Similarity searching

Version Compatibility

Reference examples tested with: RDKit 2024.09+, scikit-learn 1.4+, annoy 1.17+, mhfp 1.9+.

Before using code patterns, verify installed versions match. If versions differ:

• Python: pip show <package> then help(module.function) to check signatures

If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.

Similarity Searching

Find structurally similar compounds and cluster libraries by similarity. The choice of similarity coefficient and fingerprint is task-aware: Tanimoto for symmetric similarity in lead optimization, Tversky for asymmetric "substructure-like" queries, Dice for higher sensitivity in low-similarity regimes, and MaxCommon Substructure (MCS) for scaffold-hopping. Tanimoto similarity above 0.7 is not a guarantee of activity preservation; activity cliffs (similar molecules with dissimilar activities) are common (Maggiora 2014).

For fingerprint choice, see chemoinformatics/molecular-descriptors. For 3D shape similarity, see chemoinformatics/shape-similarity.

Similarity Coefficient Taxonomy

Coefficient	Formula	Range	Symmetric	Use case	Fails when
Tanimoto	c / (a + b - c)	0-1	Yes	Default for ECFP4 similarity, ranking analogs	Saturates at low similarity (drug vs natural product)
Dice	2c / (a + b)	0-1	Yes	More sensitive than Tanimoto in 0.3-0.5 range	Bit-vector only; analog choice subjective
Cosine (Ochiai)	c / sqrt(a*b)	0-1	Yes	Count vectors, weighted similarity	Not standard for bit vectors
Tversky alpha,beta	c / (alpha*(a-c) + beta*(b-c) + c)	0-1	No when alpha != beta	Asymmetric "is A a substructure of B" queries	Parameter choice subjective; alpha=1,beta=0 = substructure-like
Hamming	(a + b - 2c) / nBits	0-1	Yes	Count vectors, when bit-wise distance matters	Bit-vector only loses scale
Russell-Rao	c / nBits	0-1	Yes	Sparse fingerprints	Biased by fingerprint density
Kulczynski	(c/a + c/b) / 2	0-1	Yes	When fingerprints have very different bit-density	Less standard

Where a = set bits in fp1, b = set bits in fp2, c = bits in common.

When to Use Which Coefficient

Scenario	Coefficient	Why
Standard analog search (drug-like, ECFP4)	Tanimoto, threshold 0.7	Industry default; calibrated against medchem judgment
Sensitive search at lower similarity	Dice, threshold 0.45	Dice is roughly 2*Tanimoto/(1+Tanimoto); more sensitive in middle range
Substructure-like ranking	Tversky alpha=1, beta=0	Asymmetric: rewards compounds containing query features
Count fingerprints (neural, atom-environment)	Cosine	Bit-vector Tanimoto loses information
Activity-cliff diagnosis	Tanimoto + property difference	Detect ECFP4>=0.85 but
Cross-target / scaffold-hopping	FCFP4 Tanimoto OR AtomPair Tanimoto	Pharmacophore-equivalent matches different scaffolds
Metabolomics / natural products	MHFP6 Jaccard	ECFP4 saturates near 0.2 across diverse classes
3D shape	Tanimoto on shape volume overlap	See shape-similarity skill

Tanimoto Thresholds (calibrated against medchem judgment)

Threshold	Interpretation	Caveat
>=0.85	Likely same scaffold + close analog	Activity cliffs still possible
0.70-0.85	Same series, R-group variation	Standard "similar" threshold
0.55-0.70	Related chemotype, different decoration	Useful for series expansion
0.35-0.55	Distant analog, possible scaffold hop	Many false positives
<0.35	Mostly noise; use 3D shape or pharmacophore instead	ECFP4 not informative

Maggiora's similarity principle states "similar molecules tend to have similar activity" -- but activity cliffs (Stumpfe & Bajorath 2012) violate this. Roughly 10-20% of activity-cliff pairs have ECFP4 Tanimoto >=0.7 with delta(pIC50) >=2.

