[1]HildaSandström<EMAIL_ADDRESS>
1]Department of Applied Physics
Aalto University
P.O. Box 11000
FI-00076 Aalto, Espoo, Finland
2]Physics Department, TUM School of Natural Sciences, Technical University of
Munich, Garching, Germany 3]Munich Data Science Institute, Technical
University of Munich, Garching, Germany

# Similarity-Based Analysis of Atmospheric Organic Compounds for Machine
Learning Applications

###### Abstract

The formation of aerosol particles in the atmosphere impacts air quality and
climate change, but many of the organic molecules involved remain unknown.
Machine learning could aid in identifying these compounds through accelerated
analysis of molecular properties and detection characteristics. However, such
progress is hindered by the current lack of curated datasets for atmospheric
molecules and their associated properties. To tackle this challenge, we
propose a similarity analysis that connects atmospheric compounds to existing
large molecular datasets used for machine learning development. We find a
small overlap between atmospheric and non-atmospheric molecules using standard
molecular representations in machine learning applications. The identified
out-of-domain character of atmospheric compounds is related to their distinct
functional groups and atomic composition. Our investigation underscores the
need for collaborative efforts to gather and share more molecular-level
atmospheric chemistry data. The presented similarity based analysis can be
used for future dataset curation for machine learning development in the
atmospheric sciences.

Aerosol particles influence our climate by sunlight reflection and absorption,
and by serving as nuclei for cloud condensation (Pörtner et al., 2022). Beyond
climate impact, aerosol particles affect air quality, causing adverse effects
on human health (Pozzer et al., 2023; Khomenko et al., 2021; Lelieveld et al.,
2020). However, the underlying molecular-level processes involving organic
molecules remain poorly understood, due to the vast number of organic
compounds participating in atmospheric chemistry. This existing gap in
knowledge hampers a comprehensive understanding of particle formation and
growth in different environments (Masson-Delmotte et al., 2021; Elm et al.,
2020). In this paper, we take an initial step to evaluate the potential of
filling this void using machine learning. We propose a molecular similarity-
based analysis to measure the overlap between atmospheric compounds and common
molecular datasets used in machine learning development. By doing so, we can
provide a tool to tailor machine learning models for studies of aerosol
particle formation and the effects human-based activities, like industry and
agriculture, on the formation process. Ultimately, such insights can lead to
more informed decisions regarding air quality and climate change mitigation.

Organic aerosol particle formation is affected by atmospheric composition and
molecular emissions into the atmosphere. Emitted molecules can transform in
reactions initiated by sunlight, to a diverse array of compounds with numerous
functional groups (Bianchi et al., 2019). These reactions are estimated to
produce between hundreds of thousands to millions of atmospherically relevant
molecules (Goldstein and Galbally, 2007; Nozière et al., 2015). Out of this
plethora, an unknown number can form or grow aerosol particles by interacting
with inorganic emissions (Schobesberger et al., 2013; Riccobono et al., 2014;
Ehn et al., 2014), or by themselves (Kirkby et al., 2016). Details of aerosol
particle formation can be uncovered through identification of relevant
atmospheric reactions (e.g., (Peräkylä et al., 2020; Iyer et al., 2023)),
aerosol forming compounds (e.g. (Franklin et al., 2022; Worton et al., 2017;
Hamilton et al., 2004; Thoma et al., 2022)) and cluster formation steps (Elm
et al., 2020).

Mapping aerosol particle formation experimentally is challenging due to the
sheer number of potentially relevant compounds. Moreover, spectrometry based
compound identification with, e.g., mass spectrometers, is hindered by the
absence of curated reference spectra for atmospheric molecules (Franklin et
al., 2022; Worton et al., 2017; Hamilton et al., 2004). The study of particle
growth is another experimental challenge due to the wide range of size scales
involved. Neither aerosol mass spectrometry nor atmospheric pressure chemical
ionization mass spectrometry alone can be used to study the entire particle
growth process (Elm et al., 2020). Thus, with a few exceptions (e.g.,
(Franklin et al., 2022; Worton et al., 2017; Hamilton et al., 2004; Sander,
2015)), curated structure-annotated molecular datasets from experiments are
lacking.

In adjacent chemical disciplines such as metabolomics, these curated molecular
datasets play a crucial role for chemical analysis. For example, they assist
in compound identification either directly (Kind et al., 2013; Sud et al.,
2007; HighChem LLC, Slovakia, ; Sawada et al., 2012; Wissenbach et al., 2011b,
a; Montenegro-Burke et al., 2020; Taguchi and Ishikawa, 2010; Oberacher, 2012;
Hummel et al., 2013; Watanabe et al., 2000; McLafferty and Wiley, 2020; Wang
et al., 2016; Wishart et al., 2022; Wallace and Moorthy, 2023; Weber et al.,
2012; MassBank consortium, 2024; of North America, 2024) or through the
development of machine learning-based identifcation tools (Heinonen et al.,
2012; Dührkop et al., 2015; Brouard et al., 2016; Nguyen et al., 2018, 2019).
These datasets also form the foundation of data-driven analysis platforms
e.g., (Nothias et al., 2020). Moreover, curated datasets contribute to the
construction of machine learning models for quantitative structure-activity
relationships, facilitating large-scale screening of molecular properties for
specific reactions or applications (Kulik et al., 2022). Thus, in order to
reach the full potential of data-driven methods we need such datasets.
Currently, in atmospheric science, computational techniques are bridging the
gap to what can be experimentally observed for atmospheric compounds.

