General Comments

This study introduces the Kinetic Model of Oxidative Potential (KM-OP), a numerical framework designed to quantify the molecular drivers of oxidative potential (OP) in ambient particulate matter (PM). By integrating laboratory-derived rate coefficients with field data from multiple cities (Grenoble, Paris, and London Summer/Winter), the authors evaluate the relative contributions of transition metal ions (TMI), quinones, and secondary organic aerosols (SOA) to reactive oxygen species (ROS) production and antioxidant depletion. A primary finding of this work is the identification of SOA as a dominant driver of antioxidant-based OP across diverse urban sites, whereas Cu was found to specifically dominate the production of hydrogen peroxide (H2O2). Overall, the study provides significant insights into the chemical mechanisms of PM toxicity. I have a few specific comments and technical questions listed below for the authors’ consideration.

Specific Comments

1. Lines 102-109: The authors mention that the system is “under-determined” and use an ensemble of parameter sets. What is the degree of variance for the rate coefficients within this ensemble? Specifically, are there key reactions (e.g., Fenton-like reactions or quinone redox cycling) that show high sensitivity or wide uncertainty ranges?
2. Line 110: Since the “Org” component parameters were ported from literature rather than fitted during the MCGA process, did the authors investigate whether the transition metal ion and quinone parameters were forced to non-physical values to compensate for any inaccuracies in the fixed organic mechanism?
3. Lines 162-164: The 2-hour filter extraction period is not explicitly modeled. Considering that ROS can be lost through aqueous-phase chemistry during this time, could this omission result in a systematic underestimation of the initial OP of the PM samples?
4. Line 181-183: For the London sites (MY and HOP), median soluble metal fractions were used in the absence of direct measurements. Given the importance of Cu and Fe in your ROS findings, how sensitive is your conclusion that metals are "minor contributors" to variations in these assumed solubility fractions?
5. Line 194: The model assumes a fixed 50% organic hydroperoxide (ROOH) content for the organic fraction. Since SOA is identified as the primary driver of OP, how would the model's performance and the "good agreement" with field data change if this fraction were varied (e.g., to 20% or 80%)?
6. Line 375: The correlation for the London Summer site is reported with a negative coefficient (R^2 = -0.06). Could the authors clarify the statistical basis for a negative R^2 in this context? Furthermore, to what specific factors is this lack of correlation attributed? While the discussion mentions the presence of labile organic compounds, it would be helpful to understand if the discrepancy might also stem from temperature-dependent kinetic effects that are not currently parameterized in the KM-OP mechanism, particularly given the high-temperature conditions noted during that sampling period.
7. Lines 385-386: Regarding the role of highly oxygenated organics, the authors suggest these species may act as ligands and enhance metal solubility. However, could these organics also sequester transition metal ions? It would be beneficial to discuss whether such metal-ligand complexation might actually reduce the concentration of free metal ions available for catalytic ROS production, and therefore act as an inhibitory factor rather than a promoter of oxidative potential.
8. Lines 415-437: The results indicate that Cu dominates H2O2 production, yet SOA is the strongest contributor to antioxidant depletion OP^AA and OP^DTT. Why does the high flux of H2O2 from Cu not lead to a more substantial depletion of AA and DTT in the model simulations?
9. Lines 483-485: The correlation between modeled OP^OH and OP^DTT (R^2 = 0.7) is lower than OP^OH and OP^AA or OP^OH and OP^DHA. Is there a distinct, non-radical-mediated oxidation or non-redox removal pathway (e.g., DTT-electrophile adduct formation via Michael addition) that remains significant? It would be helpful to discuss whether the presence of such non-redox removal pathways contributes to the observed discrepancy in the DTT results compared to the other antioxidant metrics.

Summary

In this study, the authors introduce a chemical kinetic model of oxidative potential (KM-OP), developed using data from laboratory studies on the OP of individual/mixtures of chemical constituents for the production of reactive oxygen species (ROS) and consumption of antioxidants such as ascorbic acid AA and antioxidant proxies such as dithiothreitol DTT. The authors subsequently apply this model to field measurement data from France and UK to predict the OP using inputs such as concentration of transition metals, quinones, and secondary organic aerosols (SOA). A major strength is the integration of literature rate coefficients with a broad compilation of lab datasets, followed by inverse modeling using the Monte Carlo Genetic Algorithm (MCGA). Given the underdetermination and non-orthogonality of parameters, the ensemble-based fitting strategy is both reasonable and scientifically mature. The results from this study revealed SOA to be the main driver of DTT and AA consumption, with only minor contributions from Cu and Fe.  