Decision Tree by Scenario

Goal	Workflow	Tools
Find analogs of a hit (lead opt)	ECFP4 Tanimoto >=0.7 search	RDKit BulkTanimotoSimilarity
Find scaffold hops	FCFP4 OR AtomPair Tanimoto >=0.5 + filter MCS	RDKit + rdFMCS
Cluster library by chemotype	Butina clustering at Tanimoto 0.6 cutoff	RDKit Butina.ClusterData
Diversity sampling	MaxMin selection on Tanimoto	RDKit rdSimDivPickers.MaxMinPicker
Nearest neighbors in >1M library	LSH (MinHash) with MHFP6	mhfp + Annoy
Activity cliff diagnosis	Tanimoto + pIC50 delta scatter	Custom analysis
3D similarity (shape)	USRCAT / Open3DAlign / ROCS	shape-similarity skill

Tanimoto Similarity (single query, large library)

Goal: Rank a library by ECFP4 Tanimoto similarity to a query molecule, returning hits above a threshold.

Approach: Generate ECFP4 fingerprints for all molecules once, then use BulkTanimotoSimilarity for O(N) lookup.

from rdkit import Chem, DataStructs
from rdkit.Chem import AllChem

def precompute_fps(smiles_list, radius=2, nBits=2048):
    fps = []
    for smi in smiles_list:
        mol = Chem.MolFromSmiles(smi)
        if mol is None:
            fps.append(None)
        else:
            fps.append(AllChem.GetMorganFingerprintAsBitVect(mol, radius, nBits=nBits))
    return fps

def search(query_smi, library_fps, threshold=0.7):
    qmol = Chem.MolFromSmiles(query_smi)
    qfp = AllChem.GetMorganFingerprintAsBitVect(qmol, 2, nBits=2048)
    sims = DataStructs.BulkTanimotoSimilarity(qfp, [f for f in library_fps if f])
    return [(i, s) for i, s in enumerate(sims) if s >= threshold]

Tversky for Asymmetric Substructure-Like Search

Goal: Rank a library by how much each compound "contains" the features of the query (asymmetric).

Approach: Tversky with alpha=1, beta=0 rewards compounds containing query bits (substructure-like) while ignoring extra bits in the compound.

from rdkit import DataStructs

def tversky_substructure_like(qfp, lib_fps, alpha=1.0, beta=0.0):
    return [DataStructs.TverskySimilarity(qfp, f, alpha, beta) for f in lib_fps if f]

Use case: identifying analogs that extend a pharmacophore vs. exact-similarity ranking.

Butina Clustering

Goal: Group a library into clusters where intra-cluster Tanimoto >= 1 - cutoff.

Approach: Compute upper-triangle distance matrix, apply Taylor-Butina with chosen distance cutoff.

from rdkit.ML.Cluster import Butina

def cluster(mols, cutoff=0.4):
    fps = [AllChem.GetMorganFingerprintAsBitVect(m, 2, nBits=2048) for m in mols]
    n = len(fps)
    dists = []
    for i in range(1, n):
        sims = DataStructs.BulkTanimotoSimilarity(fps[i], fps[:i])
        dists.extend([1 - s for s in sims])
    return Butina.ClusterData(dists, n, cutoff, isDistData=True)

cutoff=0.4 means clusters share Tanimoto >= 0.6. The first molecule in each returned cluster is the cluster centroid.

Trade-off: Butina is O(N^2) and scales to ~100k molecules. For 1M+ libraries, use approximate nearest-neighbor (Annoy with MHFP6).

Diversity Selection (MaxMin)

Goal: Select N diverse compounds from a library by maximizing the minimum pairwise distance.

from rdkit.SimDivFilters import rdSimDivPickers

picker = rdSimDivPickers.MaxMinPicker()
n_pick = 100
n_lib = len(fps)
selected = picker.LazyBitVectorPick(fps, n_lib, n_pick, seed=42)

LazyBitVectorPick is memory-efficient (does not materialize full distance matrix).

Maximum Common Substructure

Goal: Find the largest substructure shared across a set of molecules.