Computational simulations and predictive modeling offer an alternative
approach to studying molecular-level atmospheric chemistry (Figure 1).
Reaction models, such as Gecko-A (Aumont et al., 2005) or the Master Chemical
Mechanism (MCM, http://mcm. leeds.ac.uk/MCM)(Jenkin et al., 1997; Saunders et
al., 2003), can be used to propose likely atmospheric reaction products based
on a set of precursor molecules, reactions and conditions. With such model
simulations, atmospheric molecular datasets like Gecko (Isaacman-Vanwertz and
Aumont, 2021) and Wang (Wang et al., 2017) have been generated. The Wang
dataset (Wang et al., 2017) was constructed using MCM (Jenkin et al., 1997;
Saunders et al., 2003) to simulate the atmospheric degradation of 143
atmospheric compounds by photolysis and reactions with OH, NO3 and O3.
Similarly, the Gecko dataset (Isaacman-Vanwertz and Aumont, 2021) was
generated by simulating the gas phase oxidation of three important atmospheric
compounds: toluene, $\alpha$ \- pinene and decane, using the Gecko-A code
(Aumont et al., 2005; Lannuque et al., 2018). Both the Wang and Gecko datasets
have been used to predict physicochemical properties such as saturation vapor
pressures and partition coefficients (Wang et al., 2017; Lumiaro et al., 2021;
Besel et al., 2023, 2024). In addition, computational simulations of particle
formation have resulted in the Clusteromics datasets containing common acid-
base clusters and their associated thermodynamic and kinetic properties (Elm,
2019, 2021b, 2021a, 2022; Knattrup and Elm, 2022). Thus, simulations and
property prediction can be used to propose important candidate compounds in
organic aerosol formation processes (Figure 1).

Figure 1: Molecular emissions react in the atmosphere to form a diverse array
of compounds, contributing to aerosol particle formation. However, identifying
these compounds remains challenging. Although experiments and field studies
can detect certain compounds in the atmosphere and within the aerosols, they
lack the ability to resolve the identity of a majority of these compounds.
Computational techniques, like reaction mechanistic simulations and property
predictions, aid in describing atmospheric reaction products and their impact
on particulate matter. Enhancing our understanding of these molecular
processes will illuminate the effects of human emissions on cloud formation,
air quality, and climate. Data-driven methods could help advance and
accelerate both the displayed experimental and computational workflow.

In recent years, machine learning methods have shown promise for accelerating
traditional computational and experimental atmospheric chemistry research
(Sandström et al., 2024; Franklin et al., 2022; Besel et al., 2023, 2024;
Berkemeier et al., 2023; Kubečka et al., 2023; Knattrup et al., 2023; Krüger
et al., 2022; Hyttinen et al., 2022; Lumiaro et al., 2021). Yet, practical
applications of data-driven methods in atmospheric chemistry are still
hindered by the aforementioned scarcity of curated experimental datasets. This
raises questions about how machine learning advancements in atmospheric
chemistry can leverage molecular datasets and models from computational
simulations or other chemical disciplines. While this approach is currently
especially important in atmospheric chemistry, it also mirrors similar efforts
of data augmentation in other fields.

Here, our goal is to assess how closely atmospheric molecular data aligns with
comprehensive curated datasets from other chemical domains. We assess the
impact of the current data gap in atmospheric chemistry on the progress of
data-driven methods in the field. We also address the potential for using
datasets and models developed in other tangential chemical domains (e.g.
metabolomics, drug design or environmental chemistry) for transfer learning or
data augmentation in atmospheric chemistry.

In our analysis, we represent atmospheric compounds by the above mentioned
Wang and Gecko datasets. In addition, we include a third atmospheric dataset
composed of quinones, organic molecules that result from oxidation of aromatic
compounds (Tabor et al., 2019; Krüger et al., 2022). Example molecular
precursors to Wang and Gecko, as well as an example quinone compound are shown
in Figure 2.

Figure 2: The three atmospheric datasets used in the comparison of this paper
are: Wang (Wang et al., 2017), Gecko (Isaacman-Vanwertz and Aumont, 2021), and
Quinones (Tabor et al., 2019; Krüger et al., 2022). The Gecko and Wang
datasets contain simulated reaction products starting from a set of precursors
(exemplified in graphic), and the Quinone dataset contains compounds from a
class of oxidation products derived from aromatics called quinones.

We explore the similarity of our atmospheric compound domain to four molecular
datasets used either for molecular property prediction (QM9 and nablaDFT) or
compound identification by mass spectrometry (MassBank Europe and MassBank of
North America, MONA). Both application areas are relevant to machine learning
in molecular atmospheric research (Sandström et al., 2024; Franklin et al.,
2022; Worton et al., 2017; Hamilton et al., 2004; Besel et al., 2023; Lumiaro
et al., 2021; Wang et al., 2017). QM9 (Ramakrishnan et al., 2014) is a
standard benchmark dataset for machine learning in molecular sciences. The
dataset was constructed by selecting molecules with up to nine non-hydrogen
atoms (limited to OCNF) from the GDK-17 database (Ruddigkeit et al., 2012).
GDK-17 is a database consisting of 166 billion enumerated molecules consisting
of up to 17 CNOS and halogen atoms. QM9 includes harmonic frequencies, dipole
moments, polarizabilities, and electronic and thermal energies for the
molecular minimum energy conformation. nablaDFT, instead, was curated from the
Molecular Sets (MOSES) dataset (Polykovskiy et al., 2020) for the purpose of
training models for quantum chemical property prediction (conformational
energy and Hamiltonian). On the other hand, the MassBanks provide data pairs
of molecular structures and their corresponding mass spectra, and have been
used to train and test machine learning models for compound identification
based on mass spectra (Heinonen et al., 2012; Dührkop et al., 2015, 2019). The
MassBanks primarily contain molecules with relevance to metabolomics or
environmental studies. While MassBank Europe contains purely experimental
data, MONA also provides computationally predicted mass spectra. Table 1
summarizes the seven atmospheric and non-atmospheric molecular datasets we use
in our analysis.

