This post describes how I extended the work in my previous post that axiomatizes neutron numbers and nucleon numbers for isotopes that appear in ChEBI as children of atom terms, then materializes isotope (same atomic number), isotone (same neutron number), and isobar (same nucleon number) relationships between them.

While the previous post was directly motivated by needs for the upcoming basis set ontology for NFDI4Chem, extending the axiomizations from partially qualified atoms (with just atomic number) to fully qualified atoms (with both atomic and neutron number) was an obvious next step once I was already familiar with the ChEBI atom hierarchy.

The code and data presented in this post were added in cthoyt/chebi-atomic-numbers-ontology@2 and cthoyt/chebi-atomic-numbers-ontology#3.

Making the ROBOT template

While ChEBI has full coverage through element 117 in the atoms branch, it only has partial coverage of isotopes. I used the following script to produce an initial ROBOT template:

import pandas as pd
import pyobo

elements_df = pd.read_csv("elements.tsv", sep="\t", skiprows=2, header=None)
rows = []
for curie, _, label, number in elements_df.values:
    for child in pyobo.get_descendants(curie) or []:
        full_name = pyobo.get_name(child, strict=True)
        name = full_name.removesuffix("atom").strip()
        _, _, total = name.partition("-")
        if total:
            total = int(total)
            rows.append((child.curie, "class", name, total, total - number))
        else:
            print(f"failed on {child.curie} - {full_name}")

isotopes_df = pd.DataFrame(rows)
isotopes_df.to_csv("isotopes.tsv", sep="\t", index=False)

Except the three isotopes of hydrogen, which each have their own labels, all isotopes’ labels have the following form: <element>-<nucleon number>. Here are few example rows from the full ROBOT template:

curie type label nucleon number neutron number
ID TYPE   SC ‘ChEMROF:nucleon_number’ value % SC ‘ChEMROF:neutron_number’ value %
CHEBI:29236 class protium atom 1 0
CHEBI:29237 class deuterium atom 2 1
CHEBI:29238 class tritium atom 3 2
CHEBI:30218 class helium-3 3 1
CHEBI:37004 class helium-8 8 6
CHEBI:30219 class helium-4 4 2
CHEBI:37003 class helium-6 6 4

This template works the same way I described in the previous post, now using two columns for data value constraints instead of just a single column. Note, the links are added here for convenience, and don’t/shouldn’t actually appear in ROBOT templates.

Interestingly, a related discussion will be taking place at the Ontologies4Chem Workshop 2026. I would like to add the missing isotopes to ChEBI, but this will probably take a while!

Materializing Relationships

I had high hopes that formalizing the atomic number, nucleon number, and neutron number would allow for me to encode inference rules to cover what it means for two fully qualified atoms to be isotopes, isobars, or isotones of each other, for example, using Semantic Web Rule Language (SWRL). However, I had a pretty typical experience that the OWL and semantic web technologies don’t directly support this (IMO) rather obvious use case.

Instead, I opted to write several SPARQL queries that can be used with robot query to manipulate OWL as RDF and add in new object property constraints directly with a command like:

$ robot query \
    --update src/isobar-construct.ru \
    --update src/isotone-construct.ru \
    --update src/isotope-construct.ru

See the full incorporation into the build in the repository’s justfile.

Isotopes

Isotopes are atoms of the same element with different number of neutrons. They can be produced, e.g., through the process of neutron capture. For example, thallium-199 (CHEBI:37805), thallium-201 (CHEBI:37804), thallium-203 (CHEBI:37802), and thallium-205 (CHEBI:37803) are isotopes of thallium.

The following SPARQL materializes isotope relationships between atoms using the ChEMROF:isotope_of relationship.

INSERT {
    ?x rdfs:subClassOf [
        owl:onProperty ChEMROF:isotope_of;
        owl:someValuesFrom ?y
    ] .
}
WHERE {
    ?atom rdfs:subClassOf [
        owl:onProperty ChEMROF:atomic_number;
        owl:hasValue ?atomic_number
    ] ;
    ?x rdfs:subClassOf ?atom .
    ?y rdfs:subClassOf ?atom .
    FILTER(?x != ?y)
}

Isotone

Isotones are atoms of different elements with the same number of neutrons. They can be produced, e.g., through the process of proton capture. For example, nitrogen-17 (CHEBI:36937) oxygen-18 (CHEBI:33815), and fluorine-19 (CHEBI:36940) each have 10 neutrons.

The following SPARQL materializes isotone relationships between atoms using the ChEMROF:isotone_of relationship.

INSERT {
    ?x rdfs:subClassOf [
        owl:onProperty ChEMROF:isotone_of;
        owl:someValuesFrom ?y
    ] .
}
WHERE {
    ?x rdfs:subClassOf [
        owl:onProperty ChEMROF:neutron_number;
        owl:hasValue ?value
    ] .
    ?y rdfs:subClassOf [
        owl:onProperty ChEMROF:neutron_number;
        owl:hasValue ?value
    ] .
    FILTER(?x != ?y)
}

Isobar

Isobars are atoms of different elements with the same number of nucleons. They can be produced, e.g., through the process of beta decay. For example, nitrogen-15 (CHEBI:36934) and oxygen-15 (CHEBI:36932) are isobars with the same nucleon number of 15.

The following SPARQL materializes isobar relationships between atoms using the ChEMROF:nucleon_number relationship.

INSERT {
    ?x rdfs:subClassOf [
        owl:onProperty ChEMROF:isobar_of;
        owl:someValuesFrom ?y
    ] .
}
WHERE {
    ?x rdfs:subClassOf [
        owl:onProperty ChEMROF:nucleon_number;
        owl:hasValue ?value
    ] .
    ?y rdfs:subClassOf [
        owl:onProperty ChEMROF:nucleon_number;
        owl:hasValue ?value
    ] .
    FILTER(?x != ?y)
}

Additional Relationships

While I exhausted the current ChEMROF predicates, there still remain a few that I found while reading up on Wikipedia:

Isodiaphers are atoms with equal neutron excess (i.e., neutron number minus atomic number). They can be produced, e.g., through the process of alpha decay. For example, carbon-13 (CHEBI:36928), nitrogen-15 (CHEBI:36934), and oxygen-17 (CHEBI:33819) are isodiaphers with a neutron excess of 1. I made a pull request to ChEMROF to add this relationship - after some discussion, I might also include an additional SPARQL query.

Mirror nuclei are atoms whose neutron numbers and atomic numbers are swapped. They can be produced, e.g., through the process of positron emission. For example, tritium (CHEBI:29238) and helium-3 (CHEBI:30218) are mirror nuclei.