1 Chemical Structure Representation and Search Systems Lecture 3. Nov 4, 2003 John Barnard Barnard Chemical Information Ltd Chemical 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 node number of edges meeting at it  leaf node a node of degree 1  path connected sequence of edges between two nodes

4 Graph Terminology  cycle path which returns to its starting node  tree graph with no cycles  subgraph graph containing a subset of the nodes and edges of another graph

5 Graph Terminology  spanning tree a tree subgraph that contains all the nodes (but not necessarily all the edges) of a graph

6 Graph Terminology  connected graph graph in which there is a path between every pair of nodes  fully-connected graph graph in which there is an edge between every pair of nodes (all nodes have degree n-1)

7 Graph Terminology  disconnected graph graph in which some pairs of nodes have no path between them  component subgraph 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  forest graph 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 of different values

13 Morgan’s algorithm 3. Recalculate labels by summing label values at neighbour nodes 4. Count number of different values

14 Morgan’s algorithm 3. Recalculate labels by summing label values at neighbour nodes 4. Count number of different values 5. Repeat from step 3

15 Morgan’s algorithm 3. Recalculate labels by summing label values at neighbour nodes 4. Count number of different values 5. Repeat from step 3

16 Morgan’s algorithm 3. Recalculate labels by summing label values at neighbour nodes 4. Count number of different values 5. Repeat from step 3

17 Morgan’s algorithm 3. Recalculate labels by summing label values at neighbour nodes 4. Count number of different values 5. Repeat from step 3

18 Morgan’s algorithm 3. Recalculate labels by summing label values at neighbour nodes 4. Count number of different values 5. Repeat from step 3 until there is no increase in the number of different values

19 Morgan’s algorithm  most nodes now have different labels  choose node with highest label as node 1  number its neighbours in order of label values

20 Morgan’s algorithm  most nodes now have different labels  choose node with highest label as node 1  number its neighbours in order of label values

21 Morgan’s algorithm  move to node 2  number its remaining neighbours in order of label values because label values are tied, choose one with higher bond order (green) first  move to node 3

22 Morgan’s algorithm  continue till all nodes are numbered  we now have a numbering for the rows of the connection table  “breadth-first” trace nodes are dealt with in a “queue” (first in, first out)

23 Morgan’s algorithm  continue till all nodes are numbered  we now have a numbering for the rows of the connection table  “breadth-first” trace nodes are dealt with in a “queue” (first in, first out)

24 Morgan’s algorithm  “depth-first” trace is also possible nodes are dealt with in a “stack” (last in, first out)  more suitable for assigning atom numbers in SMILES where we want consecutive numbers to form a path OC(=O)C(N)CC1C=CC(O)=CC=1

25 Symmetry perception  if ties between label values cannot be resolved on basis of atom/bond types, the atoms are symmetrically equivalent, and it 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 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 + components where 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

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

32 Which rings to perceive?  Sometimes a large envelope ring may be aromatic, when smaller 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

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 by tracing appropriate paths in the graph  subgraphs may overlap

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 in several colours at once!)

36 Substructure fragments fragments provide “index terms” for a chemical structure o analogous to keywords in a text document they can be used in searching for structures o retrieved structures must contain the same fragments as the query “ambiguous” representations o many different structures can have the same fragments, connected together in different ways fragments to be used may be a closed list o 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 manually o 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 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 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 Ltd o 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 (sp 2 vs sp 3 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 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 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 molecule o is this molecule in the database? or tautomers, stereoisomers etc. of it, substructure search o query is a pattern of atoms and bonds o does this pattern occur as a substructure (subgraph) of any of the molecules in my database?