Approach: rdFMCS.FindMCS with parameters controlling atom/bond equivalence.

from rdkit.Chem import rdFMCS

def mcs_smarts(mols, timeout=60, ring_match='strict', atom_match='elements'):
    params = rdFMCS.MCSParameters()
    params.Timeout = timeout
    if ring_match == 'strict':
        params.BondCompareParameters.MatchRingFusion = True
        params.BondCompareParameters.RingMatchesRingOnly = True
    if atom_match == 'elements':
        params.AtomCompareParameters.MatchValences = False
    result = rdFMCS.FindMCS(mols, params)
    return result.smartsString, result.numAtoms, result.numBonds

Use cases: identify scaffold across a series, build scaffold hopping queries, generate consensus pharmacophore.

Limit: MCS scales exponentially with molecule overlap. For >50 molecules or molecules >30 atoms, raise timeout and accept partial results.

Activity Cliff Diagnosis

Goal: Detect pairs of similar molecules with dissimilar activities (cliffs).

Approach: Compute pairwise ECFP4 Tanimoto + pIC50 delta. Flag pairs with high similarity and large activity gap.

def activity_cliffs(df, sim_threshold=0.85, activity_gap=2.0, activity_col='pIC50'):
    fps = [AllChem.GetMorganFingerprintAsBitVect(Chem.MolFromSmiles(s), 2, nBits=2048)
           for s in df['smiles']]
    cliffs = []
    for i in range(len(fps)):
        sims = DataStructs.BulkTanimotoSimilarity(fps[i], fps[i+1:])
        for j_off, sim in enumerate(sims):
            j = i + 1 + j_off
            if sim >= sim_threshold:
                gap = abs(df[activity_col].iloc[i] - df[activity_col].iloc[j])
                if gap >= activity_gap:
                    cliffs.append((i, j, sim, gap))
    return cliffs

Activity cliffs flag (a) measurement noise, (b) cryptic SAR (e.g. ring-flip changing dihedral), (c) protein conformational selection, or (d) actually informative SAR. Cliffs are an opportunity for medchem investigation, not necessarily an error.

Large-Library Nearest Neighbor (MHFP6 + Annoy)

For libraries >1M compounds, direct pairwise Tanimoto is impractical. MHFP6 (MinHashed fingerprint) + Annoy (LSH) gives approximate top-k in seconds.

from mhfp.encoder import MHFPEncoder
from annoy import AnnoyIndex

encoder = MHFPEncoder(2048)

def build_index(mols, fname):
    idx = AnnoyIndex(2048, 'hamming')
    for i, mol in enumerate(mols):
        fp = encoder.encode(mol, radius=3)
        idx.add_item(i, fp)
    idx.build(50)
    idx.save(fname)
    return idx

def query_index(idx, qmol, k=10):
    qfp = encoder.encode(qmol, radius=3)
    return idx.get_nns_by_vector(qfp, k, include_distances=True)

Annoy distance: Hamming on MinHash, related to Jaccard. Trade-off: ~95% recall on top-10 nearest neighbors vs full-Tanimoto search.

Per-Tool Failure Modes

ECFP4 Tanimoto -- saturation in diverse libraries

Trigger: Library spans drug-like + natural products + peptides + metabolites.

Mechanism: ECFP4 bits sparsely cover macrocycles, peptides, glycans; most pairwise Tanimoto reports 0.1-0.3.

Symptom: Pairwise Tanimoto distribution narrow; ranking is dominated by noise. Quantitative diagnostic: if mean pairwise Tanimoto on a random sample of N>=1000 from the library is < 0.20, ECFP4 is saturated.

Fix: Use MHFP6 (MinHash) or MAP4 (atom-pair MinHash); calibrated for chemical diversity. Re-check mean Tanimoto > 0.30 with new fingerprint.

Butina clustering -- O(N^2) memory blowup

Trigger: Library >100k molecules.

Mechanism: Butina requires upper-triangle distance matrix, ~5e9 floats for 100k compounds.

