bio-similarity-searching

Version Compatibility

Reference examples tested with: RDKit 2024.09+, scikit-learn 1.4+, 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	Bit or nonnegative sparse-count vectors when Dice semantics are intended	Thresholds depend on vector type; 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	Binary bit vectors when bit-wise disagreement matters	Does not preserve count magnitude
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, start near 0.7	Repository starting heuristic; calibrate against project actives and analog judgments
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 (Repository Starting Heuristics)

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

These bands are working defaults for ECFP4-like fingerprints, not transferable calibration. Inspect the target dataset's similarity distribution and known series before setting a cutoff. Maggiora's similarity principle states "similar molecules tend to have similar activity" -- but activity cliffs (Stumpfe & Bajorath 2012) violate this. Treat high ECFP4 similarity as a prioritization signal, not evidence that activity will be preserved.

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 forest with MHFP6	mhfp.lsh_forest.LSHForestHelper
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 rdFingerprintGenerator

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

def search(query_smi, library_fps, threshold=0.7):
    qmol = Chem.MolFromSmiles(query_smi)
    if qmol is None:
        raise ValueError('invalid query SMILES')
    generator = rdFingerprintGenerator.GetMorganGenerator(radius=2, fpSize=2048)
    qfp = generator.GetFingerprint(qmol)
    valid = [(i, fp) for i, fp in enumerate(library_fps) if fp is not None]
    sims = DataStructs.BulkTanimotoSimilarity(qfp, [fp for _, fp in valid])
    return [(source_i, sim) for (source_i, _), sim in zip(valid, sims)
            if sim >= 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 around Taylor-Butina centroids whose assigned neighbors are within the selected distance 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):
    generator = rdFingerprintGenerator.GetMorganGenerator(radius=2, fpSize=2048)
    fps = [generator.GetFingerprint(m) 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 each assigned member was a neighbor of its selected centroid at Tanimoto >= 0.6. It does not guarantee that every pair of non-centroid members has Tanimoto >= 0.6. The first molecule in each returned cluster is the cluster centroid.

Trade-off: Butina materializes O(N^2) pairwise distances. Benchmark memory and runtime on the actual library; for much larger collections, use an approximate method such as an MHFP6 LSH forest.

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.MatchFusedRings = True
        params.BondCompareParameters.MatchFusedRingsStrict = 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 search can become combinatorial as input count, size, and structural divergence grow. Set a finite timeout, inspect result.canceled, and consider pre-clustering or reducing the comparison set; no molecule-count or atom-count boundary guarantees tractability.

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'):
    generator = rdFingerprintGenerator.GetMorganGenerator(radius=2, fpSize=2048)
    mols = [Chem.MolFromSmiles(s) for s in df['smiles']]
    if any(mol is None for mol in mols):
        raise ValueError('activity-cliff input contains invalid SMILES')
    fps = [generator.GetFingerprint(mol) for mol in mols]
    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 + LSH Forest)

For large libraries, direct all-pairs comparison becomes expensive. The mhfp package provides an LSH-forest helper for approximate nearest-neighbor retrieval over MHFP6 fingerprints. Measure recall and latency against an exact subset for the project dataset.

from mhfp.encoder import MHFPEncoder
from mhfp.lsh_forest import LSHForestHelper

encoder = MHFPEncoder(2048)

def build_index(smiles_list):
    forest = LSHForestHelper()
    fingerprints = []
    for i, smiles in enumerate(smiles_list):
        fp = encoder.encode(smiles, radius=3)
        fingerprints.append(fp)
        forest.add(i, fp)
    forest.index()
    return forest, fingerprints

def query_index(forest, qmol, fingerprints, k=10):
    qfp = encoder.encode_mol(qmol, radius=3)
    return forest.query(qfp, k=k, data=fingerprints)

The returned neighbors are approximate in MHFP6 space. Benchmark them against an exact MHFP-distance search on a representative subset before choosing LSH parameters.

Per-Tool Failure Modes

ECFP4 Tanimoto -- saturation in diverse libraries

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

Mechanism: A local circular fingerprint may not preserve the distinctions needed for a particular mixed-modality retrieval task.

Symptom: Known relevant neighbors are not enriched above background, or retrieval metrics and neighborhood stability are poor on target-relevant controls. A low mean pairwise similarity alone is not a universal saturation test.

Fix: Benchmark ECFP4 against alternatives such as MHFP6 or MAP4 using held-out analog recovery, scaffold-aware retrieval, or another task-aligned metric. Do not transfer raw-score thresholds between fingerprint families.

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: A folded hashed fingerprint can map distinct atom environments to the same bits; collision frequency depends on molecule size, radius, and fingerprint length.

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 the threshold per fingerprint and dataset. AtomPair ~0.55, MACCS ~0.85, ECFP4 ~0.7, and FCFP4 ~0.6 are repository starting heuristics, not universal equivalents.

Reconciliation: Cliffs Across Methods

If a pair flags as an activity cliff under one representation but not another, treat that as representation sensitivity. Inspect atom mappings, fingerprint environments, assay uncertainty, and the exact structural change; disagreement alone does not establish which substituent caused the activity difference.

Common Errors

Symptom	Cause	Fix
BulkTanimotoSimilarity output is treated as bit counts	The API returns similarity values, normally floats	Keep the returned values as similarities; inspect input vector types if the output is unexpected
Reported similarity > 1	Custom formula, malformed data, negative features, or an incorrectly normalized external implementation	Verify the coefficient definition and inputs; standard nonnegative RDKit Tanimoto and Tversky similarities are bounded by 1
Cluster centroids change when input order changes	Taylor-Butina tie handling and assignment are order-sensitive	Standardize and sort inputs by a stable identifier before clustering; record reordering and the input order
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. 1:882-894 (2002) -- integration of virtual and high-throughput screening. https://doi.org/10.1038/nrd941
• Maggiora et al., J. Med. Chem. 57:3186-3204 (2014) -- molecular similarity in drug discovery. https://doi.org/10.1021/jm401411z
• Stumpfe & Bajorath, J. Med. Chem. 55:2932-2942 (2012) -- activity cliffs. https://doi.org/10.1021/jm201706b
• Tversky, Psychol. Rev. 84:327-352 (1977) -- features of similarity (Tversky coefficient). https://doi.org/10.1037/0033-295X.84.4.327
• Probst & Reymond, J. Cheminformatics 10:66 (2018) -- MHFP6 MinHash fingerprint. https://doi.org/10.1186/s13321-018-0321-8
• O'Boyle & Sayle, J. Cheminformatics 8:36 (2016) -- fingerprint similarity benchmark. https://doi.org/10.1186/s13321-016-0148-0
• Butina, J. Chem. Inf. Comput. Sci. 39:747-750 (1999) -- Taylor-Butina clustering. https://doi.org/10.1021/ci9803381
• RDKit, rdFMCS API documentation -- MCS ring-comparison parameter names and semantics. https://www.rdkit.org/docs/source/rdkit.Chem.rdFMCS.html

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