Moderate revision. The authors perform a thorough and well sound analysis of the relationship between spectral slope and Lempel Zip Complexity during sleep, in a short period before (‘spontaneous’) or after (‘evoked’) auditory stimuli. Their findings are very interesting and well documented, with some minor exceptions. The authors should be given a chance to improve their manuscript before publication.
Moderate concerns:
1. In the abstract results/discussion, address the hypothesis. The abstract state a hypothesis (that spectral slope would discriminate sleep stages not only in spontaneous activity, but also in evoked responses), yet it is not clearly stated whether the hypothesis is met, and whether spontaneous activity has higher discriminative capacity over auditory responses.
1.1. The results strongly speak for a higher sleep-stage discriminative capacity of the spectral exponent ( F(3,41) = 415.48, F is higher in spontaneous but similar to the evoked F =405.65) with respect to the LZC ( F(3,41) = 184 for the evoked, which is possibly significantly higher than the evoked-F, 166.94 , see below for comparing models) . The different performances of the two metrics should be properly discussed and stated in the abstract.
2. Baseline as spontaneous activity. ‘Spontaneous’ term is used to refer to the baseline period. It is not really self-evident that a baseline period can be considered spontaneous, (comparing results with literature speak for it, but a comparison with truly spontaneous activity was not directly tested). This is not only a methodological aspect, and should be properly mentioned through the manuscript sections (ideally also in the abstract). Using a different term is worth to distinguish previous analysis on truly spontaneous activity (e.g. page 19, line 19)

1. The statistical mixed-effect model described does not seem to match the used one.
   To legalize all the post-hoc tests performed, the authors prepared some mixed effects models. This is fine, but please correct the description of the models or the models themselves to better suit their goals.
   3.1. Epochs available within stage (to account for a different number of participants reaching a sleep stage). I would expect that all participants reached all sleep stages through the night (correct? Else add a table to report how many participants per stage), but each one might have a different number of epochs within that stage. How did the authors handle the epochs for slope and LZc? If slope epochs are entered in the model, this should be not possible for the LZc (estimated by concatenating epochs?) ? Please clarify in the methods.
   3.2. Unclear goal of the model Currently, the mixed model only accounts for a different intercept for each participants, but does not seem to account for the ‘dependency of stage WITHIN participants’. What did they mean with such phrasing? Perhaps the authors intended to add a different slope for each participant, Values ~ stage + ( 1 + stage | participants) ?! (This is not a necessary thing to do, I am just trying to interpret).
   3.3. Consider adding SpontaneousOrEvoked main term and an interaction effect ? On a related note, separating the analysis of evoked/spontaneous data is ok, but did the authors consider using a model with both spontaneous and evoked values together and its interaction with stage ?
   Values ~ stage + spontOrEvoked + stage*spontOrEvoked + ( 1 | participants) ? This might help clarify whether indeed LZc evoked discriminative performance of vigilance stages is higher for evoked vs spontaneous, as it seems to be the case looking at the F values.
   3.4. Terminology for categorical variable? Also, the term (vigilance) stages is used in the methods, but the phrasing sleep/wake state is used in the results (the second term suggests a binary value). Is stage inserted as a categorical variable as it should, or is it instead inserted as an ordinal variable (or as a dichotomic variable??)? Please correct accordingly.
   3.5. Add the ANOVA in the methods. Please make explicit that an ANOVA was run to evaluate the main effects of the mixed model (since F values are reported in the results)
   3.6. Please report the (main effects) of the mixed effects results in a table

2. Implausible explanation for spectral slope staging performance
   Trying to explain the sleep-stages discriminative performance of the 2-20 Hz slope, sleep spindles are called in the mix. This is not a good explanation since 1) peaks are excluded from the spectral slope estimation, and 2) if at all, strong sigma power/spindles should bias the slope estimation in the opposite direction to that observed (leading to a flatter decay in deeper sleep). A better explanation may rely on the increased amount of slow (arrhythmic?) activity with deeper sleep stages

3. Discuss negative finding ….However, no correlation between slope and N3 slow wave density was found by the authors, thus making the sentence ‘this is not surprising’, a little out of context. Please discuss this negative finding, which was indeed expected (also consider the new suggested improvements on slow wave analysis).

