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  1. Author Responses

    Reviewer 2 (Public Review):

    This work analyzes, for the first time, changes in information flow in developing dissociated neuronal cultures using their recently developed continuous-time transfer entropy (TE) estimator. This is a timely study, since the field of network and systems neuroscience critically needs better estimators for structural, effective and/or functional connectivity. Recent technical developments allow us to track hundreds, and even thousands of neurons during development (both in vitro and in vivo) in several organisms. However, current tools to assess changes in connectivity across time are severely lacking, and this study directly tackles this problem. Their method is the state of the art and appears to be extremely well suited to this task since it is able to deal with information flow across multiple time-scales and deals with the sparsity/multiple comparisons problem with strict statistical testing.

    The authors apply their transfer entropy estimator to a publicly available dataset (Wagenaar et al, 2006) consisting of multielectrode array (MEA) recordings from dissociated cortical cultures during development. The original dataset consists of over 50 cultures from 8 different batches (with different plating densities) recorded between DIV (day in vitro) 3 to 35. For this study the authors selected 4 cultures at 3-4 time points to claim that 1) Information flow undergoes a dramatic increase during development. 2) The spatial structure of information flow is “locked-in” early. 3) During bursting activity, nodes (neurons/electrodes) play a specialized role that is also “locked-in” early.

    The activity of dissociated cultures is highly heterogeneous, and an appropriate sample size is needed to assess the significance of any observed features or patterns. This is well described in the original work that provided the dataset used in this study “An extremely rich repertoire of bursting patterns during the development of cortical cultures”, (Wagenaar D.A., et al, 2006, BMC Neurosci). For example, in the discussion section they state “[...] that cross-plating variability was larger than variability between sister cultures implies that it is crucial to use cultures from several different platings to obtain unbiased results.” The current study uses only 4 cultures (from 2 different batches) recorded at 4 time points (sampled around 1 week apart on average) that might belong to the original categories of “fixed-bursting” and “superbursts”. In this work, results from these 4 cultures are often reported on a case-by-case basis, and sometimes without any statistical significance assessment and with unclear summary statistics. Given that, the validity and significance of the results is difficult to assess in their current form.

    We agree with the reviewer that clarifying summary statistics and statistical significance across cultures will improve the paper, and have addressed this as follows:

    The new Tables III and IV in the revised manuscript contain summary statistics of the results across the different cultures, including significance tests of these summary statistics. These tables are referred to and interpreted in the main results text.

    We further agree with the reviewer that the analysis will be improved by including more data.

    A major strength of the TE estimator framework developed by the authors is that it can account for the statistical significance of any TE estimate. However, it is unclear how this significance test is used throughout most of the results. Figures 1a and 3 to 8 appear to consistently include points with 0 TE that have an impact on the measured quantities, like means, quartiles and correlations.

    In all the analyses presented in the paper, whenever the null hypothesis of zero TE between a given source and target could not be rejected (that is, the TE estimate was not found to be statically significant), then the value of the TE between that source and target was set to zero for all subsequent analysis. It is important to still retain that zero value in analysis so as to see the overall trends in how the information flows or lack thereof change. For the means for example, if we were to remove an edge with zero TE from the mean on an earlier day, that would artificially inflate the earlier day’s mean in comparison to the mean information flow on a later day.

    This step in the analysis (setting non-significant values to zero and retaining them in analysis) was strongly implied in the original submission (for instance, see line 113 of the original submission). However, it was only explicitly stated as a step in the construction of the functional networks. This was an oversight on the part of the authors. We thank the reviewer for bringing this to our attention.

    We have added sentences explicitly stating that we used a value of zero whenever the TE was not significant on lines 135-137 and lines 181-183 of the revised manuscript.

    Additionally, the correlation plots across days (figures 3 to 7) include least-squares fits that are often dominated by what appear to be outliers in the data (or possibly non-significant TE values). The estimates of Spearman correlation might also suffer of a similar issue due to “ties”.

    We do agree that the plotted least squares fits appear at times to be dominated by outliers in the data: this is precisely the reason that we utilised Spearman instead of Pearson correlations for the quantitative analysis of the relationships here.

    Further, the Spearman correlation deals naturally with ties by taking the mean rank of all tied points [1].

