General comments:



The manuscript describes an improved protocol for estimating isotope fractionation by RubisCO enzymes (though it could also be applied to other carboxylases, as long as they are mostly irreversible!).  Improvements include 1) the convincing demonstration that absolute enzyme purification not necessary in some cases, as long as the appropriate controls are run in parallel (absence of substrate, e.g., RuBP).  This is a huge benefit, since high enzyme activities are needed for these experiments, and extensive purification steps tend to diminish both yield and specific activity; 2) increased precision by sampling strategically along the timecourse, guided by modeling of carbon fixation; and 3) the introduction of instrumentation (Apollo-Picarro spectrometer) which permits the simultaneous quantification and isotope ratio determination for each sample, avoiding errors introduced by splitting a sample for measuring each of these parameters individually.

They reproduce epsilon values previously determined in the literature (spinach, Synechococcus) as well as a new one (coccolithophore G. oceanica) that compares favorably with the e value determined for coccolithophore E. huxleyi.

Their simplified partial purification protocol (run as they describe with the appropriate controls), as well as their simplification in instrumentation, and the modeling to improve sample timing, are all a great benefit for measuring this important parameter.  Expanding the dataset of e values beyond the few that are currently available will be a huge benefit to the interpretation of d13C values of contemporary and fossil organic matter from a variety of habitats.

Specific comments:



The manuscript is very clearly written.  My comments, accordingly, are few:

1. Line 122 what is PIC?

2. Line 425 issues with sample foaming during injection into analytic systems.  This is not really a comment on the manuscript, just a suggestion for subsequent analyses: try adding antifoam A to the acid instead of using centrifugal filters; there will be less chance of introducing atmospheric CO2.

This is a very informative and well-written study on constraining ε_Rubisco values based on Rayleigh fractionation principles. The study shows that using partial purification (vs. full purification) of Rubisco is sufficient for acquiring adequate ε_Rubisco values. The study emphasizes the wide range of possible ε_Rubisco values (13 – 30 ‰) across and within the different Rubisco Forms. Specifically, the study confirms the low ε_Rubisco values observed in Gephyrocapsa/Emiliania species (cf. Boller et al., 2011).  Using additional modeling based on Michaelis-Menten kinetics with competitive inhibition (by xylulose 1,5-biphosphate), the authors accurately show the underlying dynamics of DIC depletion by Rubisco, which helped to strengthen their experimental design. This modelling approach is a true added value to the experimental study.

General comment:

• Your new simplified approach, consisting of semi-purified extracts and the Apollo-Picarro DIC-δ¹³C analyzer, gives accurate results while saving time and effort. I would recommend to present this specific new methodology in the abstract. I would also recommend to introduce the approach at the end of the introduction, so that it’s clear for the reader what you are going to do.

Specific comments:

