C-STABILITY an innovative modeling framework to leverage the continuous representation of organic matter

The understanding of soil organic matter (SOM) dynamics has considerably advanced in recent years. It was previously assumed that most SOM consisted of recalcitrant compounds, whereas the emerging view considers SOM as a range of polymers continuously processed into smaller molecules by decomposer enzymes. Mainstreaming this new paradigm in current models is challenging because of their ill-adapted framework. We propose the C-STABILITY model to resolve this issue. Its innovative framework combines compartmental and continuous modeling approaches to accurately reproduce SOM cycling processes. C-STABILITY emphasizes the influence of substrate accessibility on SOM turnover and makes enzymatic and microbial biotransformations of substrate explicit. Theoretical simulations provide new insights on how depolymerization and decomposers ecology impact organic matter chemistry and amount during decomposition and at steady state. The flexible mathematical structure of C-STABILITY offers a promising foundation for exploring new mechanistic hypotheses and supporting the design of future experiments.

This is an interesting and thought-provoking extension of older models of soil carbon. It goes beyond standard pool models by challenging their descriptions as homogenous and continuous models by adding microbial dynamics explicitly. Yet, it comes at a price, more parameters are required and the task of testing it against observations of soil C dynamics that rarely include more than total C is not obvious.
Specific comments 1. Line 119. It is strange that microbial uptake rate had no effect. It should change the growth rate of microbes and hence microbial biomass. Explain. Is it a consequence of other parameter choices that make the quantities of C available for uptake very small? 2. Figure  This study by Julien et al. detailed the process of substrate degradation by exoenzymes via representing depolymerization as a continuous process, as opposed to the prevailing scheme of either Michaelis-Menten or reverse MM-based on degradation. The presentation is in such a high quality, but I do not quite agree with the message this piece is trying to articulate. Although mechanistically this model pushes forward one process in the SOM-Microbes system, substrate polymerization, toward being more explicit by incorporating the insights of theoretical and experimental understanding of SOM's continuous nature, I do not believe this work with this model elucidates any process with new insights in the carbon-microbes system.
The study highlighted substrate accessibility in influencing carbon turnover, which, however, is a recognition existing for not a short time period. So I am hesitated to say this study contributed much to our understanding with enough novelty. In addition, from the perspective of modelling accuracy in soil systems carbon dynamics, this work lacks model-data comparison. Therefore, it's hard or still early to claim this model is better than others. From both the perspective of shedding new light on processes and the perspective of improving simulation accuracy, this work did not convince me with enough novelty.
In detail, this model makes substrate degradation explicit by treating it as a continuous process with an introduction of parameters including cleavage, and min and max of depolymerization of each substrate. On the one hand, these parameters introduced more uncertainty. At the same time, representing the microbial community with coarse guilds and microbial cell metabolism with a parameter CUE (which should be an emergent property) is mechanistically a step backwards relative to existing models that already make community relatively more explicit. This tradeoff in development makes me reluctant to accept that making one process explicit while sacrificing the explicitness of other processes can warrant a claim of a better model developed, at least for now without a systematic comparison. For example, how do we know models using MM or reverse MM to capture substrate degradation is worse in capture system dynamics than this substrate-continuum one?
Reviewer #3 (Remarks to the Author): General comments: Julien and co-authors present an interesting modeling paper that documents a novel approach for representing enzyme and microbial decomposition of organic matter substrates. My chief concern, however, is that at its core this is really a model development paper that may be more appropriate for a more discipline specific journal that will allow more space for an in-depth description (and review) of the model's structure, assumptions and parameterizations (e.g. SBB, FEMS, or ISME?).
My second concern is that with a structure and parameterization as complicated as C-STABILITY should be able to be configured to capture many of the behaviors that are illustrated in the text. These capabilities ARE interesting, but it also makes me think the model is likely over-parameterized for application at larger scales. Specifically, it's not clear from me how one moves beyond these nice idealized experiments to actually simulate this complexity of across multiple sites for long periods of time (which seems to be implied in the abstract and discussion)? This can be rectified by clearly managing reader (and reviewer) expectations from the start. The model captures a bunch of really interesting behavior related to enzyme depolymerization to microbial community dynamics in theoretical space. It also helps clarify some key uncertainties or and assumptions in the model that could be validated with future experimentation. In my mind these are the strengths of the paper and revisions are warranted to help make these insights clearer.