4. Negative peaks of slow waves in average reference ?!
   the idea of detecting slow waves based on negative peak excursion was formulated for when slow waves on the scalp all had the same polarity, i.e. when having a mastoid reference. Electrodes near the mastoid in the EGI net are too noisy to provide a reliable pseudo-mastoid reference, so I would choose a different strategy. It is better to instead consider the full excursion of the slow waves (min to max) across the full period wave (not just the negative polarity in the half wave) when considering average reference. Alternatively, (perhaps a less elegant strategy) would be to consider also positive waves separately and run supplementary analysis.
   On a related note, did the authors choose the 50 microVolt threshold for SW empirically? Others have chosen a higher threshold (when Slow Wave excursion was all on the negative side).

Minor points:
7. Correlation analysis not described in the methods. Please introduce correlation analysis in the methods and the eventual strategy for multiple comparisons
8. Empty circles not empy
The described ‘empty circles’ in the graphs were actually filled with white (hiding some datapoints). If possible, make them truly hollow. Please describe what each circle represents in the figure captions (average across electrodes and epochs?
9. EGI hydrocel for long-term monitoring?
Is a saline solution providing stable acceptable impedances for a full night recording? Please elaborate in the methods to justify the acquisition set-up.
10. Describe Filters. Filters are only partially described by their cutoff. Please describe filter type, forward or fwd and reverse direction, and filter order (additionally consider mentioning the FWHM).
11. ICA Is ICA activity performed across all sleep stages at once? If so, discuss the limitation of this choice, i.e. improper un-mixing of sources across different vigilance stages; risk of rejecting activity in one stage showing another behaviour in another stage.
12. Slope bias due to filter choice. On a related note, a 40 Hz cutoff for the filter is likely to bias all the slope estimates of the 20-40 Hz band towards more negative/steeper values. This is not a problem for the study per se, as the bias is consistent across all electrodes/subjects, however it will make comparison across studies harder. Please mention this bias in the limitations.
13. Consider the aetiology of coma patients in previous findings
Page 5, line 6. ‘In deeply unconscious acute coma patients’. Please explicitly mention that the patients had a cardiac arrest/were post-anoxic. A change in spectral slope has been recently found in other aetiologies, but not in post-anoxic patients. Colombo et al., 2023 https://doi.org/10.1093/cercor/bhad031
14. LZC specific methodology underlying differences with slope results? The authors choose to concatenate all sleep epochs rather than averaging LZc estimates across shorter epochs/intervals. Please motivate the choice, and discuss possible impact of the specific methodology used. Boncompte et al found that LZc and slope have a strong monotonic correlation; could you elaborate upon the discrepancies between LZc and Slope in the light of these results?
V. Medel, M. Irani, T. Ossandon, G. Boncompte; Complexity and 1/f slope jointly reflect cortical states across different E/I balances; bioRxiv, 298497 (2020), 10.1101/2020.09.15.298497
15. Perturbational literature improperly cited as spontaneous
Casali et al, 2013 cited in page 17 line 15 (possibly elsewhere) as spontaneous
16. Findings mistakenly reported in the opposite direction
page 17, line 19, (possibly elsewhere, check also results) When consciousness diminishes….the spectral exponent typically flattens  steepens!?
page 19, line 2> the spectral slope…flattened after auditory stimulation  steepened!?
17. Consider both complexity and spectral slope in the discussion. When summarizing results, the discussion is sometimes only speaking about complexity measures, but spectral slope/exponent should also be mentioned.
instances: page 16 line 15 (only complexity is mentioned, although its results are much weaker than those of the slope)
Page 17, line 12 (only the term slope is used rather than spectral slope)
18. Relevant review for claims Page 3, a large body of literature... A recent review on complexity measures in neuroscience would fit this statement (that only has two references of original findings). This review is already cited elsewhere (Sarasso et al., 2021)
19. ‘Speed’ of decay Page 3, line 18. ‘The speed of decay’, please use better alternative phrasings, such as decay rate or similar.
20. Figure 1.A, PSD not depicted. The picture displays an example hypnogram, but does not show the PSD used to compute spectral slope parameters. I suggest to move the hypnogram to the supplementary, and instead display the PSD across stages for spontaneous and evoked data (with a central tendency measure used across epochs, and participants). Different graphical options are available, yet, spectral data should be presented somehow.
21. Figure 1 X axis Positive time is used to depict timing during the baseline. This is atypical, please use negative times, relative to the beep onset. Also, the dots used in the figure suggests a time period is present between .5 spontaneous and 0 evoked, but reading the methods the two chunks seems to be always adjacent.
22. Figure 1A result. N3 sleep shows some fluctuations in the baseline. Is this the residual effect of averaging several large slow waves or the tail of an unfinished response to a previous sound/voice?
23. Discuss that beeps used are always followed by a natural sound/voice. Please discuss possible effects of this pairing page 18, line 7 (we show that this effect is not only present for stimuli with high information content). Well, a beep always(?) predicting a sound is arguably highly informative, so the statement is misleading.
24. Discuss EEG findings in the light of intracortical results.
A steepening of the spectrum is observed (only in the wake) EEG for the 2-20 Hz (not for the 20-40 Hz); whereas intracranial activity shows a flattening of high-frequencies following visuomotor task or motor task. Discuss the findings also in the light of intracortical results, and try to speculate on a possible reason for the discrepancy (highly localized effect ? frequency range? Task vs passive listeing? )
A unifying principle underlying the extracellular field potential spectral responses in the human cortex
Ella Podvalny, et al., https://doi.org/10.1152/jn.00943.2014
Spectral Changes in Cortical Surface Potentials during Motor Movement , 2009
K. Miller, E. Leuthardt, G. Schalk, Rajesh P. N. Rao, N. Anderson, D. Moran, John W. Miller, J. Ojemann
Journal of Neuroscience 28 February 2007, 27 (9) 2424-2432; DOI: https://doi.org/10.1523/JNEUROSCI.3886-06.2007
25. Other sleep references More EEG sleep studies have considered the spectral slope, for instance
Sources of Variation in the Spectral Slope of the Sleep EEG
Nataliia Kozhemiako, Dimitris Mylonas, Jen Q. Pan, Michael J. Prerau, Susan Redline, Shaun M. Purcell
eNeuro 19 September 2022, 9 (5) ENEURO.0094-22.2022; DOI: https://doi.org/10.1523/ENEURO.0094-22.2022
Bódizs, R., Szalárdy, O., Horváth, C. et al. A set of composite, non-redundant EEG measures of NREM sleep based on the power law scaling of the Fourier spectrum. Sci Rep 11, 2041 (2021). https://doi.org/10.1038/s41598-021-81230-7
26. Verb form. Page 14 line 12. A steepening suggests a dynamic change, while ‘steeper’ is more correct when comparing across space
27. Similar sentence repetition page 20, line 11, line 23 propose a similar sentence with results stated differently. The second sentence (discriminated between wake and sleep) is less ambiguous (spectral slope 20-40 Hz did NOT discriminate between wake and EACH sleep stage, as suggested by the phrasing ‘between wake and all sleep stages’)
28. Unclear phrase
page 21, line 16 ‘found a correlation to LZC IN the spectral slope….as well as a negative corr. Between LZC and the slope in the same frequency range’. Please rephrase this unclear sentence.

