Similarity Methods C371 Fall 2004

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

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

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

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

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.

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

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)

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)

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.

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

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

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

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

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.

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

Maximum Common Subgraph

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

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

Tanimoto Coefficient to Find Compounds Similar to Morphine

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

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 http://www.ma.psu.edu/~csb15/pubs/searle.pdf

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

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

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

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

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

For additional information . . . See Dr. John Barnard’s lecture at: http://www.indiana.edu/~cheminfo/C571/c571_Barnard6.ppt