Specific and technical comments:
In my estimation the title borrows too heavily from the Lehmann and Kleber (2015) paper and should be more original.
Lines 7-8 this sentence is phrased awkwardly and can be edited for clarity.
Lines 10-11 I'm not sure where this feature of the model is demonstrated in the manuscript, and while I understand this is the aim of the authors it has not yet been shown and suggest removing the sentence.
Lines 49-52. While it's true that compartment models cannot describe a continuum of decay or enzyme diversity, it has also not been shown that this level of detail is actually necessary to capture litter decay or SOM stabilization dynamics. I would avoid making this kind of logical fallacies when justifying the need for the approach taken here. This comes up again in lines 84-85. And while it's nice to be able to simulate the "organic forms generated by enzyme depolymerization", I'm not sure this is critical to improving our projections on SOM dynamics under climate change? Line 73, what are 'lowly polymerized molecules'?
Line 74-75 details of how the model handles the spatial arrangement of substrates and minerals in the soil matrix seems important to describe here, especially if the aim is to make projections at larger spatial and temporal scales? Details of how results in Fig. 3c were generated would be helpful. These findings seems interesting, but the methods are too sparse to understand or evaluate.
Line 134 is embedment a word? Line 204, it seems the details of how the C-STABILITY handles mineral association are critical for the long-term projections from the model, but missing from the manuscript. There's a wealth of information crammed into this figure that is sparingly described and barely interpreted. What are readers supposed to take home from this display item?
Line 231, I'm not sure what "a parsimonious number of parameters" is intended to convey, but I worry that the model may be over-parameterized for broad-scale application. It's also not clear to me why it's critical to simulated this level of detail related to 'substrate accessibility and selective depolymerization".
Line 241-247, While I agree with this assessment of continuous and compartment model classes, it's not clear to me how C-Stability avoids the pitfalls of either approach (or indeed inherits them both)! Lines 282-286. I'm intrigued about the specifics of how this could be done. The text jumps from global-scale aspirations to a discussion of proteomics and metabar coding and then back to Earth system prediction. I wonder how a model like C-STABILITY helps to bridge that mismatch in scales? Sainte-Marie and co-authors report on the development of a novel model to describe organic matter decomposition dynamics. Their work differs from previous models in that organic matter pools are described as polymerization length distributions which are modified by enzymes that can exhibit distinct preference for endo-and exo-cleavage. The authors studied the models behavior in four scenarios spanning a gradient of complexity from single-substrate decomposition to a complete organic soil layer.

References
The authors address an important topic of great interest to the research community -how can organic matter decomposition be described mathematically. Their approach has important advantages compared to previous models and holds great potential for improving our understanding of this important process. The manuscript is well written and clearly of great interest to the readership. The authors' model is at an early development stage, and the authors focus on demonstrating the overall validity of the model and its potential in simple scenarios. This means that many processes and relations that are common to soils are not incorporated into the model (e.g., effects/limitations of nutrient availability of enzyme production and microbial substrate use efficiency, potential changes in the abundance of exo-and endo-cleaving enzymes at different decomposition stages, difference in the accessibility of organic matter to exo-and endo-cleaving enzymes). However, the authors make it clear in the discussion that they aim for a low level of complexity at this stage of the model development.
I think that the manuscript is in a great shape and only minor revisions are necessary for publication. In my opinion, there are two ways in which the manuscript could be further improved: -the manuscript describes the behavior of the model, but rarely discusses what the model tells about the modeled system. The manuscript could thus be improved by more explicitly discussing how the model results presented within this manuscript contribute novel insights to our understanding of decomposing organic matter/soil systems.
-generally, the manuscript text could be edited to further ease readability. While some complexity in the writing is unavoidable when describing mathematical formulations, I think carefully editing the text for during a revision for easier reading would improve the reach of the manuscript. In particular, it feels like many of the figures are only scarcely explained/referred to in the main text, and it's not always clear why a certain dataset is depicted.
Minor comments: L191: some comment is needed why the impossible C content of 1.5 gC/gsoil is a reasonable result. I would suggest that C content on a weight or volume content basis is a poor way to describe organic soil layers, where the total weight/volume of the soil (e.g., per m2 surface) changes depending on the amount of organic material present (i.e., gC/gsoil in these systems remains fairly constant around 0.5, with differences in OM amounts changing the organic layer thickness rather than it's carbon content.) L326: "Each microbial group" instead of "each microbe"