    Regarding the “locked-in” information flow, evidence is always presented through Spearman correlations across TE scores at different days. These values are often not significant or show a weak correlation (Figures 3 and 4). An early “lock-in” of information flow would imply not only pairwise correlations, but also a long temporal correlation of a node (or edge) TE score across several days.

    As above, we have provided a more systematic analysis of summary statistics / statistical significance of the trends across all experiments. To clarify the point that we are making with respect to lock in: our argument is that once the information flows are established, they are then substantially correlated with flows on later days. The early recordings in this dataset have either none or very few statistically significant information flows: without such information flows established yet in these early recordings, we’re unable to observe longer correlations of them.

    We have added a brief discussion to the second last paragraph of section II E of the revised submission discussing the lack of information flows on these earlier days to be locked in.

    The study of information flow within bursts is really interesting. As the authors point out, TE appears to be well poised to measure this contribution, and their burst-local TE measure appears to be equivalent to other methods that condition TE estimates on population-wide activity levels, e.g., Stetter et al, PLOS Comp Biol, 2012. In here, they analyze the correlations between the burst-local TE measures and the burst position (in time) of a node.

    We thank reviewer for highlighting the work of Stetter et. al. which calculated the TE conditioned on bursting activity. As there are some similarities between that work and our burst-local TE, it is definitely worth highlighting where the similarities and differences between these approaches lie. We thank the reviewer for bringing this to our attention. We would point out, however, that Stetter et. al. extract the bursting activity and then calculate the (conditional) TE based on this bursting activity alone. By contrast, we are just extracting the contributions from the spikes that occur during bursts. The core difference comes down to how, for the burst-local TE, the non-bursting activity is still used in the estimation of log probability densities for the contributions of the spikes that occurred during bursts. In the Stetter et. al. approach, the non-bursting activity is ignored in the estimation of these densities.

    We have added a brief discussion of the work of Stetter et. al. to the end of section IV H of the revised submission.

    For the existence of time ordering the authors mention “[...] cultures often follow an ordered burst propagation [23, 36]”. But that does not appear to be a universal property of developing cultures. It is unclear whether the cultures used in this study show consistent temporally ordered bursting patterns. From the 2 cited references, in Maeda et al, the bursting pattern and temporal ordering changes from burst to burst (see Fig. 3). It is uncertain that an average “burst position” can be defined for any given node. Similarly, in Schroeter et al, there are several characteristic MUA patterns (Fig 4C), and even there, it might not be possible to define a consistent temporal ordering.

    With regard to the burst ordering, it was not our intention to imply that there is a consistent ordering in the burst propagation. Rather, our claim is that some nodes tend to burst earlier or later on average and that this average burst location is correlated with the burst-local information flow. Indeed, in Schroeter et. al., although they do point out in Fig 4C that there are several characteristic MUA patterns, in Fig 4B they plot the average “MUA flow profile”. From that figure, it is clear that some nodes exhibit a remarkably clear tendency to spike earlier in the burst propagation than other nodes. Indeed, they then base much of their further analysis on this fact by comparing “the relative mean of peak times in the propagation chain” (that is, the mean burst position) of each node with the node’s degree in the functional network. In terms of the Wagenaar dataset, by inspecting the plots in Figs 5a and 5c of the revised and original submission, where we plot the mean burst position vs the burst-local TE, we see that there is a wide dispersion in these mean positions. This indicates that certain nodes exhibit a clear tendency to burst either later or earlier in the burst propagation.

    The reviewer has highlighted to us that we have perhaps not sufficiently emphasized the fact that we are analyzing the mean burst position of what might be an inconsistent burst ordering. We thank the reviewer for bringing this to our attention.

    In the abstract, we have changed “spike ordering” to “average spike ordering”. In the author summary, we have changed “burst position” to “average burst position”. We have also made changes to line 70, as well as extensive changes to section IV D and some more minor changes to the 7th paragraph of the discussion.

    References

    [1] Jerome L Myers, Arnold D Well, and Robert F Lorch Jr. Research design and statistical analysis. Routledge, 2013.

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  2. Evaluation Summary:

    This work analyzes how meaningful connections develop in the nervous system. Studying the dissociated neuronal cultures, the authors find that the information processing connections develop after 5-10 days. The direction of the information flow is influenced by neuronal bursting properties: the early bursting neurons emerge as sources and late bursting neurons become sinks in the information flow.

    (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. The reviewers remained anonymous to the authors.)

