1. Reviewer #3 (Public Review):

    Sorrentino et al. utilise Magnetoencephalography (MEG) and diffusion MRI tractography to investigate the mapping between the structure and function of the human brain and any constrains imposed from this coupling. Their work builds upon a growing number of studies that use functional Magnetic Resonance Imaging (fMRI) to provide evidence of structure shaping neural functioning. In this case, the authors utilise the fine temporal resolution of MEG to explore the propagation of the neural signal and investigate how this can be linked to a structural connectome derived from deterministic diffusion MRI tractography. Following critical dynamics analysis pipelines, they identified neuronal avalanches in the MEG data and showed that their spread is more likely between pairs of grey matter regions with increased structural connectivity strengths, quantified by the streamline count among them. This result provides new evidence on how the structural architecture of the human brain can influence intrinsic neural dynamics and suggests a potential mechanism, based on scale invariant properties in space and time, for similar previous findings based on the slower temporal scales of fMRI.

    The analyses presented are clear and concise. They highlight an efficient and clever way to combine MEG and diffusion data, maximising the benefits of both modalities, to explore structure-function associations. The authors have tested a number of different configurations, using multiple connectome mapping pipelines, atlases, as well as a replication sample from the Human Connectome Project and the results were robust both at the individual and the group level, which is reassuring and impressive.

    Given the short report format of the manuscript, it is understandable that some additional information and results were described very briefly or omitted altogether. However, there are a few points that, I think, if discussed (even succinctly) could improve the strength of the presented evidence and increase the manuscript's impact to the field. For example:

    Given that the foundations for all subsequent functional analyses are the time bin length and the branching parameter, it would be useful to have a couple of graphs showing their relationship. i.e. a graph showing the association between bin size and σ, for a wider range of bins (in addition to 1, 3, and 5 that are reported). Is bin size 3 the only bin size that σ = 1 and if not, how does this affect the rest of the results (especially the transition matrix). A second interesting graph dealing with avalanche dynamics would be to show the avalanche size distributions for a single subject and the group, for different bin lengths, highlighting whether they are following a power law, indicator of critical dynamics, and briefly discussing their power law exponents, α.

    The correlation between the structural connectivity and randomised transition matrices still seems relatively high. It'd be of interest for the authors to provide a brief interpretation of this, along with a justification for keeping the spatial structure unchanged during their randomisation routine.

    As the different size of parcels in the atlases can have an effect for both structural and functional analyses, it would be of interest to know if the authors controlled for that and how.

    Given the varying SNR that the AAL parcels will have due to their location, it could be of interest to present some information about the avalanches' spatial distribution (i.e. but not limited to a whole-brain map, where each parcel's intensity could correspond to the number of times it goes supra-threshold on average). This could highlight any issues where avalanches involve some parcels more (or less) than others due to challenges in recording and localising their activity.

    In addition to the above challenges with MEG, deterministic tractography analyses also present limitations on how accurately they can describe the underlying structural connectome. i.e. issues with crossing fibres (of varying degree among parcels due to their location), spurious tracts, and invalid, non-biologically plausible connections. A brief mention of these challenges both for MEG and DWI and how they might affect and impose limitations on the manuscript's results would be beneficial.

    Finally, values in the scatter plots in Figure 2 are probably mean centered? For visualisation purposes it might be better if they were not, as it seems a bit odd to have negative values or numbers higher than 1 for structural connectivity and transition probabilities. Also, there seems to be lots of ROI pairs with 0 structural connectivity but high transition probabilities, which might justify a brief mention in the manuscript and an interpretation.

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  2. Reviewer #2 (Public Review):

    Is this submission Sorrentino and co. are investigating the relationship between the structural and electrophysiological functional connectome. In particular they are asking whether the white matter structure is a large contributor to the patterns of function we see, and (importantly) whether this is or not a source-reconstruction artefact. The relationship between structure and the emergence of these functional networks is of interest to many, it has been previously shown in fMRI and I believe a lot of modelling work to match empirical observations of the electrophysiology has been previously done.

