What is your "Tanimoto coefficient"?

A well-known index when talking about the similarity of compounds is the "Tanimoto coefficient". However, there are quite a few people who only say "Tanimoto coefficient", and there are quite a few opportunities to agonize over "Isn't that enough to explain?"

For example, use the following compound set

The number of compounds is 10.

smiles = [
    'C1=CC=C2C3CC(CNC3)CN2C1=O',
    'CN1c2c(C(N(C)C1=O)=O)[nH0](CC(CO)O)c[nH0]2',
    'CN1C2CC(CC1C1C2O1)OC(C(c1ccccc1)CO)=O',
    'CN1C2CC(CC1C1C2O1)OC(C(c1cccnc1)CO)=O', #Similar to the compound above
    'CN(C=1C(=O)N(c2ccccc2)N(C1C)C)C',
    'CN(C=1C(=O)N(C2CCCCC2)N(C1C)C)C', #Similar to the compound above
    'OCC1C(C(C(C(OCC2C(C(C(C(OC(c3ccccc3)C#N)O2)O)O)O)O1)O)O)O',
    'OCc1ccccc1OC1C(C(C(C(CO)O1)O)O)O',
    'OCc1cc(N)ccc1OC1C(C(C(C(CO)O1)O)O)O', #Similar to the compound above
    '[nH0]1c(OC)c2c([nH0]cc[nH0]2)[nH0]c1',
]

Generating compounds with RDKit from SMILES notation

from rdkit import Chem

mols = [Chem.MolFromSmiles(smile) for smile in smiles]

Generate Morgan fingerprint (a type of)

from rdkit.Chem import AllChem

fps = [AllChem.GetMorganFingerprint(mol, 3, useFeatures=True) for mol in mols]

Calculate Tanimoto coefficient

from rdkit import DataStructs

sim_matrix = [DataStructs.BulkTanimotoSimilarity(fp, fps) for fp in fps]

Distribution of Tanimoto coefficient

By doing this, you can see the distribution of the Tanimoto coefficient. It seems that the molecule with Tanimoto coefficient = 1 is the same molecule, but there are other molecular pairs with higher Tanimoto coefficient. Find out (or imagine) what it is

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

plt.hist(np.array(sim_matrix).flatten(), bins=20)
plt.grid()
plt.show()

And there are various things in the Morgan fingerprint

The Morgan fingerprint also has various parameters, and changing them also changes the value of the Tanimoto coefficient.

fps = [AllChem.GetMorganFingerprint(mol, 2, useFeatures=True) for mol in mols]
sim_matrix = [DataStructs.BulkTanimotoSimilarity(fp, fps) for fp in fps]
plt.hist(np.array(sim_matrix).flatten(), bins=20)
plt.grid()
plt.show()

fps = [AllChem.GetMorganFingerprint(mol, 1, useFeatures=True) for mol in mols]
sim_matrix = [DataStructs.BulkTanimotoSimilarity(fp, fps) for fp in fps]
plt.hist(np.array(sim_matrix).flatten(), bins=20)
plt.grid()
plt.show()

fps = [AllChem.GetMorganFingerprintAsBitVect(mol, 3, 1024) for mol in mols]
sim_matrix = [DataStructs.BulkTanimotoSimilarity(fp, fps) for fp in fps]
plt.hist(np.array(sim_matrix).flatten(), bins=20)
plt.grid()
plt.show()

fps = [AllChem.GetMorganFingerprintAsBitVect(mol, 3, 2048) for mol in mols]
sim_matrix = [DataStructs.BulkTanimotoSimilarity(fp, fps) for fp in fps]
plt.hist(np.array(sim_matrix).flatten(), bins=20)
plt.grid()
plt.show()

And there are other fingerprints

There are only two because it is difficult to calculate everything. One of the important things is that in the calculation results below, there are 10 or more cases with a Tanimoto coefficient of 1.0. In other words, be aware that the Tanimoto coefficient can be 1.0 even if they are not the same molecule.

fps = [AllChem.GetMACCSKeysFingerprint(mol) for mol in mols]
sim_matrix = [DataStructs.BulkTanimotoSimilarity(fp, fps) for fp in fps]
plt.hist(np.array(sim_matrix).flatten(), bins=20)
plt.grid()
plt.show()

fps = [Chem.RDKFingerprint(mol) for mol in mols]
sim_matrix = [DataStructs.BulkTanimotoSimilarity(fp, fps) for fp in fps]
plt.hist(np.array(sim_matrix).flatten(), bins=20)
plt.grid()
plt.show()

You can also define the Tanimoto coefficient using MCS.

from rdkit.Chem import rdFMCS

matrix = []
for mol1 in mols:
    for mol2 in mols:
        mcs = rdFMCS.FindMCS([mol1, mol2])
        a1 = len(mol1.GetAtoms())
        a2 = len(mol2.GetAtoms())
        matrix.append(mcs.numAtoms / (a1 + a2 - mcs.numAtoms) )

plt.hist(np.array(matrix).flatten(), bins=20)
plt.grid()
plt.show()

MCS also has various options

from rdkit.Chem import rdFMCS

matrix = []
for mol1 in mols:
    for mol2 in mols:
        mcs = rdFMCS.FindMCS([mol1, mol2], atomCompare=rdFMCS.AtomCompare.CompareAny)
        a1 = len(mol1.GetAtoms())
        a2 = len(mol2.GetAtoms())
        matrix.append(mcs.numAtoms / (a1 + a2 - mcs.numAtoms) )

plt.hist(np.array(matrix).flatten(), bins=20)
plt.grid()
plt.show()

from rdkit.Chem import rdFMCS

matrix = []
for mol1 in mols:
    for mol2 in mols:
        mcs = rdFMCS.FindMCS([mol1, mol2])
        a1 = len(mol1.GetBonds())
        a2 = len(mol2.GetBonds())
        matrix.append(mcs.numBonds / (a1 + a2 - mcs.numBonds) )

plt.hist(np.array(matrix).flatten(), bins=20)
plt.grid()
plt.show()

from rdkit.Chem import rdFMCS

matrix = []
for mol1 in mols:
    for mol2 in mols:
        mcs = rdFMCS.FindMCS([mol1, mol2], bondCompare=rdFMCS.BondCompare.CompareOrderExact)
        a1 = len(mol1.GetBonds())
        a2 = len(mol2.GetBonds())
        matrix.append(mcs.numBonds / (a1 + a2 - mcs.numBonds) )

plt.hist(np.array(matrix).flatten(), bins=20)
plt.grid()
plt.show()

So, what is your "Tanimoto coefficient"?