The authors replied satisfactorily to all my comments and the work deserves publication in the near future. I have few questions and comments that I would like to see a reply to before I can fully endorse the study.

-Why did the largest discriminatory power shift from spectral slope to LZC with the new model?
I am a bit puzzled by the change in the F relative to the wake/sleep stage discrimination, that the new model leads to: in the older model reported the F was substantially larger for the spectral slope than for LZC (i.e. before adding the interaction term conditionstage and the random slopes of stage for participants); now the F values have flipped, although they are more even.
Maybe the key to this change in F values is in the mixed effect part of the model ( random slope for participants), OR maybe in the way the model deals with the new fixed effect part ( conditionstage interaction, which leads to a high F for LZC, in contrast to that of the spectral slope). Can you elaborate on this please? Related to this, can you specify which Sum of Square type did you use for the ANOVA? Type I II or III differ in the way they assign weight to the interaction terms, and might give a clue on why the F values are now shifted to favour the LZC rather than the spectral slope.

-Ambiguous statement ‘Absence of stimulation’
The authors mention ‘Overall, our work aims at bridging these two fields investigating consciousness measures, by showing that metrics of information content can be applied similarly to EEG signals following auditory stimulation, as to the EEG signals recorded in the absence of external stimulation’.
The phrasing ‘in absence of external stimulation’ is a bit misleading, what you can conclude from your work is that the pre and post stimuli can be used equally well to discriminate vigilance stages; yet you only considered very short periods in absence of stimulation. Thus, whether vigilance discrimination during resting state is truly similar to that obtained during an auditory paradigm remains an open question, and this should be explored by future studies.