• The methods section (2.2.) contains a description of the partial- and full purification method. However, at this point in the text it is not yet clear why these different methods are applied (e.g., why not only use the full purification method? See general comment). Only in the results section (3.1.) this becomes clear (fast/simple versus time-intensive). I would recommend integrating section 3.1 with methods section 2.2 for clarity.
• Furthermore, section 3.1. mentions the assessment of the degree of Rubisco purification for the two methods using SDS-PAGE. This abbreviation (SDS-PAGE) is however not yet described in the text. Therefore, I would include a short explanation of SDS-PAGE in the Methods section.
• Lines 159 – 165 (or whole section 2.3): Can't this be integrated with section 2.4.2? It feels a bit redundant to explain the Apollo-Picarro method and GasBench method twice, in other words.
• Lines 214 – 215: In your case, the standard deviation of the Gaussian error propagation represents the uncertainty of the parameter (ε_Rubisco) estimate. Therefore, it serves as the standard error of the parameter. Perhaps it would be informative to mention this, as this makes it clearer later in the text when you're comparing calculated ε_Rubisco values with other ε_Rubisco values from literature. It makes statements like ‘statistically indistinguishable’ (line 363), 'virtually identical' (line 417), or ‘…falls within a similar range…’ (line 414) more substantive.
• Figure 2: From the figure and caption alone it is not clear that the dark and light green circles represent the two different Rubisco concentrations. This is only mentioned in line 291-292 in-text.
• Table 1: From the table + caption alone it is not clear why the mean ε_Rubisco value of S. oleracea is only based on replicates 2 and 3. Only in lines 296 – 300 (in-text) this is clarified, as this paragraph explains which Rubisco concentrations (70 – 80 μg/ml) result in optimal experimental performance. I would recommend adding information to the table caption to clarify this.
• Line 313: Please also show statistics when stating ‘the difference is not statistically significant’ (e.g. t-test). This also goes for line 428.
• Considering ~70% of proteins is Rubisco for the partially purified extracts, the Rubisco concentration for replicate 2 is likely around 97 μg/ml. Considering this, the v_max value is substantially lower for the partially purified Rubisco as compared to the fully purified Rubisco. What could be the reason for this? Does this mean the Rubisco in the partially purified extract is actually less catalytically active than the Rubisco from the fully purified extract? This would contradict what you state in line 261: “…approximately 63% of the Rubisco in the fully-purified extract and nearly 100% in the semi-purified extract was catalytically active”. Do the impurities inhibit the activity of Rubisco? I would recommend clarifying this.
• Line 394 - 397: You implemented different values for the inhibitory constant (K_I) for S. oleracea, Synechococcus, and G. oceanica, considering S. oleracea and Synechococcus are associated with Form IB, and Gephyrocapsa is associated ID. This is not entirely clear from this sentence. From first reading this sentence it seems the K_I value for all species is derived from Rubisco Form ID of Galdieria sulphuraria, although this is only the case for G. oceanica. I would recommend clarifying this.

Technical corrections:

• Line 84: S. oleracea is not previously mentioned in the introduction using full species name. I would recommend writing it in full species name here, so Spinacia oleracea.

The carbon kinetic isotope effect (KIE) of rubisco is a critical measurement used across a variety of fields using stable isotopes to study carbon cycling across environments and time scales. This value is used to constrain the burial of organic matter over time, the productivity of the oceans in the modern, and to calculate the amount of anthropogenic carbon dioxide sequestered by the biosphere. Though diverse organisms utilize rubisco, its carbon KIE values have been measured from an extremely limited diversity of organisms. As Wijker et al. note, this is because the measurements are difficult as they require execution of two technically challenging feats – purification of rubisco and an in vitro isotopic kinetic assay. Wijker et al. address this challenge 1) developing a new spectroscopic approach which they 2) apply to partially purified rubisco samples. The result is a simpler approach to measurement of rubisco KIEs. Overall, we found this to be a high-quality manuscript that is of interest to the field and recommend publication with minimal revisions.

High level comments

Regarding protocol complexity: on L8 the authors write that their simplified approach eliminates the need for “complex purification protocols, specialized equipment, and experimental designs that yield little CO2 fixation and high uncertainties.” To us it seems that the cavity ringdown spectrometer is a specialized piece of equipment and its use introduces the need for additional preparatory steps (e.g., filtration, dilution) that produce some measurement artifacts (L320). It would help to simply describe what the key equipment is and why it is cheaper, simpler, or more accessible than the standard approach. This would improve the abstract, introduction (L80) and discussion.



Moreover, as is made clear near L195, calibration of the Apollo-Picarro system was done by comparison with IRMS. If an IRMS is required for calibration, then the equipment demands of this protocol are really no simpler than the standard approach.

Regarding novelty: the issue of rubisco purity has also been previously addressed by Estep et al. 1978 Plant Physiol but see further discussion below on why the community tends to not cite this paper. The authors should cite this work and generally avoid excessive claims of novelty. The paper is an excellent resource without. Moreover, it represents the first measurement of the G. oceanica rubisco KIE, which bolsters the low KIE value from E. huxleyi and S. costatum by Boller et al. 2011 and 2015 respectively.

Regarding correction for rubisco side reactions (L74): As far as we understand, the side reactions are not expected to affect the KIE even though they would affect the net rate of carboxylation. Moreover, it is common and appears to be defensible to monitor rubisco reactions  to ≈50% completion to fit the Rayleigh curve and derive the KIE (see Guy et al. 1993). 

