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

$\mathrm{RCI}(R)=\mathrm{CR}(R)=\frac{\mathrm{SREL}(R)}{\mathrm{SEL}(R)}$
$\mathrm{SREL}(R)$ counts the total number of atom participations across all rings, including duplicate counts if atoms belong to multiple rings. $\mathrm{SEL}(R)$ is the number of unique atoms that appear in at least one ring.
CR (Complexity Ratio) of ring systems R, CR(R) measures how much ring overlap exists. Higher CR(R) indicates more shared atoms between rings, hence greater complexity.

$RCI=\frac{TRS}{nRingAtoms}$
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==2025.03.2
scipy==1.15.1

How to install the tool

QRCI can be installed from pypi (https://pypi.org/project/qrci).

pip install qrci

Usage

from QRCI.QRCI import QRCICalculator, get_QRCIproperties
from QRCI.RCI import RCICalculator

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, TRS=41, nRingAtom=32, nFusedRing=4, SF=1.0857142857142856)

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.