QRCI

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

Quantitative Ring Complexity Index

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

• 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.

$RCI=\frac{TRS}{nRingAtoms}$, where TRS is the total ring size and nRingAtoms is the number of atoms belonging to a ring.

Reference: 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

Installation

The reproducible project environment is defined in environment.yml:

conda env create -f environment.yml
conda activate qrci

For pip-based local development:

pip install -r requirements.txt

For package-only use from PyPI:

pip install qrci

#https://pypi.org/project/useful-rdkit-utils/
pip install useful-rdkit-utils

#https://pypi.org/project/mols2grid/
pip install mols2grid

Current project environment targets:

Python==3.13.2
rdkit==2026.03.4
scipy==1.15.1

Usage

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

smiles = "C1=CCOCc2cc(ccc2OCCN2CCCC2)Nc2nccc(n2)-c2cccc(c2)COC1"

rci_calc = RCICalculator()
print(f"RCI: {rci_calc(smiles):.4f}")

qrci_calc = QRCICalculator(weights="mean")
score_mean = qrci_calc(smiles)
print(f"QRCI(default/mean weights): {score_mean:.4f}")
# QRCI(default/mean weights): 4.0330

mol = Chem.MolFromSmiles(smiles)
props = get_QRCIproperties(mol)
print(props)

Notebooks

• QRCI_calculate_pip_v2.1.ipynb: compact QRCI/RCI calculation example using the pip-compatible package API.
• QRCI_calculate_v1.1.ipynb: extended analysis workflow with QEPPI, SA score, NP score, QED, and plotting.

Data

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

Analysis Helpers

Molecular Standardization

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

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

Spacial Score

from rdkit.Chem.SpacialScore import SPS

sps_score = SPS(mol, normalize=True)

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

SA Score and NP Score

The extended notebook uses RDKit contrib modules:

import os
import sys

sys.path.append(os.path.join(os.environ["CONDA_PREFIX"], "share", "RDKit", "Contrib"))
from SA_Score import sascorer
from NP_Score import npscorer

sascore = sascorer.calculateScore(mol)
fscore = npscorer.readNPModel()
npscore = npscorer.scoreMol(mol, fscore)

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

QEPPI

QEPPI support is provided by the QEPPIcommunity package. The package installs as QEPPI:

from rdkit import Chem
from QEPPI import QEPPI_Calculator, get_qeppi_properties

q = QEPPI_Calculator()
q.read()

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))
print(get_qeppi_properties(mol))

QEPPIcommunity

https://github.com/AspirinCode/QEPPI-community

Figures

License

Code is released under the 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.