REVIEWERS' COMMENTS
Reviewer #2 (Remarks to the Author): I appreciate the effort by the authors in providing such a detailed, well-constructed response to my concerns.
Among the many revisions, I particularly like the major changes made to the concerns regarding the novelty of this model. The authors further highlighted the novelty of building such a model to help elucidate the mechanisms underlying enzyme-organic matter interactions. Further, the authors toned down the claim of a "better" model in terms of capturing complicated soil carbon dynamics. Again, it COULD be, which, however, at this stage without model comparisons and data integration, cannot be judged. In short, underscoring its continuous modelling in potentially contributing to better understanding of carbon behavior may be a better selling point of this work, which, to me, is solid without overselling.
With these points considered, I do not have any more comments on this manuscript.

Reviewer #3 (Remarks to the Author):
I appreciate revisions made to this manuscript and largely only offer editorial suggestions to improve readability of the text.
I like the questions being used to guide the study (last paragraph of introduction) and assume that these questions correspond to each sections of the results (2.1-2.4). I would suggest that the: 1) Language used in result subheadings more closely correspond to the questions outlined in the introduction and 2) Authors explicitly address each question in the results. For example, from 2.1 make it painfully clear to readers "How catalytic processes a critical regulator of SOM decomposition" and "How the coordinated action of enzymes regulates complex substrate decomposition". NOTE, this is done in the Discussion (text ~ line 300), but I feel it would also be helpful in the results.
I also would take care to craft the questions guiding this paper carefully to illustrate the points you're really trying to make. For example, I would argue that we've known for a long time that catalytic processes are a critical regulator of SOM decomposition, indeed that's the one thing that the muchmaligned discrete pool, microbial implicit models actually capture (see Schimel & Shaeffer 2012). Instead, it seems the new insight provided by C-STABILITY is what is the new insight you're trying to highlight the importance of depolymerization (and enzyme behavior) as a major rate limiting step controlling microbial uptake and decomposition of organic matter.
Line 62: Change to unrealistic Line 80-81: It seems references needed to support this assertion Line 83. Should this be enzyme or enzymes' (possessive) Line 87, SI Table 1. Maybe also refer to the method here, as this is where 'scenarios' are all described.
SI Table 1, scenario 4 should be described as the "Chemical characterization of organic…" Line 132, again should this be changed to enzymes' (possessive)?
Revisions to Fig 4 and section 2.2 are appreciated, but at first glance it still seems like the 'inaccessible' cellulose is 'decomposing' first (not just being transferred into the enzyme available pool). This is more clear in the movie and I'm not sure what suggestions to make for Fig 4 to avoid confusion for readers that may be quickly looking through figures to get a sense for this work.
I'd recommend changing the last sentence of the Fig 5 caption. "When cheating occurs, plant decomposers are outcompeted by microbial residue decomposers, which results in the persistence of lignin.
Line 257-261. These conclusions seem to be an artifact of the configuration of the simulations. Without any mechanism for microbial residue persistence, it's not surprising that CUE and enzyme traits only effected the variation in plant residues turnover (which also form the bulk of steady-state SOM pools).
Line 270 should this be enzyme and microbial access to substrates, not the other way around, as currently written?
Line 271, I'm not sure I agree with this claim. In Table 1 tau_enzyme for cellulose > tau_enzme for lignin. It seems like this parameterization results in the same net effect that cellulose has an intrinsically faster decomposition rate than lignin, as in most 'compartment models'.
Line 272. What are the "local environment properties" being referred to here? I would assume this includes abiotic factors like soil temperature, moisture availability, and mineralogy-none of which appear to modify the microbial activity or soil biochemistry from the simulations illustrated here. Maybe just leave out the text "local environment properties".
Line 298-as above, what are 'environmental conditions' here?
Line 308, Please replace 'key capacity' here with 'goal' or 'aim'. These long-term projections are an appropriate long-term goal for C-STABILITY, but I'm not sure this work demonstrates this capacity in the model. This is the revised version of a manuscript I have reviewed previously. I found that the manuscript was a very good state in the first place, and the authors have fully addressed all comments raised by me.
I appreciate revisions made to this manuscript and largely only offer editorial suggestions to improve readability of the text.
I like the questions being used to guide the study (last paragraph of introduction) and assume that these questions correspond to each section of the results (2.1-2.4). I would suggest that the: 1) Language used in result subheadings more closely correspond to the questions outlined in the introduction and 2) Authors explicitly address each question in the results. For example, from 2.1 make it painfully clear to readers "How catalytic processes a critical regulator of SOM decomposition" and "How the coordinated action of enzymes regulates complex substrate decomposition". NOTE, this is done in the Discussion (text ~ line 300), but I feel it would also be helpful in the results. I also would take care to craft the questions guiding this paper carefully to illustrate the points you're really trying to make. For example, I would argue that we've known for a long time that catalytic processes are a critical regulator of SOM decomposition, indeed that's the one thing that the much-maligned discrete pool, microbial implicit models actually capture (see Schimel & Shaeffer 2012). Instead, it seems the new insight provided by C-STABILITY is what is the new insight you're trying to highlight the importance of depolymerization (and enzyme behavior) as a major rate limiting step controlling microbial uptake and decomposition of organic matter.
The Authors: We thank the referee for his/her recommendation to clarify the points we are willing to demonstrate so as to better highlight the new insights brought by C-STABILITY .
- Line 83. Should this be enzyme or enzymes' (possessive) The Authors: We thank the referee for this notification and modified the text.
Line 87, SI Table 1. Maybe also refer to the method here, as this is where 'scenarios' are all described.
The Authors: Change done SI Table 1, scenario 4 should be described as the "Chemical characterization of organic…" The Authors: We thank the referee for this notification. It was the French writing. Now this is corrected and written into English.
Line 132, again should this be changed to enzymes' (possessive)?