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  3. Reviewer #1 (Public Review):

    The work nicely demonstrates that neurons tend to assume the specialized computational roles of either transmitters, receivers or mediators of information flow, depending on burst position, i.e., early, middle and late bursters behave respectively as transmitters, mediators and receivers. A main strength of the work is the tool used for the analysis, i.e. a continuous-time estimator of the transfer entropy (TE) which was demonstrated in a recent work by the same authors to be far superior than the traditional discrete-time approach to TE estimation on neural data. The main weakness identified relies on a limited reference to previous literature analyzing the same publicly available data.

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  4. Reviewer #2 (Public Review):

    This work analyzes, for the first time, changes in information flow in developing dissociated neuronal cultures using their recently developed continuous-time transfer entropy (TE) estimator. This is a timely study, since the field of network and systems neuroscience critically needs better estimators for structural, effective and / or functional connectivity. Recent technical developments allow us to track hundreds, and even thousands of neurons during development (both in vitro and in vivo) in several organisms. However, current tools to assess changes in connectivity across time are severely lacking, and this study directly tackles this problem. Their method is the state of the art and appears to be extremely well suited to this task since it is able to deal with information flow across multiple time-scales and deals with the sparsity / multiple comparisons problem with strict statistical testing.

    The authors apply their transfer entropy estimator to a publicly available dataset (Wagenaar et al, 2006) consisting of multielectrode array (MEA) recordings from dissociated cortical cultures during development. The original dataset consists of over 50 cultures from 8 different batches (with different plating densities) recorded between DIV (day in vitro) 3 to 35. For this study the authors selected 4 cultures at 3-4 time points to claim that 1) Information flow undergoes a dramatic increase during development. 2) The spatial structure of information flow is "locked-in" early. 3) During bursting activity, nodes (neurons/electrodes) play a specialized role that is also "locked-in" early.

    The activity of dissociated cultures is highly heterogeneous, and an appropriate sample size is needed to assess the significance of any observed features or patterns. This is well described in the original work that provided the dataset used in this study "An extremely rich repertoire of bursting patterns during the development of cortical cultures", (Wagenaar D.A., et al, 2006, BMC Neurosci). For example, in the discussion section they state "[...] that cross-plating variability was larger than variability between sister cultures implies that it is crucial to use cultures from several different platings to obtain unbiased results." The current study uses only 4 cultures (from 2 different batches) recorded at 4 time points (sampled around 1 week apart on average) that might belong to the original categories of "fixed-bursting" and "superbursts". In this work, results from these 4 cultures are often reported on a case-by-case basis, and sometimes without any statistical significance assessment and with unclear summary statistics. Given that, the validity and significance of the results is difficult to assess in their current form.

    A major strength of the TE estimator framework developed by the authors is that it can account for the statistical significance of any TE estimate. However, it is unclear how this significance test is used throughout most of the results. Figures 1a and 3 to 8 appear to consistently include points with 0 TE that have an impact on the measured quantities, like means, quartiles and correlations. Additionally, the correlation plots across days (figures 3 to 7) include least-squares fits that are often dominated by what appear to be outliers in the data (or possibly non-significant TE values). The estimates of Spearman correlation might also suffer of a similar issue due to "ties".

    Regarding the "locked-in" information flow, evidence is always presented through Spearman correlations across TE scores at different days. These values are often not significant or show a weak correlation (Figures 3 and 4). An early "lock-in" of information flow would imply not only pairwise correlations, but also a long temporal correlation of a node (or edge) TE score across several days.

    The study of information flow within bursts is really interesting. As the authors point out, TE appears to be well poised to measure this contribution, and their burst-local TE measure appears to be equivalent to other methods that condition TE estimates on population-wide activity levels, e.g., Stetter et al, PLOS Comp Biol, 2012. In here, they analyze the correlations between the burst-local TE measures and the burst position (in time) of a node. For the existence of time ordering the authors mention "[...] cultures often follow an ordered burst propagation [23, 36]". But that does not appear to be a universal property of developing cultures. It is unclear whether the cultures used in this study show consistent temporally ordered bursting patterns. From the 2 cited references, in Maeda et al, the bursting pattern and temporal ordering changes from burst to burst (see Fig. 3). It is uncertain that an average "burst position" can be defined for any given node. Similarly, in Schroeter et al, there are several characteristic MUA patterns (Fig 4C), and even there, it might not be possible to define a consistent temporal ordering.

    Was this evaluation helpful?