Table 1: The molecular datasets used in our similarity analysis comparing
atmospheric compounds to metabolite and drug compounds. The datasets were
downloaded January 8th 2024 in SMILES (Simplified molecular-input line-entry
system) format (xyz in the case of QM9). The reported dataset sizes were
obtained after data preprocessing, which involved removing unparsable SMILES
representations and eliminating duplicate entries.

Name | Data instances |  Type of compound |  Elements |  Exp. data |  Comp. data | Ref.
---|---|---|---|---|---|---
Gecko | 166434 |  Atmospheric |  C, O, H, N |  N |  Y | (Isaacman-Vanwertz and Aumont, 2021)
Wang | 3414 |  Atmospheric |  C, O, N, H, Cl, S, Br |  N |  Y | (Wang et al., 2017)
Quinones | 69599 |  Atmospheric |  C, N, O, H, P |  N |  Y | (Tabor et al., 2019; Krüger et al., 2022)
nablaDFT | 1004918 |  Druglike |  Br, C, N, H, O, S, Cl, F |  N |  Y | (Polykovskiy et al., 2020; Khrabrov et al., 2022)
QM9 | 133885 |  Druglike |  O, C, H, N, F |  N |  Y | (Ruddigkeit et al., 2012; Ramakrishnan et al., 2014)
MONA | 681692 |  Majority metabolites and drug molecules |  H, C, O, Cl, Si, I, S, N, Br, F, Na, P, Co, B, K, Fe, Ge, Sn, Cu, Mg, Pd, Al, Ni, Pt, Cr, Au, Se, Zn, Hg, As |  Y |  Y | (MassBank of North America, 2024)
MassBank Europe | 21772 |  Small molecules relevant to metabolomics, exposomics and environmental samples |  C, O, H, Cl, Si, I, S, N, B, Br, F, P, As, Ge, Sn, Cu, Na, Pd, Al, Co, Ni, Pt, Se, Zn, Hg, K |  Y |  N | (MassBank consortium, 2024)

The paper is organized as follows. We present our molecular similarity
analysis method in Section 1. Section 2 presents the outcomes of our
similarity based comparison. In Section 3 we discuss our findings and in
Section 4 we provide an outlook on how our similarity based analysis can be
used to guide data curation for model development in atmospheric research.

##  1 Methods

###  1.1 Molecular similarity

In our similarity-based analysis, we measure the overlap between atmospheric
compounds and other sets of molecules using the two similarity metrics
t-stochastic neighbor embedding (t-SNE (Maaten and Hinton, 2008), as
implemented in scikit-learn v. 1.2 (Pedregosa et al., 2011)), and the Tanimoto
similarity index (Tanimoto, 1958) as implemented in RDKit version 2022.09.3
(Landrum, 2022). These metrics utilize a molecular representation in the form
of a binary vector (see Molecular descriptors below). Both t-SNE and the
Tanimoto similarity index are standard tools to measure chemical diversity
(see e.g., (Soleimany et al., 2021; Nakamura et al., 2022)) for out-of-domain
applications and uncertainty quantification (Moret et al., 2023; Hirschfeld et
al., 2020; Scalia et al., 2020; Janet et al., 2019; Liu et al., 2018; Sheridan
et al., 2004). t-SNE is an unsupervised machine learning method that embeds
high-dimensional data into lower dimensions while preserving distances from
the higher-dimensional space. The low dimensional embedding can be used to
draw qualitative conclusions about data structure and similarity. We tested
three different perplexity values of 5, 50 and 100. We pre-process the
molecular fingerprints by performing a principal component analysis and select
the 50 first components. The t-SNE clusters depend on a perplexity
hyperparameter which in brief balances the preservation of global and local
aspects during projection from high to low-dimensional space. Thereafter, we
run the t-SNE clustering with random initialization for a maximum of 5000
iterations.

By contrast, the Tanimoto index, $S_{A,B}$, offers a quantitative measure of
similarity. $S_{A,B}$ is calculated as the fraction of present features
(represented by non-zero bits) that are shared compared to the number of
unshared features between molecules A and B, according to

$S_{A,B}=\frac{\sum_{A\cap B}1}{(\sum_{A\cup B}1-\sum_{A\cap B}1)}.$ (1)

If the two molecules A and B share all features, the Tanimoto index equals to
one and if they instead share no features, equals to zero. We note that both
similarity metrics depend on the choice of molecular representation. Here, we
performed the analysis with two types of molecules representations (see
Molecular descriptors below).