On clarity: because the methods section precedes the results, it was unclear to us what the model of rubisco inactivation is for. On first reading we thought that the model of activation state was directly related to the KIE measurement. We only realized later upon re-reading that its purpose is to estimate the right amount of rubisco to assay. This could be made clearer by simply stating the purpose of this model up front, e.g. in the methods section and appropriate text. For example, the text near L290 could be moved to the beginning of S3.2

A technical comment on the kinetic model of rubisco inhibition: it seems that the authors fit a 2-parameter model (unknown k_acc and v_max) from a single time-course. It seems that this would produce ambiguous fits with high uncertainty because the same trace might be compatible with either lower v_max or higher k_acc. Some uncertainty quantification, e.g., estimating posterior parameter ranges, would be helpful here as the authors present this fitting procedure as an integral part of their method. 

On transparency of analysis: we did not see any links to source code for the data analysis performed. Please publish all relevant code – this is an essential component of scientific reproducibility and especially important for a methods paper. 

On citation of unpublished work: the authors cite an unpublished study of their own. This citation is not essential to any of the arguments presented and could be omitted. 

On evolutionary constraints in section 3.6: We found this discussion of evolutionary constraints on rubisco to be out of place in an otherwise excellent methodological paper. The review of prior literature is somewhat out of date, omitting key references that posit alternative mechanisms that can affect rubisco carbon KIEs (Tcherkez et al. 2013 Biochemistry; Tcherkez et al. 2013 Plant Cell Environ; Bathellier et al. 2020 PNAS; Tcherkez and Farquhar 2021 J Plant Phys). In addition, if the authors do want to rely on the Tcherkez et al. 2006, they must also measure rubisco oxygen KIEs as a key aspect of that argument is that the oxygen KIE does not vary with specificity while the carbon KIE does. 

We strongly recommend that the authors omit or heavily trim this section. 

Figure 1: since these data are presented quantitatively in the text, please give the quantification in a second panel, e.g. as a bar plot. 

Figure 2: the number of colors used in the figure is excessive. A legend would help a lot. Also, the dark green marks in panel (a) are not described in the figure or caption, but only in the text. In principle, Figure 3 could be part of this figure. 

Figure 4: a legend would help here to define what the diamonds/triangles are. 

Figure 6: again, why proliferate colors? 

Figure 7: it is irresponsible to report an R2 value to a manually selected subset of the data. We strongly encourage the authors to (1) omit this fit line from the figure and (2) tone down their discussion of its evolutionary implications. There is simply too little data to draw solid conclusions from. Even in the case of rubisco reaction kinetics (e.g., Flamholz Biochem 2019), where there is far more data, such conclusions are not easy to come by. 

Table A1: This table should be expanded and provided in excel or CSV. It would be helpful to specify which reference provides the KIE and which the specificity. It is worth citing multiple measurements when available and useful to report additional kinetic parameters, e.g., k_cat and K_m values, by examination of recent meta-analyses, e.g. Flamholz et al. Biochem 2019 and Iniguez et al. 2020. Please also comment in the text and caption as to whether this collection of rubisco carbon KIEs is complete. 

Specific Comments

L39: refer to table A1 here. 

L41: this sentence is cuttable, especially as it cites an unpublished work. 

L45: why is KIE variation important? 

L71: explain why this method no longer requires accounting for oxygenation-derived 3PGA. 

L75: give reference to studies that report experiments with < 30% DIC consumption

L78: cite Estep et al. 1978 Plant Physiol for prior work on testing whether rubisco purity matters. See their Table 2 for carbon KIEs from spinach prepared to different purities; they conclude, like the authors here, that “It can be seen that fractionation is independent of enzyme purity.” This is a landmark study in our field, but it is unfortunately infrequently cited because the absolute KIE values are off for reasons unrelated to the important conclusions about purity and metalation state.

L83: “a single instrument” – specify which instrument. 

L275: worth noting other other reasons why rubisco deviates from Michaelis-Menten kinetics beyond inhibitor formation. For example, the activation state can be changed, and many organisms express catalytic chaperones (rubisco activases) that catalyze the disinhibition of the enzyme complex, etc. 

L324: why is the dilution required? 

Table 1: what does it mean when you write “2-3”? That you pooled samples? Please clarify in place. 

L425: This filtration step seems like it exposes the rubisco reaction to air, which deserves more prominent mention and discussion than it is given. Please find a place to explain why this does not affect the KIE measurement much.