General Comments

The development of a kinetic model based on laboratory studies to quantify the OP of PM based on the chemical composition of PM is a topic of significant relevance and importance in enhancing our understanding of the health impacts of PM. The successful development of a robust and accurate kinetics-based model to predict the OP of PM will allow us to quantify OP without needing to measure it. I commend the authors on their attempts to address this ambitious challenge.

The main strengths of the manuscript are the robust incorporation of the wide array of chemical reactions into the model, and a decent agreement between the model and the laboratory-based kinetic OP experiments using 1 or 2 chemical reagents.  In general, I think the manuscript is a bit lengthly, and could be shortened a bit.

However, several critical flaws undermine the robustness of the results and the representativeness of the model, undermining its broader applicability, some of which are

• Inconsistency in the OP-assays and OP-measurement protocols between sites that were used to predict the OP based on chemical composition. Two sites used offline measurements of OP-DTT and OP-AA, while the third site measured OP-DHA using online measurements. The OP was not predicted for any sites that measured OP-OH or OP-H₂O₂. The comparison could either be limited to only the OP that overlaps between sites, or the number of predicted sites could be increased to encompass all five OP-endpoints predicted using the model.

• Methodology has a lot of assumptions that are incorrect and could lead to severe oversimplification of the OP prediction and its underestimation.

• The modelled kinetics of DTT/AA consumption deviate a lot from experimentally quantified kinetics, with no reasons provided for this deviation.

The predicted OP values seem to be a large underestimation from the measured OP values in at least two of the six comparisons, and give trends that are contradictory to the experimentally determined values.

• The field validation conclusions of this study are over definitive. It is implied satisfactory performance across all three sites in the abstract and conclusions section, but the London summer data comparison yields poor results (R² = -0.06), and the London winter data still exhibits underestimation. This is insufficient to constitute reliable multi-site validation.
• SI is not well organized and does not follow the flow of the manuscript. Figures is SI seem to be like placeholders with no description accompanying them.

Despite this, study is interesting and potentially valuable, and appropriate for the journal’s readership. However, the methodological and interpretive issues may limit the strength of the manuscript in its current form. These critical flaws impact the results and their interpretability. This also limits the wider-applicability and robustness of the model. In my opinion, after careful revision that addresses or clearly highlights these limitations (for future work to identify and address them), this manuscript could be a useful contribution to the literature.

Specific Comments

Abstract:

Comment #1 (Minor Comment):

1. Although Dithiothreitol is a reducing agent with antioxidant properties that replicates biological mechanisms, it should not be considered a conventional antioxidant. It is not naturally present in the human body, nor is it synthesized biologically, nor is it present in foods that we intake. Therefore, it should not be called an antioxidant. A more appropriate term for DTT in place of “antioxidant” would be a “surrogate for biological reductants”.
2. Please use the correct chemical notation for hydroxyl radical (⋅OH or OH^.) in place of OH.
3. It would be better to introduce the name of the chemical Hydrogen Peroxide (H₂O₂) when introducing its chemical formula.

Introduction

Comment #2 (Minor Comment): Lines 30-35 – Page 2; Keep consistent terminology for the OP measured using the hydrogen peroxide method (i.e., ). Presently its being presented as both  and  in this section.

Methods

Comment #3 (Minor Comment): Lines 90 – 95 – Page 4; Provide a few references of other studies that have used the stiff differential equation solver ode23tb in Matlab.

Comment #4: Lines 95 – 100 and the SI in general: In its current form, the SI is not organized as per the order of its first mention in the main manuscript. For example, it is mentioned in lines 95 – 100 of the manuscript; however, this section is only on page 39 of SI and not the start.

This makes it difficult and distracting to the reader as the SI flow does not follow the manuscript flow, and readers would need to keep going back and forth within the SI to follow the order of the manuscript.

Please change the SI ordering to match the referencing in the manuscript so that the readers can easily move from one section of the SI to the next one as they are reading the manuscript.

