the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 15 Jul 2026
FRISO (v1.0): A physiological carbon flux model for simulating algal 13C-fractionation
Abstract. The CO2-dependaency of stable carbon isotope fractionation (εp) during marine algal carbon acquisition is widely used as a proxy for past atmospheric pCO2. However, a mechanistic model linking εp and pCO2 that explains observations in the modern ocean, culture experiments and across Pleistocene glacial-interglacial cycles is still lacking. Here, we present a multi-compartment model of an algal cell that simulates environmental control on passive CO2 diffusion, active HCO3− transport, and 13C fractionation during C-fixation. Relative to previous models, our main new implementations include light-sensitive HCO3− acquisition and calcification, and daylength-dependent pyrenoid permeability, based on physiological expectations. The model is fitted to and tested with culture data of multiple dinoflagellate species and the coccolithophore Gephyrocapsa huxleyi. This shows robust performance across a wide range of parameter values from culture experiments, implying an appropriate representation of the mechanistic control of 13C-fractionation in algal organic matter, potentially paving the way for sedimentary work.
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RC1: 'Comment on egusphere-2026-3713', Edward Laws, 23 Jul 2026
- AC1: 'Reply on RC1', Yannick Bats, 09 Sep 2026
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RC2: 'Comment on egusphere-2026-3713', Anonymous Referee #2, 31 Aug 2026
The manuscript describes a new model for phytoplankton carbon isotope fractionation, which includes parameterizations of carbon uptake and intercompartment transport based on light intensity and photoperiod. This is a complex topic for which a mechanistic understanding is still very much in discussion, because the processes are set within the cell where there are few direct constraints. The model is interesting and explores some interesting new parameterizations for cellular carbon fluxes and I think the model is worth being published and put on the table as part of ongoing dialogue to better understand the processes.
There are a few issues that should be addressed. The referencing of previous multi-compartment models needs to be expanded and more balanced in the introduction. In some parts of the discussion it would be worth contrasting again the parameter solutions in this model with the approaches of some previous models.
A key scientific limitation is that the model for coccolithophores relies heavily on light modulation of calcification rates, but there is not presented any validation data of the implied PIC/POC ratios or calcification rates compared to experimental data. Therefore it is currently hard for the reader to assess if this mechanism is a viable novel mechanism or not – and it is the key process invoked to produce greater POC fractionation than possible from Rubisco as the only enzyme. The authors should address this using calcification data for experiments where they are available (such as experiments of Rost) and for experiments without measured calcification the authors should show that the model simulated rates and PIC/POC are within realistic ranges for those culture conditions, given the great wealth of calcification data produced over the last two decades by the ocean acidification communities.
Detailed suggestions are provided below.
The introduction provides a simple explanation of the original diffusive model, however it needs to provide a comparable overview of the subsequent step in the development of multi-compartment models accounting for active carbon uptake and CCM. The current paragraph is not effectively organized to build up to the new issue taken up in this paper. And, line 42, the first sentence of the paragraph is not a fair synthesis of the array of mechanistical models developed (and no one really knows what it means to “ accurately simulate” the mechanistic processes because the actual mechanistic parameters remain very underconstrained). The authors should approach this more fairly – previous models made advances in simulating mechanistic processes, and the author’s new model offers a new parameterization of some of the mechanistic processes in these multi-component models. So I suggest starting line 42, revising the paragraph in a more constructive approach (as taken with the previous paragraph) to highlight:
Several models have evaluated the organic matter fractionation resulting from the uptake of both CO2 and HCO3 and the intracellular transport and conversion of these carbon sources. Carbon flows into cytosol and intracellular compartments such as the cholorplast and pyrenoid have been simulated in models of diatoms (Hopkinson et al 2014). An array of multi-component models including chloroplast and calcification compartments for coccolithophores have used diverse parameterizations to investigate the impact of active bicarbonate uptake and intracellular transport on fractionation, focusing on the effects of CO2 and growth rate and cellular carbon allocation (Bolton and Stoll, 2013; Holtz et al 2017; McClelland et al 2017). A few models have additionally sought to evaluate potential mechanisms by which light availability affects fractionation, since culture experiments with coccolithophores (Rost et al) and with diatoms (eg refs in Cassar) show unique impacts of light on fractionation. Cassar et al (2006) assessed mechanisms by which light limitation impacted energetics of active HCO3 transport for diatoms. Wilkes and Pearon, 2019) proposed that light dependent enzymes supporting active HCO3 transport constituted a key mechanism for the light-dependence of ep.