-Section ‘Information content in the post-auditory stimulation EEG
(..) Evidence of the prognostic and diagnostic value of quantification of AEPs and neural information content for assessing consciousness levels, or the integrity of neural functions in reduced consciousness conditions is growing (Aellen et al., 2023; Alnes et al., 2021; Bekinschtein et al., 2009; Benghanem et al., 2022; Colombo et al., 2019, 2023; Comanducci et al., 2020; Liu et al., 2022; Morlet & Fischer, 2014; Pfeiffer et al., 2018). Measures based on information content can differentiate levels of consciousness (Casali et al., 2013), while both measures based on information content and AEPs are promising as prognostic tools for patients with disorders of consciousness (Alnes et al., 2021; Colombo et al., 2023; Fischer et al., 2004; Liu et al., 2022; Pfeiffer et al., 2018; Tzovara et al., 2013)’

The title of the paragraph neglects the spectral slope, which I think should be inserted somehow in the title. Indeed, in this paragraph, some sentences already refer to the spectral slope. Further, some references related to spectral slope are used to talk about information content; so both measures, related to spectral and temporal complexity, should be somehow acknowledged in the text.

-Section ‘Information content in the pre- vs. post-stimulation EEG’
The same comment stated above applies: the parapgraph well covers the spectral slope but the title does not. Please adjust accordingly.
-Unclear phrasing ‘Conversely, LZc across the scalp did not differ between the pre- and post-auditory stimulation EEG in wakefulness, but decreased in all sleep stages, as previously reported (Andrillon et al., 2016). ‘
Given the title of the parapgrah, I assume that ‘decreased in all sleep stages’ refers to: ‘the post-stimulation LZC decreased across all sleep stages’, which is not strictly obvious from the current phrasing

-Spectral bend, not knee.
On a related note, you use the word ‘knee’ to refer to a ‘bend’ in the PSD. The terms point to different concepts (the knee being a frequency region where the PSD transition from flat to a decaying region, the bend is a narrow frequency where two different slopes occur) , but they are sometimes mixed in the literature, so it’s best to set the record straight.
You mention that you fit the two regions 1-20 Hz and 20-40 Hz independently, where a spectral bend (not an actual knee) occurs.

-FOOOF knee parameter.
Has the FOOOF toolbox been used with the knee fitting mode set to off? The knee mode can sometimes yield very odd estimates of the slope and introduces a new term that impedes the interpretation of the spectral slope independently form the knee frequency.
https://fooof-tools.github.io/fooof/auto_tutorials/plot_05-AperiodicFitting.html?highlight=knee

-Mismatch between regional and scalp-average findings of the pre-post stimuli difference in spectral slope.
Whereas scalp-average data showed a significant difference in pre to post stimuli activity, for the spectral slope in wake and REM for both low and high frequency ranges, there are no significant electrodes for this difference at the single-electrode level. This mismatch in the findings points to a harsh correction for multiple comparison used (a.k.a. ‘throwing away the baby with the water’) considering electrode-wise analysis. Thus, in the lack of a better explanation for the mismatch, the harsh correction should be acknowledged in the results section, or a softer threshold should be applied.

-Conflation of periodic and aperiodic activity of the PSD
Finally, looking at the PSD in Figure 1, it is rather obvious that the PSD content is smeared across frequencies (consider for instance the broad and shallow alpha peak during wakefulness. See for instance https://sapienlabs.org/lab-talk/factors-that-impact-power-spectrum-density-estimation/). This is inherently due to the experimental constraint of considering only 500 ms (before or after stimuli), and to the sampling frequency used, leading to reduced spectral resolution and to spectral leakage. In turn, the smearing of the spectral peaks across frequencies hampers the discrimination between aperiodic and periodic activity. I suggest mentioning this issue in the limitations, mentioning that future work should consider longer windows whenever allowed by the experimental design.

-On the lack of correlation between SW density and low-frequency spectral slope.
Given that the PSD is estimated from 500 ms windows, it is evident that the low frequency content below 2 Hz can not be estimated at all, and that the low frequency content is sampled from a low number of cycles included in a periodogram (<2 cycles for frequencies below 4 Hz). Thus, the PSD in the delta band is only partially and poorly estimated. Furthermore, the FOOOF algorithm estimates the power-law exponent of the PSD using an exponential function fit to a log-linear representation of the PSD (log PSD and linear frequencies), rather than evenly sampling the PSD across logarithmically spaced frequency bins, leading to an under representation (low leverage) of the low vs the high frequency portion of the spectrum. These issues should be mentioned when commenting the lack of a correlation between slow wave activity and the low-frequency spectral slope.

The authors have addressed all the reviewer's comments and the article deserves to be published.