Symptom: OOM error or hours of CPU.

Fix: Use approximate clustering (HDBSCAN on UMAP-reduced fingerprints) or LSH-based clustering on MHFP6.

MCS -- exponential timeout

Trigger: Mol set with low overlap, large molecules, or many input mols.

Mechanism: MCS search is NP-hard; algorithm tries every atom-mapping permutation within timeout.

Symptom: Returns small partial MCS or empty result.

Fix: Raise timeout; reduce input mol count; pre-cluster by Tanimoto first then MCS within clusters.

Tanimoto = 1.0 != same molecule

Trigger: Comparing fingerprints between two molecules that hash to the same bits.

Mechanism: Hashed Morgan with nBits=2048 has bit-collision rate ~1-5% for drug-like molecules.

Symptom: Two structurally different molecules report Tanimoto 1.0.

Fix: For exact identity, compare canonical SMILES or InChIKey, not fingerprint. Use unhashed sparse fingerprint to disambiguate.

Similarity threshold transfer fails

Trigger: Threshold tuned on ECFP4 applied to RDKit FP, AtomPair, or MACCS.

Mechanism: Bit-density and fragment-resolution differ; Tanimoto distributions shift.

Symptom: "Similar" set is much larger or smaller than expected.

Fix: Re-tune threshold per fingerprint. AtomPair similar threshold ~0.55; MACCS ~0.85; ECFP4 ~0.7; FCFP4 ~0.6.

Reconciliation: Cliffs Across Methods

If a pair flags as an activity cliff in ECFP4 but not in MCS-based, the local environment differs at a single key atom (e.g., -F to -OH). If it flags in MCS but not ECFP4, a remote substituent affects activity (e.g., para vs meta). Use both views to localize the SAR.

Common Errors

Symptom	Cause	Fix
BulkTanimotoSimilarity returns ints	Bit-vector with single bit per atom	Already correct; ints are bit counts
Tanimoto > 1	Wrong coefficient (Tversky alpha+beta != 1, count vector)	Use bit vector + Tanimoto
Cluster centroids change between runs	Order-dependent Butina	Sort molecules first or use stable random seed for tie-breaking
MaxMinPicker returns first N inputs	All-zero initial similarity matrix	Seed picker explicitly: picker.LazyBitVectorPick(fps, n_lib, n_pick, seed=42)
Activity cliff "false positives"	Bit-collisions inflate similarity	Use sparse Morgan or compare canonical SMILES for exact ID
Diverse subset has duplicates	Standardization not applied	Canonicalize via chemoinformatics/molecular-standardization first
Tanimoto incompatible with neural fingerprint	Continuous-valued fingerprint	Use cosine or sklearn cdist with 'cosine' metric

References

• Bajorath, Nat. Rev. Drug Discov. 1:882 (2002) -- molecular similarity principle review.
• Maggiora et al., J. Med. Chem. 57:3186 (2014) -- molecular similarity in drug discovery.
• Stumpfe & Bajorath, J. Med. Chem. 55:2932 (2012) -- activity cliffs.
• Tversky, Psychol. Rev. 84:327 (1977) -- features of similarity (Tversky coefficient).
• Probst & Reymond, J. Cheminformatics 10:66 (2018) -- MHFP6 MinHash fingerprint.
• O'Boyle et al., J. Cheminformatics 8:36 (2016) -- comparing fingerprints for similarity.
• Butina, J. Chem. Inf. Comput. Sci. 39:747 (1999) -- Taylor-Butina clustering.

Related Skills

• chemoinformatics/molecular-descriptors - Generate fingerprints for similarity
• chemoinformatics/molecular-standardization - Canonicalize before comparing
• chemoinformatics/substructure-search - SMARTS pattern-based searching
• chemoinformatics/scaffold-analysis - Scaffold-based similarity (Bemis-Murcko, MMPA)
• chemoinformatics/shape-similarity - 3D shape similarity (USRCAT, ROCS)
• machine-learning/biomarker-discovery - ML on similarity features