Comment #4: Lines 115 – 185, Page 5-7 and corresponding SI:

• To my understanding, the HULIS data, the ion chromatography data, etc., from the Grenoble sites are not used as input parameters in the model. If so, these details are not pertinent to the topic of discussion in the manuscript and can be removed.
• Table S3 is misaligned in the SI when moving from page S27 to S28 and S29. Please align this to improve the readability of the table, as the table headings are only given on the first page. This comment applies to the tables for the other three sites, too.
• The authors mention in lines 160 -165, that the PM samples were extracted using a Gamble + DPCC solution and vortexed for 2h for the OP analyses. It is also mentioned that the soluble concentrations of Cu, Fe, and Mn were used as inputs in the model based on the table captions in S3 and S4. By soluble fraction of metals, are the authors referring to the water-soluble metal concentrations or Gamble + DPCC-metal concentrations?
• Were the extraction procedures same for the ICP-MS analyses of the soluble-metals as they were for OP? As the metals have soluble metal concentrations as inputs for the model, were the extraction procedure for the OP and soluble-metal analyses using the same solvent and vortex duration. This is critical information that needs to be provided to ensure that the model input is the same as the metal concentration in the OP extract.
• The OP measured in London summer site is using an online instrument that incorporates a PILS, as the authors mention in lines 175 – 180. To my understanding, if the OP of the liquid suspension in PILS is analysed, it would also account for the OP of the water-insoluble metal components as well. Please provide information as to whether these measurements were water-soluble or total OP, as solubility factors were incorporated to get the metal inputs for the model? Moreover, it would be optimal to use metal solubility factors from literature that are from the same sampling site. Was this the case for the literature presented in Table S6, as the metal solubility factor data show very large variations for the same metals Fe (0.08 – 0.42), Cu (0.29 – 0.94), and Mn (0.16 – 0.45).
• No data is provided for the London Winter as the authors mention that the data will be presented in a future publication. However, if that data is used as input to the model and presented as outputs in this publication, I think it should at least be provided as a separate review-only SI. Were the metals for this site also solubility adjusted?
• The OP measurements in the sites employing offline (France) and online (UK) protocols are using different solvents to measure the OP of PM. This will severely impact the final OP measured using the two methods. Therefore, I am not sure how representative it would be to model both of them kinetically, without accounting for the differences in the solvents used for the OP measurement.

Comment # 5: Lines 190 – 210: Several assumptions made in the section about the application to field data are unreasonable due to being incorrect and severely undermine the representativeness of the model.

1. It is mentioned that Organics and Quinones were assumed to be fully soluble. This is incorrect and severely undermines the representativeness of the model and its generalizability, especially for the offline samples (and the online samples if the OP measured there are water-soluble OP and not total OP).

Water-soluble organic carbon (WSOC) is usually much smaller than Organic Carbon (OC), and studies have reported that WSOC only constitutes around 20 – 65% of the total OC.^1,2  These solubilities are comparable to or smaller than those of Cu and Mn in tables S3-S6. Moreover, quinones are well known to be insoluble or have very low solubility in water, too.

I acknowledge that the offline OP analyses were in a different medium other than water (Gamble + DPCC), and that organics and quinones may have different solubility in this medium as compared to water. Is this a polar solvent, and have studies explored the solubility of quinones and organics in this medium? This assumption of organics and quinones being soluble is only valid if there is sufficient evidence that quinones and organics are highly soluble in this medium.

I recommend incorporating the appropriate solubility factors for organics and quinones and using that as the model input to obtain a more representative model.

1. The authors assume the organic peroxide content in organic aerosol to be 50%. This number is very high. Are the authors referring only to secondary organic aerosols? If so, this needs to be specified.

1. The authors assume the insoluble particles are not redox-active. This is incorrect, as Gao et al.³ reported that water-insoluble PM species contribute to 20% of the total OP. Similarly, studies quantified the methanol-soluble OP (as this increases the solubility of organics and quinones) have also consistently reported the methanol-soluble OP to be over 50% higher than the water-soluble OP, indicating water-insoluble substances contribute to the OP of PM.^4,5 Water-insoluble species such as quinones are also well known to contribute to OP-DTT.⁶

Results

Comment #6: Figure 3 and associated text:

The results obtained from the KM-OP model here corresponds and compares well with what has been reported in Charrier et al. 2014, 2015.^7,8 In figure 3c, the datapoints presented do not match with those reported in Charrier et al. 2015⁷, which only show concentrations till 1000 nM, and also report a linear increase in ⋅OH generation with increasing Fe concentrations unlike the KM-OP model simulations in Figure 3C. Are there any reasons behind this mismatch between the experimentally determined results and the model simulations?

