equivalent, andit doesn’t matter which is chosen next

Morgan’s algorithm is thus also useful for identifying symmetry in molecules

26 Morgan’s algorithm

Provides canonical numbering for the nodes in a graph that doesn’t depend on any original numbering

Works by taking more of the graph into account at each iteration

• essence of “relaxation” technique is iteratively updating a value by looking at its immediate neighbours

It is not infallible• some graphs are known where the algorithm cannot distinguish

nodes that are not symmetrically equivalent There are many variations on it

• and several theoretical papers analysing it mathematically• O. Ivanciuc, “Canonical numbering and constitutional symmetry”,

in J. Gasteiger (Ed.) Handbook of Chemoinformatics, Vol 1, pp. 139-160. Wiley, 2003

27 Canonicalisation

Algorithms are applied to graphs not chemical structures

Issues such as aromaticity, tautomerism and stereochemistry need to be addressed before canonical numbering of the graph• Daylight’s canonicalisation algorithm for SMILES

perceives aromatic rings (using its own definition of aromaticity) as first step

28 Ring perception

How many rings are there in these structures and which ones are they?

rings are important features of chemical structures• nomenclature generation• aromaticity perception• synthetic significance• fragment descriptor generation

29 Rings and ring systems

A ring system is a subgraph in which every edge is part of a cycle

30 Ring perception

Euler Relationship nodes + rings = edges + componentswhere rings is the number of edges that must be removed from

the graph to turn it into a tree• rings is also called the Frerejacques number or nullity

• this is the minimum possible number of rings; it may be useful to identify others

6 + 1 = 6 + 1 10 + 2 = 11 + 1 7 + 2 = 8 + 1

23 + 5 = 25 + 3

31 Which rings to perceive?

Usually the smallest set of smallest rings• two 6-membered rather than

one 6- and one 10-membered• two 5-membered rather than

one 5- and one 6-membered

But there may be more than one SSSR• C-S-C-C-C-C• C-C-C-C-O-C• C-S-C-C-O-C

three different 6-membered rings

S

O

S

OO

S

32 Which rings to perceive?

Sometimes a large envelopering may be aromatic, whensmaller rings are not

Ring perception is a complex area where there are no right answers• there is a lot of literature on the subject

33 Ring perception by spanning tree

start at an arbitrary node “grow a spanning tree”

• add neighbours of current node to a queue

o provided they are not already in it

• move to the next node in the queue• repeat until queue is empty

those edges from original graph not in the spanning tree are ring closures

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34 Substructure Fragments

Subgraphs can be identified in a structure graph corresponding to functional groups, rings etc. • –OH• –NH2• –COOH• phenyl

this can be done bytracing appropriatepaths in the graph

subgraphs may overlap

OH

CH2

CHNH2

OH

O

35 Substructure Fragments

More systematic subgraphs can also be identified(easier to do algorithmically)• paths of connected atoms• every atom and its

immediate neighbours• rings

Subgraphs can overlap• (it’s difficult to show

pictures with atoms inseveral colours at once!)

OH

CH2

CHNH2

OH

O

36 Substructure fragments

• fragments provide “index terms” for a chemical structureo analogous to keywords in a text document

• they can be used in searching for structureso retrieved structures must contain the same fragments as the

query

• “ambiguous” representationso many different structures can have the same fragments,

connected together in different ways

• fragments to be used may be a closed listo controlled “vocabulary” (dictionary) of structural features

• or an open-ended list (like free text searching)o e.g. all unbranched paths of up to 6 atoms

37 Fragment codes

• many early chemical information systems were based on identifying fragments of this sort

o originally the fragments were identified manuallyo and represented on punched cards

• special fragment codes (dictionaries of fragments) were devised for different systems

o some of these are still in use, though with automated encoding of structures

o particularly important are the systems for “Markush” structures in patents (e.g. Derwent WPI code)

38 Fingerprints

the fragments present in a structure can be represented as a sequence of 0s and 1s

00010100010101000101010011110100• 0 means fragment is not present in structure• 1 means fragment is present in structure (perhaps

multiple times)

each 0 or 1 can be represented as a single bit in the computer (a “bitstring”)

for chemical structures often called structure “fingerprints”

39 Fingerprints

fingerprints are typically 150-2500 bits long where a fixed dictionary of fragments is used there

can be a 1:1 relationship between fragment and bit position in fingerprint• sometimes several related fragments will “set” the same

bit

disadvantage is that if structure contains no fragments from the dictionary, no bits are set• can be avoided if “generalised” fragments are used

(involving e.g. “any atom”, “any ring bond” types)

40 Fingerprints

if fragment set is open-ended, the fragment description (e.g. C-C-N-C-C-O) can be “hashed” to a number in fixed range (e.g. 1 to 1024) and this is the bit number to be set

disadvantages:• different and unrelated fragments may “collide” at the

same bit position• difficult to work back from bit position to fragment• this usually causes only slight degradation in search

performance (false hits), but can be more of a problem in other applications of fingerprints

41 Fingerprints

Hashed fingerprints• typically used in software from Daylight

Chemical Information Systems Inc. Dictionary fingerprints

• Chemical Abstracts Service• MDL Information Systems Inc

o ISIS or MACCS keys (166 and 960 bits)

• Barnard Chemical Information Ltdo customised dictionaries

42 2D structure depiction

if structures are stored without 2D display coordinates, we need to generate them• SMILES

“depiction” algorithms are used for this identify and lay out ring systems first

• complications over orientation of some systems• Chemical Abstracts stores “standard depictions” of all

ring systems it has encountered

then add side chains, avoiding collisions• many features can be added to improve appearance

43 3D structure depiction

much more complicated than 2D need to store standard bond lengths and angles need to distinguish atoms in different hybridisation states

(sp2 vs sp3 carbon) need rotate single bonds to avoid “bumps” sophisticated “conformation generation” programs identify

low-energy conformers• very useful for identifying molecules with the correct shape to fit

into biological receptor sites

J. Sadowski, “3D structure generation”, in J. Gasteiger (Ed.) Handbook of Chemoinformatics, Vol 1, pp. 231-261. Wiley, 2003

44 Nomenclature generation

most systematic nomenclature is based on ring systems• need to identify/prioritise ring systems first• identify standard numbering for system

o frequently need to store this

• add side chains and substituents with appropriate locants

J. L. Wisniewski, “Chemical nomenclature and structure representation: algorithmic generation and conversion”, in J. Gasteiger (Ed.) Handbook of Chemoinformatics, Vol 1, pp. 139-160. Wiley, 2003

45 Conclusions from Lecture 3

there are several important jargon terms used in graph theory, which crop up in chemical informatics

canonicalisation provides a unique numbering for the atoms in a molecule

• Morgan algorithm can be used to achieve it it’s not always obvious how many rings there are, or which

ones they are fingerprints represent the presence or absence of

substructure fragments in a molecule• they are ambiguous representations of structure

46 Topic for Lecture 4: Structure searching

two main varieties of search • full structure search

o query is is complete moleculeo is this molecule in the database?

• or tautomers, stereoisomers etc. of it,

• substructure searcho query is a pattern of atoms and bondso does this pattern occur as a substructure (subgraph)

of any of the molecules in my database?