In this study, we extend previous work to further explore potential processes which may be responsible for the observation of ep dependence on light intensity and photoperiod. We develop a four component model…
Line 109 – clarify what is the evidence that the electron transport rate is forced by light. Also keep in mind the surprising finding of Torres et al 2025 PNAS suggesting that deuterium fractionation did not provide support a greater chloroplast CO2 concentration in higher light.
Line 115 – are you suggesting more diffuse with increasing light intensity (add increasing or decreasing for clarity)? Add another sentence to explain why you interpret that the pyrenoid volume is related to its permeability, and below the equation give the range of fpd and its specific relation to day length.
Lines 128 and Figure 1 imply that CA is present at every step. Include some citations on the presence and location of CA in the modeled organisms and/or indicate that it is an assumption based on the the location of CA in other organisms , or if it is a pure assumption.
What I am missing between Fig 1 (schematic) and Fig2 (plots of model ep) is a figure where you illustrate the variation of they key parameters with light and photoperiod – your equation mentions only “ proportional to” but a figure is needed to illustrate the range of variation in your parameter for a given range in PFD and day length.
Line 176 – indicate how significant is the temperature dependent fractionation between HCO3 and CO2. Eg over a typical range in culture from 10C to 25C, is it 1 permil or 5 permil? From Fig 2a this looks minimally significant, so the explanation can be brief and indicate this is done for completeness but is not a main factor.
Line 195 – Explain the choice of the culture datasets to simulate vs datasets excluded (Tchernov 2014, McClelland et al 2017). Also eExplain why only G. huxleyi but not other Gephytrocapsa culture data (Rickaby, McClelland, Torres) were targeted for simulation.
Section 3.1 – This is model behavior and a sensitivity study. I am not sure that bullet points are stylistically the best way to present this. I suggest going to a paragraph format and it would be helpful to cite the Figure and panel (Fig 2a) after each statement.
Is the removal of 13C enriched HCO3 from the cytosol into coccoliths consistent with the observed range of d13C of coccoliths?
Fig 3 – calcification rate needs more clarification of the units, what PIC/POC is implied. Also I think an additional post-hoc comparison of the modeled vs observed PIC/POC is very important, please add this. Also in 3.2.2 clarify how does the modeled calcification rate increase with PFD and daylength change (if at all) the PIC/POC production rate in the model? Is the modeled PIC/POC consistent with the observations in Rost et al? This needs to be illustrated in Fig. 5 – there are many, many experiments of calcification of Ehux at different
Figure 7 and resulting discussion. For huxleyi, there are significant differences in the inferred HCO3 fluxes and HCO3/CO2 ratios – produced in the same laboratory – based on either the 14C disequilibrium method vs the MIMS method. The two methods make different assumptions about the data processing. It is important to represent these two options in the figures and discussion because this accurately reflects how underconstrained the actual information on uptake and intracellular fluxes is for coccolithophores. This will make the authors discussion a bit easier regarding agreement with estimated fluxes. See the following:
Kottmeier, D.M., et al., Strong shift from HCO3− to CO2 uptake in Emiliania huxleyi with acidificaon: new approach unravels acclimation versus short‐term pH effects. Photosynthesis research, 2014. 121(2‐ 3): p. 265‐275.
Kottmeier, D.M., S.D. Rokitta, and B. Rost, H+‐driven increase in CO2 uptake and decrease in HCO3−uptake explain coccolithophores' acclimation responses to ocean acidification. Limnology and Oceanography, 2016. 61(6): p. 2045‐2057.
Fig 8 – Refer again to equation 25 to clarify that ePIC is defined relative to CO2 aq since it has often been defined relative to DIC.
In section 3.3.2 It would be worth referring to models which used a coccolith vesicle to calculate the ePIC in conjunction with ep (eg Bolton and Stoll, 2013; McClelland et al 2017; Holtz et al 2017) and commenting what additional processes were used in those models or additional tuning which led to better fits and whether such tuning is compatible with your model.
Citation: https://doi.org/10.5194/egusphere-2026-3713-RC2 - AC2: 'Reply on RC2', Yannick Bats, 09 Sep 2026
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