We make a statistical analysis of the Tanimoto similarities between pairs of
molecules from different datasets, comparing two sets at a time. Initially, we
select either the Wang dataset or the Gecko dataset as our reference dataset.
Then, we compute the Tanimoto similarity for each molecule in the non-
reference dataset against every molecule in the chosen reference dataset. This
process yields a distribution of pairwise similarities, illustrating the
degree of resemblance between molecules in the non-reference dataset and those
in the reference dataset. Additionally, we calculate the self-similarity
within the reference dataset by determining the Tanimoto similarity for all
pairs of molecules within it. Analyzing the obtained similarity distributions
allows us to assess the relationship between the datasets and understand both
the inter-dataset similarities and internal similarity of the reference
dataset. We interpret our results by introducing a high and low similarity
reference values. This choice is motivated by previous studies of Tanimoto
similarity (Liu et al., 2018; Moret et al., 2023). A similarity of 0.1 or less
is considered to indicate no significant molecular similarity (Liu et al.,
2018). Moreover, a nearest neighbor similarity to the training set greater
than 0.4 has been shown to indicate improved machine learning model prediction
performance (Liu et al., 2018) and confidence (Moret et al., 2023).

###  1.2 Molecular descriptors

As mentioned above, we perform our similarity analysis with two different
molecular representations as implemented in RDKit: the RDKit topological
fingerprint (Landrum, 2022) and the Molecular ACCess System (MACCS)
fingerprint (Accelrys, 2011). The MACCS fingerprint consists of 166 keys
(RDKit’s version has 167 keys as key 0 is an unused dummy key) which represent
different molecular features (e.g., number of rings or atoms of a certain
element, Figure 3b).The topological fingerprint is based on enumeration of
paths in the 2D-molecular structure (Figure 3c). We used default
hyperparameter values for the topological fingerprint (a maximum path length
of seven, two bits per hash, and a fingerprint length of 2048 bits). A wide
variety of fingerprints and molecular representations have been developed in
cheminformatics and more recently in chemistry, physics and materials science
(Himanen et al., 2020; Langer et al., 2022). In this paper, we limit ourselves
to the topological and the MACCS fingerprints out of practicality and
relevance. Both fingerprints have been used in atmospheric chemistry machine
learning applications (Lumiaro et al., 2021; Besel et al., 2023, 2024) and are
therefore pertinent for our comparison.

Figure 3: Pictoral overview of the two molecular fingerprints used in our
analysis. (a) A ball-and-stick representation of o-benzoquinone. (b) The MACCS
fingerprint contains 166 keys which correspond to answers to yes-or-no
questions regarding the presence of molecular features, such as whether there
is a ring and if it is 6-membered (keys 163 and 165), or if there is more than
one oxygen, or more than one double bonded oxygen (keys 136 and 146). (c) The
topological fingerprint encodes paths in the two-dimensional molecular
structure. The panel shows an example path length traversing four atoms.

We performed a molecular structure analysis in RDKit, and the functional group
analysis using the APRL-substructure search program (Ruggeri and Takahama,
2016). For the sake of clarity we chose not to display the following
categories returned by the program (Figures 4 and 5 in Results) due to
redundant information (’ester, all’,’carbon number’), or lack of
correspondence to a functional group (’zeroeth group’, ’C=C-C=O in non-
aromatic ring’, ’aromatic CH’, ’alkane CH’, ’C=C (non-aromatic)’, ’alkene CH’,
’nC-OHside-a’ and ’carbon number on the acid-side of an amide (asa)’).

##  2 Results

In what follows we describe our similarity analysis of atmospheric molecules
and how they compare to other compounds found in public molecular datasets.
Our initial focus is on molecular structure and composition, followed by a
comparison of molecular fingerprint representations. Subsequently, we
illustrate the implications of our analysis in two central applications for
machine learning in atmospheric chemistry: computational property prediction
and the analysis of mass spectra.

###  2.1 Molecular structure comparison

Figure 4 presents a selected number of molecular features for the three
atmospheric datasets included in our work. In Panel a, the molecular size, as
measured by the number of non-hydrogen atoms, varies across datasets,
averaging to approximately 10, 20, and 30 for the Wang, Gecko, and Quinone
datasets, respectively. The non-hydrogen atoms are mainly oxygen and carbon
atoms (see Table 1 and Figure 4b). The high average O:C ratio of the Gecko
molecules suggests that they are appreciably more oxidized than the Wang and
Quinone compounds. The Wang molecules are more saturated, as indicated by
their high H:C ratio. Functional group analysis reveals common oxygen carrying
groups to be hydroxyl, carbonyl, ketone and carboxylic acid groups in all
three sets (Panel c). Furthermore, over half of the Gecko molecules contain
hydroperoxide and nitrate groups, unlike the Wang (approx. less than a third)
and Quinone (absent) compounds.

Figure 4: Molecular structure analysis of the atmospheric molecules in terms
of molecular size as represented by non-hydrogen atom count (a, histogram
normalized so bar heights sum to one), atomic ratios (b), and functional
groups (c, present in $\geq$ 10 $\%$ of dataset).

