QRCI

A Quantitative Ring Complexity Index for Profiling Ring Topology and Chemical Diversity

Quantitative Ring Complexity Index

$\mathrm{QRCI}=\frac{\mathrm{TRS}}{N_{\mathrm{ra}}}\left(1+\frac{N_{\mathrm{fr}}}{N_{\mathrm{r}}+1}\right)+\sum_{r}\left[\frac{360}{360-\alpha_{\mathrm{ideal}}(\ell_{r})}\cdot\frac{1}{\ell_{r}}\cdot\lambda_{M}(\ell_{r})\right]+\frac{\sum W_{i}\cdot D_{i}}{\sqrt{N_{\mathrm{ra}}\cdot\mathrm{TRS}}}+\frac{\log(N_{\mathrm{ta}})}{N_{\mathrm{r}}+1}+W_{m}\cdot\frac{N_{\mathrm{mr}}}{N_{\mathrm{r}}+1}$

• TRS (Total Ring Size): Sum of all ring sizes.
• $N_{\mathrm{ra}}$: Total number of atoms in all rings.
• $N_{\mathrm{r}}$: Total number of rings
• $N_{\mathrm{fr}}$ (Fused Rings): Count of rings sharing atoms or bonds.
• $N_{\mathrm{ta}}$: Total number of atoms
• $N_{\mathrm{mr}}$: total number of macrocycles
• $W_{m}$: Weight for macrocycle descriptors.
• $W_{i}$: Weight for topological descriptors.
• $D_{i}$: Topological ring diversity descriptor.

Ring Complexity Index

$RCI=\frac{TRS}{nRingAtoms}$
where TRS is the total ring size and $nRingAtoms$ is the number of atoms belonging to a ring. Ref: Gasteiger, J., & Jochum, C. (1979). An Algorithm for the Perception of Synthetically Important Rings. Journal of Chemical Information and Computer Sciences, 19(1), 43–48. https://doi.org/10.1021/ci60017a011

Distribution of RCI for approved drugs of DrugBank

Requirements

Python==3.13.2
rdkit==2024.09.6
scipy==1.15.1

Data

• DrugBank
• iPPI-DB
• COCONUT: the COlleCtion of Open NatUral producTs
• ChEMBL35
• PubChem

Molecular Standardization

https://www.rdkit.org/docs/source/rdkit.Chem.MolStandardize.rdMolStandardize.html

https://github.com/rdkit/rdkit/blob/master/Docs/Notebooks/MolStandardize.ipynb

QRCI calculation

QRCI/QRCI_calculate_v1.1.ipynb

Example:Pacritinib

qrci_calc = QRCICalculator(weights='mean')
score_mean = qrci_calc('C1=CCOCc2cc(ccc2OCCN2CCCC2)Nc2nccc(n2)-c2cccc(c2)COC1')
print(f"QRCI(default/mean weights): {score_mean:.4f}")
#QRCI(default/mean weights): 4.0330

***************************************************************************************
mol = Chem.MolFromSmiles('C1=CCOCc2cc(ccc2OCCN2CCCC2)Nc2nccc(n2)-c2cccc(c2)COC1')
props = get_qrci_properties(mol)
print(props)
#QRCIproperties(nAromHetero=1, nAromCarbo=2, nAliHetero=2, nAliCarbo=0, nSatHetero=1, nSatCarbo=0, nMacrocycles=1)

Distribution of QRCI for approved drugs of DrugBank

Analysis

Spacial Score

rdkit.Chem.SpacialScore.SPS(mol, normalize=True)

https://rdkit.org/docs/source/rdkit.Chem.SpacialScore.html

https://github.com/frog2000/Spacial-Score

SAscore

#Calculating SAscore
import sascorer
sascore = sascorer.calculateScore()

https://greglandrum.github.io/rdkit-blog/posts/2023-12-01-using_sascore_and_npscore.html

QED

from rdkit import Chem
from rdkit.Chem import QED

smiles = "C=CCN1CC(C(=O)N(CCCN(C)C)C(=O)NCC)C[C@@H]2c3cccc4[nH]cc(c34)C[C@H]21"
mol = Chem.MolFromSmiles(smiles)

qed_score = QED.qed(mol)
print(f"QED Score: {qed_score:.3f}")
#QED Score: 0.605

https://www.rdkit.org/docs/source/rdkit.Chem.QED.html#module-rdkit.Chem.QED

QEPPI

quantitative estimate of protein-protein interaction targeting drug-likeness

#Calculates QEPPI
q = ppi.QEPPI_Calculator()
print("QEPPI.model LOADING...")
q.load("./QEPPI/QEPPI.model")

smiles = "C=CCN1CC(C(=O)N(CCCN(C)C)C(=O)NCC)C[C@@H]2c3cccc4[nH]cc(c34)C[C@H]21"
mol = Chem.MolFromSmiles(smiles)
print(q.qeppi(mol))

https://github.com/ohuelab/QEPPI

Others

Drug Data From the ChEMBL

https://github.com/PatWalters/practical_cheminformatics_tutorials/tree/main/misc

Trend of RCl/QRCl Over Time (approved drugs of ChEMBL 35)

License

Code is released under MIT LICENSE.

Cite

• Gasteiger, J. and Jochum, C., 1979. An algorithm for the perception of synthetically important rings. Journal of Chemical Information and Computer Sciences, 19(1), pp.43-48.
• Ertl, P., Schuffenhauer, A. Estimation of synthetic accessibility score of drug-like molecules based on molecular complexity and fragment contributions. J Cheminform 1, 8 (2009). https://doi.org/10.1186/1758-2946-1-8
• Krzyzanowski, A., Pahl, A., Grigalunas, M., & Waldmann, H. (2023). Spacial Score─A Comprehensive Topological Indicator for Small-Molecule Complexity. Journal of medicinal chemistry, 66(18), 12739–12750. https://doi.org/10.1021/acs.jmedchem.3c00689
• Wang J, Xu K, Ma T, Zhang X, Ma P, Li C, et al. A Quantitative Ring Complexity Index for Profiling Ring Topology and Chemical Diversity. ChemRxiv. 2025; doi:10.26434/chemrxiv-2025-mlqwl-v2 This content is a preprint and has not been peer-reviewed.