The main takeaway in my understanding from this section is in figures S1-S3, where the dominant reactions that lead to H₂O₂ and ⋅OH generations in different concentration regimes of quinones and Cu are presented. However, the figures are shown only in the SI with very limited textual explanation, making it very difficult to fully interpret these results. What is the definition of normalized sources of H₂O₂ in those figures? Please provide a detailed explanation of those figures in the SI.

Comment #7: Figure 4 and associated text:

• In Figure 4a, it looks like the fit ensemble of the model consistently overestimates the AA consumption rates compared to all three experimental conditions. The AA concentration in the experimental data is almost on the cusp of the model uncertainty and is sometimes higher than the model range.
• In the case of Cu, the model data shows an exponential reduction in the AA concentration, which is unlike experimental data that shows a linear reduction in AA. What is causing this large deviation in the kinetics of AA consumption due to the presence of Cu?
• In table S1, what are the values given in the range? Is it the kinetic rate coefficients? If so, what are the units? Please provide these details.
• Why is the range of values for a lot of reactions that are not from literature very high, spanning 4-6 orders of magnitude?

Comment #8: Figure 5 and associated text:

• There is clear differences between the model simulations of Cu in Charrier et al. 2012, ⁶ and Exposito et al. 2024, reflecting the differences in the experimental data due to the differences in their respective DTT concentrations, 100 and 50 μM, respectively. Which of these two simulations was incorporated to predict the OP-DTT of the field data from Grenoble and Paris? What were the DTT concentrations for OP measurements for those samples from Grenoble and Paris?
• The DTT loss-rates become non-linear at higher quinone concentrations using the KM-OP model for 1,2 NQN and PQN in figure 5d. What is the reason or mechanistic explanation behind this, as this does not match with the previously reported literature using laboratory experimental data?
• In 5d, yet again, we observe that the model simulates an exponential reduction in the DTT concentrations due to reactions with PQN and 1-2 NQN. This does not align with what was reported experimentally in Xiong et al. 2017.⁹ Moreover, we see that the experimental results are on the upper bound of the error of the model simulations, with the model ensemble mean overestimating the DTT loss rates. Please comment on what may be causing this mismatch between the model simulations and experimental measurements?
• Please provide detailed explanations for the figures S6 – S9 in the SI.

Comment #9: Figure 7 and associated text:

1. As the reaction rates of organics, which are not really shown in prior sections or SI, how did the model use the organic model input data to predict the OP presented in Figure 8?
2. The model correlation is good, and the MLSE is low. However, it is difficult to ascertain the degree of underestimation in the OP from the model output and compare it to the experimental data due to the use of a logarithmic scale. Please provide this value by either providing the average slope of the best-fit line in a linear graph or calculating the average of the ratios of the modelled/measured data for each site and OP endpoints, and mentioning this in the manuscript. This is critical information to evaluate the model performance.
3. Provide the average±SD values of the model output and compare them with the measurement data average±SD for each site and OP endpoint.

Comment #10: Figure 9 and associated text:

• The modelled OP in Figure 9 does not follow the trends of the measured OP and is contradictory to the measured data. For example, the OP-DHA values from the field data in London during both summer and winter are clearly much higher than the OP-AA values in both Grenoble and Paris. However, this seems to be contradictory to the model output in figure 9 where the values are higher in France.
• The values of OP-OH and OP-H₂O₂ can be put on a different scale with pmol/(min.m³) instead of being shown as a multiple of 10 or 30 to avoid confusion.
• The average OP-DHA values in the UK measured experimentally seem to be roughly around 10 nmol/(min⋅m³), based on figure 7 (please provide the exact values). However, the model only predicts this to be around 1 nmol/(nmol⋅m³). This is almost an order of magnitude lower. Similarly, I also think the model output for the French data is a significant underestimation of the measurements.
• Provide the error bars for the model output in figure 9.

References

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