We now turn our focus to the non-atmospheric molecules which primarily
comprise metabolites and drug-like compounds. Figure 5 compares QM9, nablaDFT,
the MassBank Europe and MONA datasets (Table 1). The molecular size in these
datasets varies over a wider range than in the atmospheric datasets. While
QM9, nablaDFT, and MassBank Europe have a similar size (average 9, 21 and 22,
respectively, as measured by the non-hydrogen atom number) to the atmospheric
compounds, the average MONA compounds are larger (68 non-hydrogen atoms). In
particular, the largest MONA molecules reach up to 230 non-hydrogen atoms.
Such large compounds are not expected to be airborne, except when volatilized
for mass spectrometry analysis, or the like. Compared to the atmospheric
molecules, these datasets are markedly less oxidized and more saturated (low
O:C and high H:C, respectively, Panel b). Oxygen-carrying groups like
hydroxyls, carbonyls, esters, and ethers appear in both atmospheric and non-
atmospheric datasets (Panel c). Functional groups like peroxides and nitrates
are less prevalent in non-atmospheric than in atmospheric compounds. Finally,
amides and amines, the most common nitrogen carrying groups in the non-
atmospheric compounds, are rare in our atmospheric datasets. We discuss
possible causes for these outlined differences in Section 3.

Figure 5: Molecular structure analysis of the non-atmospheric molecules in
terms of molecular size as represented by non-hydrogen atom count (a,
histogram normalized so bar heights sum to one), O:C, N:C, H:C atomic ratios
(b), and functional groups (c, present in $\geq$ 10 $\%$ of dataset).

###  2.2 Molecular fingerprint similarity

The molecular structure comparison presented above can be used to identify
similarities between atmospheric molecules and other compound classes.
However, in machine learning applications, the molecules are often represented
in a different way, e.g, using molecular fingerprints. Below, we make a
similarity comparison using two types of fingerprints: the topological and
MACCS fingerprints, to inspect molecular similarities as they would appear to
a machine learning algorithm.

####  2.2.1 t-SNE clustering

Figure 6: Results of t-stochastic neighbor embedding (t-SNE) analysis of
different atmospheric and non-atmospheric molecular datasets using a
perplexity of 50 and 5000 as the maximum number of iterations. (a) Similarity
of topological fingerprints. (b) Similarity of MACCS fingerprints.

In Figure 6, we compare the atmospheric and non-atmospheric molecules using
t-SNE. In t-SNE plots, the degree of similarity among different molecular
datasets is discerned by the presence of shared clusters. Figure 6a shows
t-SNE clustering using the topological fingerprint as the molecular
representation. What stands out is the encompassing cluster or halo of MONA
molecules, which does not overlap with molecules from the other datasets.
Meanwhile, the nablaDFT dataset forms a central cluster which overlaps with
MassBank Europe as well as MONA molecules – an expected result due to the
presence of drug-like molecules in all three datasets. On the left, a group of
smaller but similar clusters appears, which also include the QM9 and MONA
datasets. Barring a small subset of the Wang and Quinone compounds, these non-
atmospheric datasets share no appreciable clusters with the atmospheric
compounds which instead form their own, separate clusters. We see both
similarities and differences among the atmospheric datasets, as the Gecko and
Wang molecules cluster together, but the Quinones form their own clusters.

In Figure 6b, we have clustered the molecules using the MACCS fingerprint
representation. We observe a similar behaviour as for the topological
fingerprint. However, the outer ring of MONA molecules now also encompasses
portions of the Quinones and Gecko datasets, suggesting that MONA is in part
atmospheric-like when viewed through the MACCS representation. In contrast,
the topological fingerprint produced more distinct clusters with little
overlap between atmospheric and non-atmospheric molecules.

We tested the robustness of our t-SNE analysis with respect to different
perplexity hyperparameter values (Supplementary information, see Figure 10 and
Figure 11 and refer to Methods for a brief explanation). For perplexities 50
and 100, we find consistent outcomes. However, for both fingerprints, one
central cluster forms at a lower perplexity of 5 encompassing molecules from
all datasets. Moreover, an outer cluster emerges of mainly MONA and Gecko
molecules, or a mixture of MONA, Gecko, and Quinones molecules, for the
topological fingerprint (see Figure 10) and MACCS fingerprint (see Figure 11),
respectively. In summary, the qualitative t-SNE analysis separates atmospheric
and non-atmospheric molecules albeit more so with the topological than the
MACCS fingerprint. This finding suggests low similarity across the different
chemical domains.

####  2.2.2 Tanimoto similarity distributions

Next, we conducted a quantitative comparison of molecular fingerprint
similarity using the Tanimoto similarity index which ranges from one for
perfect to zero for no similarity (see Section 1). We utilized either Gecko or
Wang as our reference atmospheric dataset for two separate comparisons. The
compounds in the reference dataset were used to compute pairwise Tanimoto
similarities with molecules from other datasets. This analysis was repeated
using both the topological and MACCS fingerprints. For facilitating the
assessment, we use a high-similarity reference value of 0.4 and a low
similarity reference value of 0.1, as detailed in Section 1.

In Figures 7a-d, we analyzed molecular similarity based on the topological
fingerprint. The figures depict normalized similarity density distributions,
providing insight into the frequency of different similarity values between
compounds in the compared datasets. We will utilize the locations of the
similarity density distribution peaks to discuss trends.

We begin by establishing a similarity relationship among compounds in our
atmospheric datasets. In Panel 7a, the distribution peaks are all below 0.1,
indicating that the Wang compounds hold, as a rule, little resemblance to
other atmospheric compounds. This is also true amongst the Wang molecules
themselves, suggesting that this dataset is diverse. In Panel 7b, we observe
that the Gecko dataset is of intermediate similarity (peak between 0.1 and
0.4) to the Quinones set. Moreover, the Gecko molecules have intermediate
similarity to each other, and are thus less diverse than in the Wang set.

