The authors have addressed my concerns and I am happy to recommend this article.

The authors made several improvements to the text which clarify the methods and results.  The authors also corrected the names of several peptides, although errors remain in the images of Figure 2 and 4, as well as in the supplementary materials. 

Researchers often face limitations in both availability of material and the quality of data that can be recovered from historical and archaeological materials and so I agree with the authors’ sentiment that it is important to have tools which can provide as much information as possible with the data that is available. I am still concerned, however, with the utility of the index when more than 50% of the data fall outside the theoretical range for the index. The authors explain this as a problem of accurate baseline correction, but I think it would be worth elaborating on this point in the discussion as to why this would/would not unduly impact the interpretation of the results. 

The manuscript describes a method to calculate the level of glutamine deamidation for several peptides by modelling the convoluted isotope distributions and combine the results to give an overall estimate of the deamidation for a parchment sample. The method is described as a simple three-step workflow, where the modelling occurs in the second and the third steps. The modelling of individual peptides uses weighted least squares regression which seems sensible for the limited data although the weights are calculated according to the noise level estimated from at most 3 observations. The details of the regression in this section somehow suggest more data than is available, possibly due to the matrix X (line 208). It could be worth linking back to the fact that n is at most 3 (sometimes just 1), and (according to Figure 2) m is at most 6 (should this be 5?). The notation is confusing as xij suggests the element in the ith row of the jth column in the matrix X, but in fact this is used to denote the model for the ith isotopic peak in the jth replicate. Perhaps the latter could be denoted yij. Also 𝛾 is of length k rather than k+1.

The third step of the process uses a mixed effects model to combine the individual deamidation estimates and the mathematical details are provided. My worry is that, for all the statistical theory, the results may not be meaningful if the data are poor. The authors perform residual analysis and apart from a few badly fitted values, seem to have obtained good results. However, these results check the fit of the model to the peaks extracted from (as the title advertises) low quality data. This depends entirely on the first step in the workflow which involves pre-processing the MALDI spectra and the only way to assess the performance here is from Figure 2. Of the 5 randomly chosen spectra, 4 appear to show only noise in all but the first peptide in Figure 2A. Maybe the much greater intensities for sample 67_19_2 make the other spectra look worse than they are. In any case, apart from this sample, Figure 2B shows just how few peaks were identified (assuming that the solid circles indicate identified peaks) and it is difficult to see why the peaks in other samples were identified. In the case of 59_I_4_2, the intensities are just too low to see anything yet peaks were identified for several peptides. Maybe the weighted (normalised) spectra should be shown instead? However, even for sample 67_19_2, the pre-processing for the last peptide does not look convincing. Are these typical spectra?

This paper presents a novel method for quantifying the deamidation of collagen peptides in parchment derived from animal skins. They present a well-written paper and a thorough, if dense, overview of the methods and results. The R-package and model developed here provide interesting new avenues to examine the treatment of animal skins in the past. I do not have the background to speak to the suitability of the statistical models developed here and will focus on the peptides. 

Peptide naming should be checked against reviewed collagen sequences to ensure correct and consistent naming throughout the paper. As this paper follows Brown et al. (2020), the peptide positions start counting from the beginning of the collagen-specific three-letter pattern (G-X-Y). Thus COL1a2 756-789 and COL1a2 535-567 in this paper are both COL1a2 756-789 and COL1a1 9-42 should be 10-42. Peptide COL1A1 375 is also referred to at certain points as 376. The reference for Brown et al. (2020) is also missing from the reference list. 

While I believe the methods touch on this topic, I feel this paper requires a clearer explanation of how missing peaks are dealt with at the replicate and sample levels. If these are being estimated, as the methods seem to suggest, what are the implications of this to the final PQI value and why is this preferred over removing replicates where peaks are missing? It seems that many of the issues discussed in the paper, such as the high proportion of PQI values above 1 and the deviation of tails on the qq plots could be alleviated by screening out poorer quality spectra or increasing the signal to noise ratio. Given these issues, it is unclear whether background noise or missing values may be conflated with the deamidation models in the paper.

One of the two masses of peptide 9-42 is suggested to be incorrectly identified due to different rates of deamidation (lines 318-322). From Table 3, it is unclear which value is being referred to as the relative rates are very close in number. In contrast COL1a2 756-789 and its variant, referred to as COL1a2 535-567 have different relative rates of deamidation. As these are variants of the same peptide, is this different important and if so, how might it impact interpretations about the use of goat skins? The finding that goat hides were more heavily limed is intriguing. However, given that goats have a different variant of peptide COL1a2 756-789, I would like to see evidence that goat parchment is more heavily deamidated across multiple peptides to rule out any effect of the different rates of deamidation across the two variants of COL1a2 756-789. 

Assuming the statistical analysis is sound, this study will make a valuable contribution to parchment production studies and the development of novel applications of MALDI-TOF in cultural heritage contexts.

This is an interesting paper that looks at deamidation as a marker of parchment quality, and allows the comparison of deamidation levels with other variables such as species and thickness of parchment to gain insight into the parchment making process. It is interesting that this baseline correction appears to improve the s/n of some peaks, but not others. I think the paper could be improved by acknowledging the limitations of the background correction technique and if possible, to draw some conclusions as to why this works for some, but not other peaks, is it to do with the s/n for the peak in the raw data? I am unable to comment on the mathematical/statistical aspects as this is outside my area of expertise.

Some minor corrections are recommended.

Lines 116-119: I don’t think this is true? You have a charge in MS2 as well, you can only see charged product ions and the product ion spectrum would be used for confirming the peptide sequence. The reason you have overlapping distributions in MS1 is due to the resolution of the instrument not the fact is the parent ion. In the future, since you have identified clear biomarkers it would be interesting to make a targeted MS method to carry out absolute quantitation using SRM on your 8 peptides.

Line 183: A s/n ratio of 1.5 is very low. Usually this is set at 3 for identification and higher than this for quantitative analysis (around 10) and what you are trying to do here is semi-quantitative.

Line 318 and 322: You could de-novo this to confirm?

Line 365: I’m not sure if authors mean that the base line correction did not work for this peptide in the sense that even after baseline correction, the s/n was too low?

Line 308: Why would a high level of deamidation in a peptide result in higher background if the background is caused by chemical interference from the MALDI matrix?

Line 384: MADI-TOF and ZooMS aren’t interchangeable. One is describing the ionisation technique/mass analyser and one is an application of MS to a sample type. Maybe better to say something like in the field of bioarcheology the application of MALDI-TOF to ancient samples is commonly referred to as ZooMS.

Line 391: I wonder if this variation due to the poor quality spectra or biological variation?

Line 400: It would be very difficult, if not impossible to validate this to EMA or FDA regulations.

Figure 2: It’s interesting that that for some peptides you can see an improvement in signal to noise when you compare them with the spectra in A vs B, but some still look poor quality after the background correction. Do you see any patterns in peptides where the correction works well for and which is doesn’t? I suspect that rather than the ionisation type, it’s the amount of collagen you are extracting in terms of s/n. If you remove deamidation levels from poor s/n spectra do your error bars change?

Figure 6: I’m not familiar with what level of spread of deamidation values you would expect for these samples but the error bars here seem quite high.

General comments: m/z should be italicised throughout.