    The paper is clear in its motivations, and I believe fairly clearly reported. The simplicity of this is definitely one of the strengths of the report. Conceptually I believe this is a plausible hypothesis and of interest and (assuming the technical methods are correct) I'd say this is an elegant approach to supporting this.

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  3. Reviewer #1 (Public Review):

    Sorrentino et al explore the possible link between 'neuronal avalanches' in resting MEG signal and structural connectivity in the human brain. They estimate neuronal avalanches by applying a threshold to identify large perturbations in the source reconstructed MEG data before binarising the time-series to define 'active' and 'passive' windows in each voxel. Sequences of 'active' voxels are identified starting with any region becoming active and ending when all voxels become passive. The probability of an avalanche transitioning between any two voxels in the MEG data is compared to network structure identified from diffusion imaging in the same individuals. The authors show that brain regions with a high function transition probability are also likely to be structurally connected. Whilst the core finding is interesting, the results are undermined by a lack of controls for confounds.

    Strengths

    This paper utilises a straightforward and intuitive analysis approach to tackle a complex question - how does functional activity spread throughout the brain? The simple thresholding in the neuronal avalanches approach avoids a number of complex steps typically associated with electrophysiology connectivity estimation such as strong filtering and complex frequency transforms. Sorrentino et al are able to show that this simple time-domain measure is able to provide an interesting overview of functional network structure. Moreover, this method naturally works to explore networks structure in transient, aperiodic signals which are often overlooked in favour of an oscillatory perspective.

    The authors consider a range of analysis pipelines to show that the core results are robust to key analysis decisions. Two different parcellations and methods for computing transition probabilities are considered and the results are shown to hold when using diffusion MR data from the HCP project.

    Weaknesses

    The authors claim that these results are unlikely to be caused or affected by linear mixing or volume conduction - however this is not clear to me based on the presented information. Specifically, if a perturbation arises in one region and is mixed by volume conduction into a second region, part of its shape will be preserved but this will be at a lower overall amplitude. Therefore, as the whole perturbation shape will be scaled down in the second mixed region, it is likely that its rising edge will reach the z-score threshold at a later time than in the original signal. In this way linear mixing by volume conduction has the potential to create spurious time-lagged in this analysis. Previous literature on neuronal avalanches in MEG have included extensive control analyses and discussions on linear signal mixing for this reason (10.1523/JNEUROSCI.4286-12.2013). This point is not tackled in the analysis and not clearly discussed in the paper.

    The correlation in Figure 2 B and C is interesting but is not supported by control analyses to account for confounds. For example, ROI size could potentially lead to more apparent structural connectivity and stronger MEG signal driving an apparent correlation between the modalities. This authors conclusions would be better supported if such effects were ruled out.

    The main results are not well developed from the available data. The group level correlations are visualised and the subject-specific correlations are brieflly shown but not described in detail. It is unclear which regions and connections show the highest correlations. Similarly, there is wide between subject variability in the structure<->function correlation which ranges betwee 0.1 and 0.35 but the analysis does not explore whether this is reproducible, neuronal variability or driven by differences in SNR.

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  4. Evaluation Summary:

    The present paper addresses the relationship between the electrophysiological and the anatomical connectomes, utilising a method to describe avalances of activity. The editors feel that this work might be pushing the limits of MEG as a modality, since it implies more spatial precision that most would assume possible, which makes the manuscript particularly interesting to M/EEG researchers. While all reviewers agree that the paper has broad interest and the method is promising, some potential concerns have however been raised that compromise the validity of the results. Most importantly: the issue of volume conduction (proximity) driving the results as opposed to anatomical connectivity, which in the worst case could deemed the results trivial. Other confounds, such as the size of the parcels and their SNR, would also require major review.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 and Reviewer #2 agreed to share their names with the authors.)

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