Next, we compare the atmospheric and non-atmospheric dataset similarities
based on the topological fingerprint in Panels 7c and d. Overall, the Wang
compounds have mostly low similarities to nablaDFT, QM9 and MassBank Europe,
albeit with visible fractions of intermediate similarities. Interestingly,
MONA is the only dataset with a similarity distribution peak in the region we
define as intermediate when compared to the Wang dataset. Meanwhile, both MONA
and nablaDFT have their similarity distribution peaks at intermediate values
when compared to Gecko. On the other hand, MassBank Europe and QM9 are on the
boundary between low and intermediate similarity values compared to Gecko.
Notably, when compared to Gecko, the Wang compounds’ similarity distribution
peak is at lower values than those of the non-atmospheric datasets (though the
Wang distribution is more right-skewed to intermediate values). In summary, no
appreciable amount of similarities of topological fingerprints were in our
high similarity region, neither when comparing atmospheric compounds to non-
atmospheric molecules, nor among different atmospheric datasets themselves.

Figure 7: The distribution of pairwise Tanimoto similarities between
topological fingerprints. The Tanimoto similarity distribution between
atmospheric molecules with the Wang (a) and Gecko (b) molecules. The Tanimoto
similarity between the non-atmospheric molecules with the Wang (c) and Gecko
(d) datasets, respectively. Vertical lines mark our high and low similarities
0.1 and 0.4. The histograms were normalized so that the area under their
respective curves integrate to 1.

An analogous comparison for the MACCS fingerprint (Figure 8) revealed similar
trends as those for the topological fingerprint. Overall, the similarity
distributions are less skewed than those of the topological fingerprint.
Moreover, molecules also appear more similar for the MACCS fingerprint. For
instance, the Gecko self similarities now peak in the high similarity region
(>0.4). Moreover, similarity distributions comparing the Quinone and Wang
datasets with Gecko compounds peak at intermediate similarity, with visible
fractions of the distributions at high similarity values. Also the Wang
compounds have appreciably higher similarities to parts of the Quinone
compounds. All non-atmospheric similarity distributions peak at intermediate
values when compared to both Wang and Gecko (Panels 8c-d). In addition, MONA
and MassBank Europe have a visible fraction of high-similarity to the Gecko
and Wang compounds. We also note that the similarity distributions between
atmospheric datasets are broader than between atmospheric and non-atmospheric
compounds.

Figure 8: The distribution of pairwise Tanimoto similarities between MACCS
fingerprints. The Tanimoto similarity distribution between atmospheric
molecules with the Wang (a) and Gecko (b) molecules. The Tanimoto similarity
between the non-atmospheric molecules with the Wang (c) and Gecko (d),
respectively. Vertical lines mark our high and low similarities 0.1 and 0.4.
The histograms were normalized so that the area under their respective curves
integrate to 1.

##  3 Discussion

In Figures 4 and 5, we observe a number of features in the molecular structure
of atmospheric molecules which set them apart from the other compound classes
in terms of functional groups, elemental composition and size (only compared
to MONA). These differences indicate what type of extrapolation a machine
learning model would have to do if transferred from one domain to the other.
In particular, atmospheric oxidation results in a set of organic compounds
with distinct atomic ratios and functional groups that are rarely found in
other domains. These compounds are primarily made up of carbon, hydrogen,
oxygen, and some nitrogen atoms. They stem from volatile emissions, primarily
composed of hydrogen and carbon, with nitrogen and oxygen introduced during
oxidation. Autoxidation, in particular, increases the oxygen content,
resulting in elevated O:C ratios in atmospheric datasets. Oxygen predominantly
incorporates into functional groups such as peroxide, nitrate, hydroxyl,
carbonyl, and ketones.

Our comparison of nitrogen-containing functional groups instead revealed a
lack in amine and amide content in atmospheric compounds compared to the other
compound classes. We note that the atmosphere is known to contain numerous
reduced nitrogen compounds (estimated to be at least hundreds (Ge et al.,
2011)). Yet, these compounds are typically presumed to quickly combine with
acidic molecules or clusters to form aerosol particles in the atmosphere.
Consequently, they are generally excluded from gas-phase oxidation reactions
in simulation models such as MCM or Gecko-A, which explains their absence in
our study. These artificial biases in the computational generation of
atmospheric compounds necessitate scrutiny and awareness when curating
atmospheric datasets and developing models based on such datasets depending on
application area.

Furthermore, the similarity between molecular representations like
fingerprints can unveil whether compounds bear similarity to a machine
learning model that utilizes such representations for molecular predictions.
Here, the t-SNE and Tanimoto-fingerprint-similarity-metrics revealed low
similarities across molecular datasets and compound classes. The t-SNE
analysis showed that the atmospheric compounds, besides a certain similarity
to MONA and nablaDFT, are distinct as seen through the molecular descriptors (
topological and MACCS fingerprint). Moreover, the Tanimoto similarity between
atmospheric and non-atmospheric molecules is low, and as a rule, below our
high-similarity reference value (Figures 7 and 8). These results reinforce the
conclusion that atmospheric compounds should be considered as out-of-domain
for models which have been trained on drug or metabolite like compounds.

