1. Similarity Methods
C371
Fall 2004

2. Limitations of Substructure Searching/3D Pharmacophore Searching
Need to know what you are looking for
Compound is either there or not
Don’t get a feel for the relative ranking of the compounds
Output size can be a problem

3. Similarity Searching
Look for compounds that are most similar to the query compound
Each compound in the database is ranked
In other application areas, the technique is known as pattern matching or signature analysis

4. Similar Property Principle
Structurally similar molecules usually have similar properties, e.g., biological activity
Known also as “neighborhood behavior”
Examples: morphine, codeine, heroin
Define: in silico
Using computational techniques as a substitute for or complement to experimental methods

5. Advantages of Similarity Searching
One known active compound becomes the search key
User sets the limits on output
Possible to re-cycle the top answers to find other possibilities
Subjective determination of the degree of similarity

6. Applications of Similarity Searching
Evaluation of the uniqueness of proposed or newly synthesized compounds
Finding starting materials or intermediates in synthesis design
Handling of chemical reactions and mixtures
Finding the right chemicals for one’s needs, even if not sure what is needed.

7. Subjective Nature of Similarity Searching
No hard and fast rules
Numerical descriptors are used to compare molecules
A similarity coefficient is defined to quantify the degree of similarity
Similarity and dissimilarity rankings can be different in principle

8. Similarity and Dissimilarity
“Consider two objects A and B, a is the number of features (characteristics) present in A and absent in B, b is the number of features absent in A and present in B, c is the number of features common to both objects, and d is the number of features absent from both objects. Thus, c and d measure the present and the absent matches, respectively, i.e., similarity; while a and b measure the corresponding mismatches, i.e., dissimilarity.” (Chemoinformatics; A Textbook (2003), p. 304)

9. 2D Similarity Measures
Commonly based on “fingerprints,” binary vectors with 1 indicating the presence of the fragment and 0 the absence
Could relate structural keys, hashed fingerprints, or continuous data (e.g., topological indexes that take into acount size, degree of branching, and overall shape)

10. Tanimoto Coefficient
Tanimoto Coefficient of similarity for Molecules A and B:
SAB = c _
a + b – c
a = bits set to 1 in A, b = bits set to 1 in B, c = number of 1 bits common to both
Range is 0 to 1.
Value of 1 does not mean the molecules are identical.

11. Similarity Coefficients
Tanimoto coefficient is most widely used for binary fingerprints
Others:
Dice coefficient
Cosine similarity
Euclidean distance
Hamming distance
Soergel distance

12. Distance Between Pairs of Molecules
Used to define dissimilarity of molecules
Regards a common absence of a feature as evidence of similarity

13. When is a distance coefficient a metric?
Distance values must be zero or positive
Distance from an object to itself must be zero
Distance values must be symmetric
Distance values must obey the triangle inequality: DAB ≤ DAC + DBC
Distance between non-identical objects must be greater than zero.
Dissimilarity = distance in the n-dimensional descriptor space

14. Size Dependency of the Measures
Small molecules often have lower similarity values using Tanimoto
Tanimoto normalizes the degree of size in the denominator:
SAB = c _
a + b – c

15. Other 2D Descriptor Methods
Similarity can be based on continuous whole molecule properties, e.g. logP, molar refractivity, topological indexes.
Usual approach is to use a distance coefficient, such as Euclidean distance.

16. Maximum Common Subgraph Similarity
Another approach: generate alignment between the molecules (mapping)
Define MCS: largest set of atoms and bonds in common between the two structures.
A Non-Polynomial- (NP)-complete problem: very computer intensive; in the worst case, the algorithm will have an exponential computational complexity
Tricks are used to cut down on the computer usage

17. Maximum Common Subgraph

18. Reduced Graph Similarity
A structure’s key features are condensed while retaining the connections between them
Cen ID structures with similar binding characteristics, but different underlying skeletons
Smaller number of nodes speeds up searching

19. 3D Similarity
Aim is often to identify structurally different molecules
3D methods require consideration of the conformational properties of molecules

20. Tanimoto Coefficient to Find Compounds Similar to Morphine

21. 3D: Alignment-Independent Methods
Descriptors: geometric atom pairs and their distances, valence and torsion angles, atom triplets
Consideration of conformational flexibility increases greatly the compute time
Relatively fewer pharmacophoric fingerprints than 2D fingerprints
Result: Low similarity values using Tanimoto

22. Pharmacophore
A structural abstraction of the interactions between various functional group types in a compound
Described by a spatial representation of these groups as centers (or vertices) of geometrical polyhedra, together with pairwise distances between centers

23. 3D: Alignment Methods
Require consideration of the degrees of freedom related to the conformational flexibility of the molecules
Goal: determine the alignment where similarity measure is at a maximum

24. 3D: Field-Based Alignment Methods
Consideration of the electron density of the molecules
Requires quantum mechanical calculation: costly
Property not sufficiently discriminatory

25. 3D: Gnomonic Projection Methods
Molecule positioned at the center of a sphere and properties projected on the surface
Sphere approximated by a tessellated icosahedron or dodecahedron
Each triangular face is divided into a series of smaller triangles

26. Finding the Optimal Alignment
Need a mechanism for exploring the orientational (and conformational) degrees of freedon for determining the optimal alignment where the similarity is maximized
Methods: simplex algorithm, Monte Carlo methods, genetic alrogithms

27. Evaluation of Similarity Methods
Generally, 2D methods are more effective that 3D
2D methods may be artificially enhanced because of database characteristics (close analogs)
Incomplete handling of conformational flexibility in 3D databases
Best to use data fusion techniques, combining methods

28. For additional information . . .
See Dr. John Barnard’s lecture at: