A kinetic box model was applied to a compilation of multiple experimental data of ROS production , as well as DTT consumption and AA oxidation in the presence of transition metal ions (TMIs: Fe(II), Fe(III), Cu(II), and Mn(II)), quinones (9,10-phenanthrenequinone (PQN), 1,4-naphthoquinone (1,4-NQN), and 1,2-naphthoquinone (1,2-NQN)) as well as organic components (Org). These species were selected due to their abundance in ambient particulate matter, their ability to form ROS, and their high reactivity in OP assays.

Figure  illustrates the chemical reaction mechanism used in this study, which integrates and builds on earlier studies investigating the oxidation of AA and DTT . The mechanism includes the production of ROS by TMIs, which then oxidize both AA and DTT. Furthermore, TMIs themselves are also able to oxidize AA and DTT. Figure A shows the main reaction pathways for ROS formation and interconversion: reduced TMIs and quinones catalyze a redox cascade from O2 to superoxide (O2⚫-) and hydrogen peroxide (H2O2). Reduced TMIs react with H2O2, leading to the formation of hydroxyl radical (⚫OH) through Fenton and Fenton-like reactions. Figure B shows that AA can cycle the oxidized forms of the TMIs (Fe(III), Cu(II), Mn(III)) and quinones (Q) back to their reduced forms (Fe(II), Cu(I), Mn(II), SQ). ROS species also react with AA forming the ascorbyl radical (AA⚫). AA⚫ forms dehydroascorbic acid (DHA) through disproportionation. DHA can undergo hydrolysis reaction to produce 2,3-diketogulonic acid (DKG). Figure C shows the oxidation of DTT in the presence of ROS, TMIs, and quinones. We also incorporated the mechanism proposed by , in which oxidation of DTT in the presence of Cu involves the formation of a Cu–DTT complex. Figure D shows the main pathway for ROS formation from organic aerosol (OA). In this study, we group OA from diverse primary (cooking, traffic, biomass burning etc.) and secondary (from biogenic and anthropogenic precursors) sources into a single species, Org, which can react as aliphatic or aromatic compound (RH) and contains a fraction of redox-active organic hydroperoxides (ROOH). The labile organic peroxides can decompose to form ⚫OH and RO⚫ radicals. These radicals can abstract an H atom from RH and can react with ROOH, yielding an alcohol and either a hydroperoxyl radical (HO2⚫) or a RO2⚫ radical, respectively. In the presence of Fe(II), the hydroperoxide groups can undergo Fenton-like reactions, leading to the heterolytic cleavage of the O–O bond in two ways: one leads to the formation of the ⚫OH radical, while the other forms the RO⚫ radical. The ⚫OH, RO⚫, and RO2⚫ radicals can react with both AA and DTT. KM-OP is an autogenerated model script based on a user-supplied chemical mechanism and consists of a system of differential equations, which are solved iteratively using the stiff differential equation solver ode23tb in Matlab, which has performed well in the past in complex kinetic models .

Since some of the kinetic rate coefficients of the chemical reaction mechanism are unknown or uncertain, we inferred them by fitting the kinetic model to experimental observations (inverse modeling). To this end, we set up the kinetic model to mimic the detailed experimental protocols from each experiment. A description of details of each model simulation can be found in Sect. S3.1–S3.7 in the Supplement. In brief, the chemical mechanism was optimized using experimental data from , , , , , and .

Inverse modeling was performed using the Monte Carlo Genetic Algorithm MCGA,. MCGA consists of two steps. The first step is a Monte Carlo search in which model parameters are randomly sampled within predefined boundaries. The globally best-fitting parameter sets are then fed into the starting population of a genetic algorithm, in which they are optimized through processes mimicking survival, recombination, and mutation in evolutionary biology. Ideally, a unique fit would result from global optimization; however, the system investigated in this study is under-determined, since it contains a large number of non-orthogonal parameters . Therefore, it is more beneficial to identify an ensemble of adequately well-fitting parameter sets and analyze the corresponding kinetic model solutions. The distributions of the optimized rate coefficients across all the parameter sets are shown in Fig. S1 in the Supplement. In this study, we apply MCGA, generate an ensemble of parameter sets, and analyze the corresponding kinetic model solutions collectively.

The chemical mechanism of organic components, Org, was not fitted, but ported from the literature . For validation, we compare the model results to DTT activity and radical production rate measured and compiled by and , respectively. Table S1 in the Supplement provides a list of all the chemical reactions used in this study and their corresponding rate coefficients.

We extrapolate the findings from the laboratory experiments to field data with detailed PM chemical characterization and source apportionment outputs at three different sites across Europe as described above in Sect. 2.3: a suburban background station near Paris, France SIRTA,; an urban background site in Grenoble, France Les Frênes,; and a roadside summer, and urban background site (winter, ) in London, United Kingdom. No fitting of model parameters was performed to match the field data (forward modeling), i.e., the model developed using the laboratory data was simply applied on the chemical composition data measured in the field, including the water-soluble fractions of TMIs, organics, and if available, quinones. While water-insoluble PM may increase total OP via surface reactions , these processes are not represented in KM-OP. Organics and quinones were assumed to be fully soluble. The TMIs are initialized as Fe(II), Cu(II), and Mn(II) in the model, and we find that their initial oxidation state has nearly no effect on OP in the calculations due to their low concentrations and fast redox-cycling. We assume an organic peroxide content in organic aerosol of 50 % . Offline OPDTT and OPAA were measured at the Paris and Grenoble sites, while online OPAA was measured in London. At the London site, OPAA was determined by the formation of dehydroascorbic acid (DHA), while at the two sites in France, OPAA was determined as consumption of ascorbic acid. For clarity, the London data will be referred to as OPDHA, while the data from France will be referred to as OPAA.

Note that in the filter-based assays used for this study, there is an extraction step during which the filter samples are shaken at physiological conditions (pH 7, 37.5 °C) in a simulated lining fluid, in the absence of a probe reactant species. While a longer extraction time increases the amount of dissolved material and thus, e.g., DTT activity , it may also lead to loss of ROS as a result of aqueous-phase chemistry . As the extraction kinetics and aqueous-phase chemistry during extraction are less well studied, the extraction period is not explicitly considered in KM-OP and simulations start with addition of the probe species. OP values may depend on the solvent medium used in the assay; however, previous studies suggested that at low PM concentrations, differences between solvents are reduced . This effect is not explicitly accounted for in the current model and may contribute to inter-site variability.

Figure  outlines the methodology used in this study. To summarize, we fit a model to laboratory data in order to infer the rate coefficients of the chemical reaction mechanism (inverse modeling step). After optimizing the model with the laboratory data and inferring the unknown or uncertain reaction rate coefficients, we apply the model using ambient chemical composition data as input, with no further fitting to predict and estimate the OP (forward modeling step).

Figure A shows H2O2 production curves of Cu(II), 1,2-NQN, 1,4-NQN and PQN in a buffered surrogate lung lining fluid containing ascorbic acid, glutathione, uric acid, and citric acid. The experimental data from (markers) is compared with KM-OP model results. The lines depict the mean of an ensemble of fits (N=15) to all the laboratory data presented in this study, and the shadings denote two standard deviations around the mean. Generally, production of H2O2 increases as the metal and quinone concentrations increase. For the quinones, the increase of H2O2 production is linear, with 1,2-NQN showing the highest reactivity.

The mechanism of H2O2 formation by quinones (Q) in KM-OP is outlined in Fig. A and B and listed below. Briefly, AA reduces quinones to semiquinones (SQ), and in turn is converted into the ascorbyl radical (AA⚫, Reaction R1). The semiquinones then reduce O2 to superoxide (O2⚫-, Reaction R2). A second equivalent of AA then reacts with HO2⚫ to H2O2 (Reaction R3), also producing another AA⚫. SQ and AA⚫ also react with O2⚫- to form H2O2 (Reactions R4 and R5). Figure S2 details the main sources of H2O2 in the simulations. As we do not assume further reaction of H2O2 with quinones or semiquinones, H2O2 formation increases linearly with quinone concentrations. R1AA+Q→AA⚫+SQR2SQ+O2→Q+O2⚫-R3AA+HO2⚫(+H+)→AA⚫+H2O2R4SQ+O2⚫-(+2H+)→Q+H2O2R5AA⚫+O2⚫-(+2H+)→DHA+H2O2R6AA+Cu(II)→AA⚫+Cu(I)R7O2+Cu(I)→O2⚫-+Cu(II)R8O2⚫-+Cu(I)(+2H+)→H2O2+Cu(II)R9H2O2+Cu(I)→⚫OH+OH-+Cu(II)R10AA+Fe(III)→AA⚫+Fe(II)R11O2+Fe(II)→O2⚫-+Fe(III)R12O2⚫-+Fe(II)(+2H+)→H2O2+Fe(III)R13H2O2+Fe(II)→⚫OH+OH-+Fe(III)R14H2O2+AA→⚫OH+OH-+AA⚫

Conversely, the production of H2O2 increases non-linearly with Cu(II) concentration, with the production rate of H2O2 plateauing at higher Cu concentrations. The H2O2 formation mechanism of Cu in KM-OP is outlined in Fig. 1A and above. Cu(II) is reduced to Cu(I) by AA (Reaction R6). Cu(I) then reacts with O2, forming O2⚫- (Reaction R7). At low Cu concentrations, H2O2 production mostly occurs through the reaction of AA with HO2⚫ (Reaction R3), while at higher concentrations of Cu, the reaction of Cu(I) with O2⚫- is most important (Fig. S3, Reaction R8). The non-linearity in H2O2 production in the presence of Cu stems from the destruction of H2O2 through the Fenton-like reaction of H2O2 with Cu(I), leading to a steady state of H2O2 production and destruction.

As experimental data for H2O2 production with Fe(II) alone is not available, we fitted published time series data that contain 20 nM 1,2-NQN at varying Fe(II) concentrations (Fig. B). Figure B illustrates that H2O2 concentration decreases as Fe(II) concentration increases. As shown in Fig. B, H2O2 destruction can equalize H2O2 production in aqueous Fe solutions. Fe(II) reacts rapidly with H2O2 via the Fenton Reaction (R13), leading to a very low steady state concentration of H2O2 (dark yellow solid line) and significant ⚫OH radical production (Fig. C).

Figure C shows the ⚫OH production-response curve for Cu(II) and Fe(II) in buffered surrogate lung lining fluid containing ascorbic acid, glutathione, uric acid, citric acid, and sodium benzoate, which is used as an ⚫OH probe. The production of ⚫OH increases non-linearly with the concentration of Cu(II), with ⚫OH production plateauing at higher Cu concentrations. At low Cu concentrations, ⚫OH production occurs mostly through the reaction of AA with H2O2 (Reaction R14), while at higher concentrations of Cu, the pseudo-Fenton reaction of Cu(I) with H2O2 (Reaction R9) is the most important (Fig. S4).

Figure A shows the modeled concentration-time profiles of ascorbic acid in the presence of Cu(II), Fe(II), and 1,4-NQN. The model output shows agreement with the published experimental data within experimental uncertainty . Here, the concentrations of Cu(II), 1,4-NQN, and Fe(II) were 0.5, 1, and 5 µM, respectively. Despite a lower concentration of Cu(II) compared to Fe(II) and 1,4-NQN, AA decays quickest in the presence of Cu. In the model, this is due to the higher reaction rate coefficient of the redox reaction between AA and Cu(II) compared to the reaction with Fe(III) (Table S1, Reactions SR16 and SR33). Note that the direct reactions of the TMIs with AA dominate over the reactions of ROS with AA. For Cu, while H2O2 concentration is higher than the concentration of Cu(II) (Fig. S5A), the best-fitting rate coefficient of AA with Cu(II) is three orders of magnitude higher than the best-fitting rate coefficient of AA with H2O2 (Table S1, Reactions SR33 and SR48), leading to an over 700 times larger turnover of AA with Cu. For Fe, the concentration of Fe(III) is higher than the concentration of ROS (Fig. S5B), and the rate coefficient of AA with Fe(III) is also higher than the rate coefficient of AA with H2O2 (Table S1, Reactions SR16 and SR48), leading to an over 4000 times larger turnover of AA with Fe under these conditions. As shown in Fig. A and mentioned above, AA reduces metals and quinones by redox cycling from their oxidized to reduced forms. The reduced metals and semiquinone can react with oxygen, leading to the formation of O2⚫-, which in turn is another reaction partner for AA. As shown in Fig. B and outlined below, in the KM-OP mechanism, the oxidation of AA leads to the formation of dehydroascorbic acid DHA; . Note, while the KM-OP mechanism includes a redox reaction for the reaction of AA and metals, a catalytic reaction mechanism has also been proposed in the literature . Figure B shows DHA concentrations as a function of Cu(II) and Fe(II) concentrations, and compares the model output to experimental data from . We find a linear increase in DHA concentration with increasing Fe(II) concentration. The largest source of DHA is the disproportionation reaction of the ascorbyl radical (AA⚫), which can be produced by the redox reaction between AA and TMIs such as Fe and Cu ions (Fig. S6). On the contrary, with Cu, the DHA concentration increases non-linearly and saturates at higher Cu(II) concentrations because DHA formation is second order with respect to AA⚫, however, DHA loss is a (pseudo-)first-order reaction in the mechanism: R15AA⚫+AA⚫→DHA+AAR16DHA(+H2O)→DKG

Figure A, B, and D show the rates of DTT loss at various concentrations of TMIs and quinones as measured by and . DTT consumption generally increases with increasing TMI and quinone concentrations, and overall, the experimental data is well captured by the model. Figure A shows that DTT oxidation in the presence of Cu(II) and Mn(II) is faster than in the presence of Fe(II). There is a linear increase in the rate of DTT loss with increasing Fe concentration. As shown in Fig.  and outlined below, in the KM-OP mechanism, DTT reduces Fe(III) to Fe(II) and in turn forms a thiyl radical . The experimental data shows a slightly higher rate of DTT loss for Fe(II) compared to Fe(III), which is not captured by the model. This may be related to Fe(III) forming precipitate in the presence of phosphate buffer , which is currently not considered in the model.

Figure B shows oxidation rates of DTT in the presence of Mn(II) as measured by . The data show that the rate of DTT loss increases non-linearly and eventually plateaus at higher Mn(II) concentrations. The largest sink for DTT at low Mn(II) concentrations is HO2⚫ (Reaction R18), while at higher concentrations, it is Mn(II) and Mn(III) (Reaction R21, Fig. S7A). This occurs because the rate coefficient of HO2⚫ with DTT is larger than the rate coefficients of Mn(II) and Mn(III) with DTT. The non-linearity stems from the fact that at high Mn(II) concentrations (>20 µM), DTT is depleted by more than 50 % (Fig. S7B), leading to an apparent slow down of the kinetics. Moreover, at higher Mn(II) concentrations, HO2⚫ undergoes a self-reaction to form H2O2, and also reacts with Mn(II) to form MnO2+ (Fig. S7C), where the latter then accumulates in the kinetic model (Fig. S7D).

Figure C shows the temporal evolution of the DTT concentration at two different concentrations of Cu(II) from the study of . The data shows that the DTT decays faster at higher Cu(II) concentrations. The loss of DTT due to Cu(II) is non-linear over time (Fig. A). As shown in Fig. , in KM-OP, the oxidation of DTT in the presence of Cu(II) involves the formation of a [Cu2+(DTT2-)2]2- complex, which has been identified as a catalyst for DTT oxidation . The DTT loss rate increases non-linearly with increasing Cu(II) concentrations because the largest sink of DTT is the formation of [Cu2+(DTT2-)2]2- (Reaction R23, Fig. S8), which is second order with respect to DTT, while the loss of [Cu2+(DTT2-)2]2- is first order (Table S1, Reaction SR63).

Figure D illustrates the oxidation rates of DTT in the presence of quinones, as measured by . Figure E shows that PQN is the most reactive quinone examined in this study, followed by 1,2-NQN and 1,4-NQN, respectively. The kinetic model simulations show that quinones are reduced by DTT, resulting in the formation of the semiquinone radical and a thiyl radical (Reaction R24), both of which react with molecular oxygen to form HO2⚫ . We find that at higher 1,2-NQN and PQN concentrations, the main sink of DTT is the quinone itself (Reaction R24), while at lower concentrations of quinones, the main sink is HO2⚫ (Reaction R18, Fig. S9A and C). For 1,4-NQN, we find a rate coefficient with DTT that is slower compared to the rate coefficient of PQN and 1,2-NQN. Thus, in the presence of 1,4-NQN, the main sink for DTT is always HO2⚫ (Fig. S9B). While the inferred reaction rate coefficient of HO2⚫ with DTT (Reaction R18) is larger than the rate coefficient of PQN and 1,2-NQN with DTT (Reaction R24), the HO2⚫ concentration does not increase linearly with the concentration of quinones, and therefore the rate of reaction of PQN and 1,2-NQN with DTT becomes dominant at high PQN and 1,2-NQN concentrations. The DTT loss rate increases non-linearly with increasing quinone concentration because at higher concentrations of 1,2-NQN and PQN, the DTT concentration decreases by more than 50 % at the end of the model simulation (Fig. S10), leading to an apparent slow down of the kinetics. R17⚫OH+DTT→DTT⚫+H2OR18HO2⚫+DTT→DTT⚫+2OH-R19H2O2+DTT→DTT⚫+H2O+OH-R20Fe(III)+DTT→Fe(II)+DTT⚫R21Mn(III)+DTT→Mn(II)+DTT⚫R22Cu(II)+DTT→[Cu2+(DTT2-)]+2H+R23[Cu2+(DTT2-)]+DTT→[Cu2+(DTT2-)2]2-+2H+R24Q+DTT→SQ+DTT⚫

To test the chemical mechanism involving organic components (Fig. D), KM-OP results are compared to DTT data presented in and radical production rate presented in . measured the formation of ⚫OH, RO^⚫, HO2⚫, and R^⚫ radicals from SOA using electron paramagnetic resonance (EPR) spectroscopy. Figure A shows the radical production rate of SOA in aqueous solution. We find a good agreement with the experimental data for isoprene and β-pinene SOA when using an organic hydroperoxide content within SOA of 10 %. For naphthalene SOA, we are able to capture the experimental data by lowering the organic hydroperoxide content to 3 % .

Figure B shows DTT activity using the same model parameters. The model results align well with the DTT activity from a majority of the chamber-generated SOA (solid line in Fig. B), including biogenic and anthropogenic precursors (isoprene, α-pinene, β-caryophyllene, pentadecane, m-xylene). However, the model underestimates the DTT activity of naphthalene SOA, which is found to be considerably higher than all other SOA. When assuming that 5 % of naphthalene SOA is 1,2-naphthoquinone , the model captures the measured DTT activity (dotted line). Note that this inclusion of naphthoquinone does not affect the results previously shown in Fig. A due to the lack of a reductant to induce redox cycling of the quinone in these experiments. However, this mechanistic explanation demands further investigation in the future. Thus, in light of the remaining uncertainties, because naphthalene SOA likely contributes only a small fraction to the total organic aerosol mass, and for simplicity, we will not differentiate between biogenic and anthropogenic organics when modeling ambient data.

further find a higher DTT activity of organic components from field studies compared to laboratory chamber measurements. As these organics are likely more aged , we increase the organic hydroperoxide content to 50 %, which in turn increases the concentration of ⚫OH and RO⚫ radicals (Reaction R25), and find that the data are generally well-captured by the model (dashed line). Note that, the DTT assay reported in protocol from uses EDTA to chelate transition metals. have shown that including EDTA when performing OP assay reduces the DTT activity from both transition metals and quinones. In the model, we account for the effects of EDTA by assuming that its addition reduces the original DTT activity to one-tenth of the initial value . R25ROOH→⚫OH+RO⚫R26⚫OH+ROOH→HO2⚫+ROHR27RO⚫+ROOH→RO2⚫+ROHR28⚫OH+Org→R⚫+H2OR29RO⚫+Org→R⚫+ROHR30AA+RO⚫→AA⚫+ROHR31AA+RO2⚫→AA⚫+ROOHR32DTT+RO⚫→DTT⚫+ROHR33DTT+RO2⚫→DTT⚫+ROOH

Figure  shows the correlation scatter plot of experimentally-determined and simulated OP for particulate matter samples collected at three different sites across Europe (Grenoble, Paris, and London). Overall, we find good agreement between model simulations and field data as evaluated by correlation coefficients, mean squared logarithmic errors (MSLE), and relative biases (bias, Sect. S3.8). For the Grenoble site (Fig. A and D), the model shows slightly better correlation (R2=0.78-0.82, MSLE=0.03-0.06) with the data compared to the Paris site (Fig. B and E, R2=0.57-0.82, MSLE=0.05-0.08) for both assays. We find that using total organic aerosol mass as input for the species “Org” in the model leads to a much better agreement with the field data than using only the fraction of SOA derived from source apportionment (Fig. S11), which suggests that organic aerosol from sources such as biomass burning, traffic, or bioaerosols, must have a significant effect on OP. Nonetheless, the model overall slightly underestimates OP in Grenoble (bias: -8.3% to -5%) and overestimates OP in Paris (bias: 13.3 %–38.7 %). This deviation of OP likely stems from the limited number of chemical species in the model, which considers only three TMIs, three quinones, as well as organic compounds, and at present does not consider other chemical species such as Zn, surface-chemistry on the insoluble fraction of PM (e.g., elemental carbon-containing particles from combustion), or possible synergetic and antagonistic effects in mixtures , which all may also contribute to OP. Furthermore, the model does not currently differentiate between biogenic and anthropogenic SOA, the latter of which has shown to be particularly OP-active in the case of naphthalene SOA (Fig. B).

For the London sites (roadside location MY in the summer, Fig. C, and urban background location HOP in winter, Fig. F), the modeled OP values generally fall within the same order of magnitude as the field data. For the HOP site, the correlation between model and field data is high (R2=0.76), but the model generally underestimates OPDHA (MSLE=0.11, bias: -34.7%). In contrast, the model shows less bias (14.2 %), but no correlation with the field data at the MY site (R2=-0.06, MSLE=0.15).

Overall, the model captures the field data at the French sites better than at the London site. This could be because some OP-active components of PM are short-lived (e.g., labile organic compounds), and while they would affect the online OP assay employed at the London site, likely contributing to more than 50 % of the online OPDHA , such compounds may not have influenced the filter-based laboratory assessment of the OP activity of organic compounds used for training of the model. This may explain why the sites using filter-based, offline, OP assays show better correlation with the model. Peroxides constitute a significant fraction of atmospheric OA, but their abundance varies widely depending on precursors and oxidative processing . A sensitivity analysis over a ROOH fraction range of 20 %–80 % of total OA indicates that the model underestimates OP at an ROOH fraction of 20 % and overestimates OP at an ROOH fraction of 80 % (Figs. S12 and S13). The overall trends and correlations with field measurements, however, remain robust. We note that the simulations with 80 % ROOH fraction resolve the underestimation of the London winter data, which uses online-OP instrumentation, by improving the bias from -34.7% to -8.3%, suggesting the presence of short-lived organic species that are only captured using the online instrument . Note that, no site-specific solubility measurements were available and we used solubility factors from the literature, which introduces additional uncertainty when modelling the London datasets. A sensitivity analysis accounting for water-insoluble organic species showed reduced absolute OP values, but consistent overall trends and site-to-site comparisons (Fig. S14). Moreover, the compositional analysis for the London dataset presented in does not contain quantitative data for quinones, which may be another reason for the underestimation of OP, especially in the winter. The poor correlation of the summer data may be due to varying degrees of photochemical aging, leading to compositional changes in the organic aerosol fraction that are not considered in the model. Additional analysis with meteorological parameters for the summer data shows some variability in model performance (Fig. S15). Model disagreement occurs at two distinct time periods. The analysis shows a slight tendency of the model to underestimate OP at lower wind speeds and exhibits a slight positive bias with increasing temperature. However, these effects are not consistent across the dataset, and no clear or systematic trends emerge. While such nuances suggest potential influences of meteorological conditions on OP, it remains unclear how these effects could be incorporated into an improved model parameterization. Highly oxygenated organics may produce more ROS directly, and may also act as ligands e.g., oxalate, enhancing metal solubility. Previous studies have shown that certain ligands, such as EDTA, can enhance Fenton-like reactivity , but other studies have demonstrated that ligand complexation can reduce OP in DTT assays . Thus, the influence of metal–ligand interactions on OP warrants further experimental investigation before incorporation into kinetic models.

To gain insight into which PM components are the key drivers of OP, we perform model sensitivity studies for each assay and each PM constituent. Figure  shows the contribution of the model species towards OPAA, OPDTT, OPOH, and OPH2O2 using the average chemical composition measured in Grenoble (Table ). The results for the other sites are shown in Figs. S16–S18. The white bar labelled “Mixture” shows the default model result with all pollutants included, as reference. The “Single pollutants” bar shows a sensitivity study that sums the OP values calculated in model runs that only contain a single PM component, determining their direct, solitary, first-order effect. The colored bar segments represent the effect of each PM component. The “Shapley values” bar is a sensitivity study that uses the Shapley method , to determine the total effect of individual PM components by determining their average marginal contribution across all possible combinations of PM component mixtures (unary, binary, tertiary etc.). The Shapley values indicate whether a PM component increases or decreases the OP of the mixture, including interaction effects. To better understand how contributions of individual PM components arise, their total Shapley values for each site are further decomposed by interaction order in Figs. S19–S22.

Model sensitivity calculations for OPAA (Fig. A) show that the dominant contributions come from Cu and organics. In the model, Cu contributes to AA oxidation through direct redox reaction with AA, but also through the production of O2⚫- that further oxidizes AA. Organic compounds contribute towards OPAA through the decomposition of organic peroxides to RO⚫ and ⚫OH , which in turn oxidize ascorbic acid (Fig. S23, Table S1, Reactions SR1, SR115). Moreover, RO2 also oxidizes AA (Table S1, SR129). OPDHA, predicted for the London sites (Figs. S21A and S22A), shows high contribution from Cu, Fe, and organics, all of which contribute to the formation of AA⚫, which then undergoes a disproportionation reaction to form DHA (Fig. S24).

Figure B shows the contribution of PM constituents towards OPDTT. We find that organics contribute most to OP, consistent with previous studies that identified organic compounds as strongly correlated with DTT loss . Cu alone contributes to OP, in line with previous laboratory studies . However, as indicated by the negative Shapley values, the presence of both Fe and Cu lowers OP in the mixture. Notably, the Shapley value for organics is smaller than its contribution as a single pollutant. This is due to the interaction with metals as shown by negative values for the respective second-order Shapley interactions in Fig. S19B. Mechanistically, this is caused by the oxidation of HO2⚫ to O2 by Cu(II) and Fe(III), (Table S1, Reactions SR21, SR40), leading to removal of ROS (Fig. S25). This is in line with , who show antagonistic effects of Cu and Fe towards OPDTT in mixtures with humic-like substances and , who show antagonistic effects of Cu in mixture with bioaerosols.

Figure C shows the normalized contribution of PM constituents towards OPOH in Grenoble. We find that organics is a major contributor to OPOH, through peroxide decomposition pathway , while Cu shows only a minor contribution (Figs. 8c and S26). Fe can show a negative contribution to OPOH as indicated by a negative second-order Shapley interaction with organics (Fig. S19C). The negative contribution from Fe is especially pronounced using the PM composition typical for Paris (Figs. S16C and S20C). Individually, both Fe and organics contribute to OPOH through Fenton chemistry (Reaction R13) and peroxide decomposition (Reaction R25), respectively. The antagonistic interactions between the PM components can be understood by considering the Fenton-like reaction of ROOH and Fe(II) to RO⚫ (Reaction R34). This reaction is a large sink of both organics and Fe(II) that does not lead to the formation ⚫OH (Figs. S27 and S28), since the reaction of ROOH with Fe(II) preferentially generates RO⚫ (Reaction R34) over ⚫OH (Reaction R35) as radical species . Hence, the presence of organics lowers the ⚫OH yield from Reaction (R13) and Fe lowers the ⚫OH yield from Reaction (R25). R34Fe(II)+ROOH→Fe(III)+RO⚫+OH-R35Fe(II)+ROOH→Fe(III)+RO-+⚫OH

These results highlight the importance of capturing reactant interactions, as they can have either synergistic or antagonistic effects in different OP assays. In general, we find that second-order interactions between the pollutants can be of a similar order of magnitude as the first-order effects, while third-order effects are only about 10 % in magnitude of the first-order effects. We note that there may also be synergistic interactions between organics and Fe as a result of Fe-organic complex formation , which may have a higher rate coefficient for the Fenton reaction than that used in this study . Nonetheless, the rate coefficient derived in this study is based on experiments containing Fe and citric acid, which form Fe-citrate complexes that likely react faster than free Fe ions .

Figure D shows the normalized contribution of PM constituents towards OPH2O2 of PM typical for Grenoble. We find that Cu is a major contributor to OPH2O2 in the model, while Mn plays a minor role. Although Cu strongly enhances H2O2 production, its contribution to OPAA and OPDTT is small because the reaction of H2O2 with AA and DTT is relatively slow. In contrast, SOA contributes significantly to the production of ⚫OH, which reacts rapidly with AA and DTT. Fe contributes negatively to OPH2O2 in mixtures across all locations considered in this study (Figs. S19D, S20D, S21D, and S22D). As shown in Fig. 3b earlier, Fe can react with H2O2 through the Fenton reaction leading to a low steady-state concentration of H2O2, and hence a lowering the OP.

Due to the absence of data on the water-soluble fractions of metals at the London sites, we performed a sensitivity analysis by varying Fe and Cu solubilities within a factor of two (Figs. S29 and S30). The sensitivity analysis shows that, while OPDHA and OPH2O2 are influenced by metal solubility, OPDTT and OPOH were less affected (Figs. S31 and S32).

Figure A uses the average chemical composition at the Grenoble, Paris, and London sites to compare the model results for the various OP assays. Overall, OP values modeled for the French sites are higher than those modeled for London, both during winter and summer. In the French data sets, the concentrations of organics and Cu are on average higher compared to London (Table ), and are strong drivers of OP in the model (Figs. , S16, S17, and S18). Accordingly, the model predicts similar OP values in Paris and Grenoble due to very similar organics and Cu concentrations. In contrast, Fe concentrations are higher in London during summer, which leads to a slightly higher OPAA compared to OPDTT since Fe has a strong negative contribution to OPDTT. Note that Fig. A compares data from two different time periods, with the London data being much more recent, and cannot be used to infer the current state of air pollution at the different sites.

Figure B shows the correlations between the different intrinsic (mass-normalized) OP assays simulated in the study. To obtain the correlation coefficients, intrinsic OP is calculated for the composition data from all locations. We find that OPAA, OPDHA, and OPDTT generally correlate well with OPOH. Nonetheless, the correlation of OPOH with OPDTT is slightly lower than that of OPOH with OPAA, or OPOH with OPDHA. The weaker correlation of OPOH with OPDTT reflects the additional DTT loss pathways not directly linked to ROS production, such as the formation of Cu(II)–DTT complexes, which constitute a sink for DTT in the model. Correlations at individual locations are shown in Figs. S33–S36. At these single locations, the correlation between OPOH and OPAA, OPDHA, and OPDTT is higher than the correlation in the full data set (Fig. B). This is because PM composition can be fairly similar at one site, but may differ strongly across sites (Table ). In France, OPOH, OPDTT, and OPAA simulated in the model are primarily driven by organics, and to a lesser extent Cu. In contrast, in London, OPDHA is also driven by Fe. The simulation results indicate that the differences in OP assays are exacerbated by larger differences in aerosol composition.

OPH2O2 shows a lower correlation with OPOH. This can be understood by considering the sensitivities to aerosol components investigated above (Figs. , S15, S16, and S17): while the majority of the OP assays are driven by organics, OPH2O2 is mostly influenced by the presence of Cu. We find negative contribution of Fe to OPH2O2. Note that, while the model was trained on ⚫OH and H2O2 formation data from the laboratory, a validation of model-predicted OPOH or OPH2O2 with field data was not conducted due to the lack of datasets combining detailed PM composition with OP measurements.