Our similarity analysis also revealed that our three atmospheric datasets,
albeit sharing molecular features, such as common functional groups and
relative atomic ratios, contain a diverse array of compounds. Relative to the
comparison of atmospheric and non-atmospheric compounds, we observed that the
three atmospheric datasets had a larger fraction of compounds of intermediate
similarity. However, we observed few to no high Tanimoto similarity pairs
between the three atmospheric datasets for the topological fingerprint, while
a larger fraction of high-similarity pairs emerged for the MACCS fingerprint.
These results could be used in future work to curate a diverse set of
atmospheric molecules for model training, or assess current blind spots in
existing sets.

Moreover, the Tanimoto similarity analysis of compounds from the same
atmospheric datasets (Gecko or Wang) revealed a difference in the degree of
self-similarity which can be traced back to how these datasets were generated.
In Figures 7 and 8, we observed that Gecko molecules exhibit greater
similarity to each other, while the Wang compounds are more diverse. This
difference in dataset homogeneity can be attributed to the distinct generation
processes of the two datasets: Wang was constructed from over 100 precursor
compounds, while Gecko from only three. Moreover, in Gecko, the much higher
average O:C ratio, and lower H:C ratio, is due to inclusion of more oxidation
steps during dataset generation compared to that of Wang.

The analyses conducted using the t-SNE and Tanimoto metrics reveal varying
perspectives on dataset similarity. In the Tanimoto similarity analysis of the
atmospheric datasets, the Gecko molecules have a greater similarity to the
Quinone molecules, whereas in the t-SNE analysis, the Wang molecules appear
more adjacent. These disparities in perceived similarity arise from the
fundamental differences in the algorithms employed by Tanimoto and t-SNE.

Tanimoto analysis only compares molecular features that are present
(represented by ones in the fingerprint) in either molecule, while t-SNE
considers both the absence and presence of features (both ones and zeroes)
when determining adjacency or similarity in high-dimensional space.
Consequently, t-SNE may group molecules based on a common lack of features
which the Tanimoto analysis does not. The absence of shared features does not
necessarily imply true similarity unless the molecular descriptor captures all
molecular structure features, highlighting a limitation of t-SNE for
similarity analysis with molecular fingerprints. This distinction in
methodology can elucidate why the Gecko and Quinone datasets appear relatively
more similar in the Tanimoto analysis compared to the t-SNE analysis, or why
the similarity between the Wang and Gecko datasets is relatively high in t-SNE
but lower in Tanimoto analysis.

Finally, our comparisons in Figure 7 and Figure 8 highlight the varying degree
of atmospheric dataset similarity depending on the molecular descriptor
utilized for representing their structures. As alluded to above, a
comprehensive molecular similarity measure should be based on an encoding of
the entire molecular structure into the descriptor. In this study, we assessed
similarity using both topological and MACCS molecular fingerprints. The
generally low levels of similarity observed across atmospheric datasets could
suggest a potential to develop molecular fingerprints tailored to atmospheric
compounds to better capture their unique molecular structure features. Such
explorations could be the topic of future work.

##  4 Outlook

Atmospheric compounds constitute a vast and diverse chemical space. Their
unique characteristics, coupled with the sheer number of atmospheric
compounds, make collecting experimental or high-accuracy computational data
both time-consuming and challenging. Thus, one major challenge to advancing
data-driven methods in atmospheric chemistry is the current absence of curated
datasets. Therefore, this paper investigated how similar atmospheric molecules
are compared to large and openly available datasets that have been utilized in
machine learning. The current challenges and data gaps elucidated by our
similarity analysis and discussion above can be addressed in future work in a
number of ways.

One primary application of our similarity analysis is to serve as a foundation
for dataset assembly and to fill data gaps for atmospheric chemistry research.
This endeavor will be based on identifying relatively similar datasets from
other chemical domains. Once identified, such molecular datasets can be used
to mend data gaps and to improve machine learning development in atmospheric
research. However, since compounds’ similarity is dependent on molecular
representation and application area, data augmentation needs to be judged on a
case by case basis. As more atmospheric research data, whether computational
or experimental, becomes available, these models can be further refined.
Below, we list additional considerations when supplementing atmospheric
datasets with larger curated ones from different chemical domains.

Currently, the limited number of atmospheric datasets lack comprehensive
coverage of multiple relevant molecular target properties. For example, a
dataset may include vapor pressures but not electronic properties or mass
spectra. This incomplete coverage leads to data gaps, even when combining
multiple datasets, as seen in our investigations.

As already mentioned, to address these cases of missing properties,
incorporating existing datasets or models from other disciplines is an
alternative to gain larger datasets and potentially improve model training.
However, in addition to structural dissimilarity issues, such data
augmentation can be challenging due potential mismatches in target property
coverage. For instance, atmospheric particle formation involves compounds with
low volatility, which can be characterized by properties like extremely low
vapor pressures. These properties often deviate from typical chemistry
contexts. In Figure 9, we have compared vapor pressure distributions between
oxidized atmospheric compounds from a subset of the Gecko dataset and
tabulated values from the Handbook of Chemistry and Physics. This comparison
illustrates the underrepresentation of low-pressure target values in generic
reference datasets.