The Authors: Change done
Revisions to Fig 4 and section 2.2 are appreciated, but at first glance it still seems like the 'inaccessible' cellulose is 'decomposing' first (not just being transferred into the enzyme available pool). This is more clear in the movie and I'm not sure what suggestions to make for Fig 4 to avoid confusion for readers that may be quickly looking through figures to get a sense for this work.
The Authors: To improve the reader's understanding, we added "decomposable" or "nondecomposable" in the headings of the graphics showing the distribution in polymerization (subpanel a). We also added a reference to the Movie at the end of the Figure 4 caption.
The Authors: We added a reference to Figure 3. The Authors: We thank the referee for this notification, we modified the text accordingly.
Line 257-261. These conclusions seem to be an artifact of the configuration of the simulations. Without any mechanism for microbial residue persistence, it's not surprising that CUE and enzyme traits only affected the variation in plant residues turnover (which also form the bulk of steady-state SOM pools).
The Authors: We propose a novel version of the text to clarify the points about CUE and enzyme traits sensitivity addressed by the referee. CUE sensitivity.  The linear relationship between microbe biomass and decomposition activity implies that CUE affects both the turnover of plant and microbe compounds. Nevertheless CUE only affects the amount of plant residues at steady-state (as shown by the numerical sensitivity analysis and the steady-state equations 27, 28, S18 and S19). The modified turn-over of microbe residues is indeed compensated by modified microbe metabolite biosynthesis. In our view, this is not straightforward and may be of interest for the reader, even if selective preservation processes that are not currently implemented in C-STABILITY may further operate in mineral soil.
Enzyme traits sensitivity.  Enzyme traits affect plant residues but also microbe residues. We now provide examples for both instead of only giving values for cellulose.
Line 270 should this be enzyme and microbial access to substrates, not the other way around, as currently written?
The Authors: We thank the referee for this notification and modified the text.
Line 271, I'm not sure I agree with this claim. In Table 1 tau_enzyme for cellulose > tau_enzme for lignin. It seems like this parameterization results in the same net effect that cellulose has an intrinsically faster decomposition rate than lignin, as in most 'compartment models'.
The Authors: We agreed, we changed our sentence into "Degradation is indeed not solely determined by any intrinsic molecular recalcitrance or specific decay rate as in many models". (Line 211) Line 272. What are the "local environment properties" being referred to here? I would assume this includes abiotic factors like soil temperature, moisture availability, and mineralogy-none of which appear to modify the microbial activity or soil biochemistry from the simulations illustrated here. Maybe just leave out the text "local environment properties".
The Authors: At this stage, we did not include temperature nor moisture in the model (even if they are important drivers of microbial activity. What we meant here is not the pedoclimate but the spatial arrangement of soil components at a very fine scale. It has been clarified in the text.