Figure 9: Computationally predicted saturation vapor pressure of atmospheric
compounds in a subset of the Gecko dataset studied here called GeckoQ at 298 K
(blue), and vapor pressures listed in the CRC Handbook of Chemistry and
Physics (Rumble, 2023) Table entitled ’Vapor Pressure for Inorganic and
Organic Substances at Various Temperatures’ computed at 298 K using the
Clausius-Clapeyron equation. The volatility regions are assigned according to
those defined by (Donahue et al., 2012): ELVOC - extremely low volatile
organic compounds; LVOC - low volatile organic compounds; SVOC - semi volatile
organic compounds; IVOC - intermediate volatile organic compounds; VOC -
organic compounds. We assumed the ideal gas law and a molecular weight of an
average molecule in organic aerosols (200 g/mol (Donahue et al., 2011)).

Moreover, assessing not only the overlap of target values, but also to
carefully examining the target data type is crucial. Each property must be
evaluated in the context of its relevance to atmospheric chemistry and its
potential impact on the overall dataset integration process. Such
considerations become particularly relevant in mass spectrometry applications.
In this study, we compared atmospheric compounds to those found in large mass
spectrometric databanks. This choice was based on the central role of mass
spectrometry in atmospheric chemistry for studying molecular-level processes
(Nozière et al., 2015).

In this study, we have found certain overlaps in terms of molecular
fingerprint similarity between atmospheric compounds and molecules in the
MassBanks (MONA in particular). However, the fragmentation mass spectrometric
techniques commonly employed when generating MassBank data diverge from the
prevailing methods utilized in field campaigns, which predominantly rely on
chemical ionization (Nozière et al., 2015; Sandström et al., 2024). Thus,
future development of machine learning tools could be directed towards
analysis of the mass spectra primarily collected in atmospheric field studies.

A second application of our similarity analysis is for curating new
atmospheric molecular datasets. The persistent challenges to collecting
experimental data for atmospheric molecules suggest that this function
primarily fits as a tool for computational studies. Here, the similarity
analysis could be used to characterize atmospheric compounds into different
types based on their location in chemical space (as defined either by the
molecular features or fingerprint, or both). As mentioned in Section 3, such
characterization can be used to create tailored datasets for analysis, or to
construct data-driven analysis tools based on either diverse or niche groups
of compounds.

Finally, our study underscores that focus should be given to initiatives aimed
at sharing atmospheric molecular data in openly accessible repositories.
Examples of such initiatives have recently been developed, such as the
Aerosolomics project (Thoma et al., 2022). Still, improving unambiguous
identification of atmospheric compounds requires collection of more relevant
reference data. Given the diverse techniques and instruments employed in
atmospheric science, standardizing data will likely remain challenging. Thus,
effective data sharing should include information on data quality and
comprehensive metadata, including instrument versions. This information could
be considered during development of general predictive models, by, for
example, mitigating the impact of instrument versions on data collection and
quality.

In this study, we compared atmospheric molecules to compounds commonly used to
train machine learning models for molecular applications. Assessing molecular
structure similarity provides a straightforward means to determine whether
atmospheric compounds fall within the scope of existing machine learning
methods. This assessment aids in directing the development of machine learning
techniques within this relatively unexplored chemical domain. Here, we focused
on comparing molecules with two molecular descriptors, the MACCS and
topological fingerprints. Analysis of both representations revealed low
similarity between progressively oxygenated atmospheric reaction products and
non-atmospheric molecules made up of primarily metabolites and drug-like
compounds. Notably, the MONA mass spectral library exhibited the highest
similarity to atmospheric compounds. Yet, upon scrutiny of molecular size,
atomic ratios and common functional groups, we observed disparities between
MONA molecules (and other non-atmospheric datasets) and atmospheric compounds.
These discrepancies highlight the need for careful testing and validation
before using models trained on MassBank like datasets in atmospheric
chemistry. The differences we observe between chemical domains and between the
atmospheric datasets can be used to guide future dataset curation for
atmospheric molecular research. Such datasets have laid the foundation for
data-driven method development in other chemical domains. Thus, we hope this
study will motivate the broader atmospheric chemistry community to establish
and contribute to infrastructure for public data-sharing. Closing the current
data gap regarding atmospheric compounds will expedite the shift towards a
data-driven era in molecular atmospheric research. This advancement will
facilitate the development of high-accuracy and high-throughput analysis
tools, offering essential insights into the molecular-level atmospheric
processes that influence both climate and air quality.

The datasets used for this analysis are all freely available from original
publications or the database website (see Table 1). Code and workflow used for
data analysis are freely available at this GitLab repository (
https://gitlab.com/cest-group/atmospheric_compound_similarity_analysis).

##  Appendix A t-SNE analysis at different perplexity values

Figure 10: (a)The t-SNE analysis of the datasets’ topological fingerprints at
perplexity values of 5 (top left), 50 (top right), 100 (bottom left). Figure
11:  The t-SNE analysis of the datasets’ MACCS fingerprints at perplexity
values 5 (top left), 50 (top right), 100 (bottom left).

H.S. - Conceptualization, Investigation, Data Curation, Formal analysis,
Visualization, Validation. Writing - Original draft. P.R - Conceptualization,
Writing - Original draft, Supervision, Funding acquisition.

The authors declare no competing interests.

###### Acknowledgements.

The authors wish to acknowledge T. Kurten and M. Rissanen for insightful
discussions. This study was supported by the Academy of Finland through
Project No. 346377 and the EU COST Actions CA18234 and CA22154. We further
acknowledge CSC-IT Center for Science, Finland and the Aalto Science-IT
project.

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