PCOMPBIOL-D-26-01170

Inferring Effective Neuronal Circuits via Network Flux Counting

PLOS Computational Biology

Dear Dr. Chen,

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Additional Editor Comments (if provided):

Please see reviewers comments as they point to important revisions that need to be address to increase the validity and applicability of the proposed approach.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: Chen and Yang introduce a novel approach to estimate the connectivity of a neural circuit from spiking activity. They treat each network state (e.g. [0,1,0]) as a node on a hypercube, with edges between those differing by a single change (e.g. compared with the previous example [0,0,0] or [1,1,0]). The rate at which those edges are traversed can be used to estimate the spontaneous rates of units, their effective coupling, and their nonlinear response functions.

The results are presented clearly with straightforward examples highlighting the advantages of this new approach. I don’t have any major theoretical criticisms of the work but do have some concerns regarding the scalability of this approach to large scale in vivo datasets and a potential degenerate situation that may yield false connections.

Major concerns:

1. While the authors raise the issue that this approach has poor scaling with the number of nodes, it is unclear how bad the problem is when going from 3 to 5 nodes, or 5 to 20, or 100. It would be informative to show the form this scaling takes, such as how the number of nodes and edges that need to be evaluated grow. In addition, it would seem as the number of units increases the sampling of specific transition rates gets lower, so how would the duration of a simulation/recording have to increase to account for this. Presumably this depends in part on the firing rate of the neurons and sliding window size of the neurons, so keep those constant to just demonstrate should be sufficient.

2. The suggested solution for large networks of neurons is to subsample pairs or triplets. The authors show that in most cases there is a positive cosine angle between the ground truth and the subsampled triplet. However, for data collected in vivo there is no ground truth, so instead it might be helpful to know what the variance would be in the estimated effective connectivity between a pair of units. To do this, you would choose a pair and then vary across multiple runs the 3rd unit in the triplet

3. There may be a degenerate case in this approach that would show a connection between two unconnected units. If two units both received input from the same third unit, but at slightly different lags, it would establish a fixed lagged relationship between their spiking. If the difference between the lags falls within the sliding window size, then that might show a connection between them. Would this pose a problem, and if not, can the authors show why? In cross-correlation analysis of point process data, this is usually dealt with by shuffling the data across trials (see https://pmc.ncbi.nlm.nih.gov/articles/PMC3856913/).

Minor concerns:

1. Line 63: should be 'a corresponding interaction scenario' or 'corresponding interaction scenarios'. The 'a' and 'scenarios' disagree in plurality.

2. How sensitive is the analysis to the chosen time scale?

3. Line 227: Not sure what is meant by the phrase ‘projection artifact.’

4. Line 239: Where is the shared excitation indicated? Is that just the fact that units spiked from baseline, e.g. [0,0,0] to [1,0,0]?

Reviewer #2: This manuscript proposes a novel method for estimating functional connectivity directly from spiking activity. The authors evaluate the performance of the method using networks of LIF neurons and demonstrate that it performs favorably, particularly in strongly coupled regimes where conventional approaches such as generalized linear models (GLMs) and Granger causality (GC) may become unstable.

A notable strength of this work is that the proposed framework does not rely on a predefined statistical model such as a GLM. Instead, it directly maps network activity into a state space and characterizes neuronal interactions through state-transition rates. This is, to my knowledge, a novel and interesting approach. Developing alternative methods for estimating neuronal connectivity is important for advancing our understanding of functional networks, and the present framework may become a useful addition to the growing set of analytical tools available for large-scale neural recordings.

The authors systematically evaluate the method under a variety of simulation conditions, including different connectivity patterns, connection strengths, and noise levels. These analyses provide valuable insight into the characteristics and limitations of the proposed approach. Overall, I view this work positively and believe it has the potential to make a meaningful contribution to the field.

That said, I believe several issues should be addressed or clarified before publication.

Major Comments

1. Scalability to large neuronal populations

The manuscript provides a thorough characterization of the method for small groups of neurons. However, it remains unclear whether the proposed framework is practical for large-scale networks (e.g., >100 neurons).

Although Figure 7 presents simulations involving 100 neurons, the analysis focuses only on neuronal triplets. Since the ultimate goal is network inference, it would be helpful if the authors could discuss in greater detail how the method scales when the number of neurons included in the analysis increases substantially (e.g., 10, 100, or more neurons). In particular, what are the practical computational and data requirements in such cases?

As noted in the Discussion, the amount of data required appears to increase rapidly with the dimensionality of the state space. Are there strategies that could mitigate this problem? For example, the authors briefly suggest constructing larger networks from smaller motifs. Could hierarchical or motif-based approaches be used to efficiently identify candidate neuron groups and reduce the combinatorial complexity of the analysis? A more detailed discussion of the scalability and practical applicability of the method would strengthen the manuscript.

2. Comparison with alternative connectivity measures

The manuscript compares the proposed method against Granger causality-based connectivity estimation. My understanding is that the implementation used here corresponds to a conventional form of Granger causality.

Have the authors considered comparing their method with variants specifically developed for spiking neural data (e.g., Kim et al., 2011, PLoS Computational Biology; Casile et al., 2021, PLoS Computational Biology)? It would be interesting to know whether such methods improve performance relative to the baseline GC implementation used in this study.

In addition, have the authors considered comparisons with Transfer Entropy-based approaches (e.g., Ito et al., 2011, PLoS ONE)? Since Transfer Entropy is often used to infer directed interactions from neural spike trains, including such a comparison—or discussing the expected differences—would provide a broader context for evaluating the advantages and limitations of the proposed framework.

3. Interpretation of the application to retinal data

Regarding the application to salamander retinal ganglion cell recordings (p.12, line 237), additional biological interpretation would be valuable.

To what extent are the inferred connectivity patterns consistent with existing knowledge of salamander retinal circuitry? What types of retinal ganglion cells were recorded, and what biological significance should be attributed to the observed interaction patterns? Were the inferred relationships expected based on previous studies?

Furthermore, the manuscript highlights a specific three-neuron relationship. Are there additional examples that support the generality of the findings? Were similar interaction patterns observed across the recorded population, or was this example selected because it was particularly illustrative? Additional examples or a more comprehensive summary of the inferred connectivity patterns would help readers assess the biological relevance of the results.

Minor Comments

p.12, lines 232–233: There appears to be a figure labeling error. Figure 5b should be Figure 5d, and Figure 5c should be Figure 5e.

Figure 6: The results may be easier to interpret if the inferred connectivity is also visualized as a network graph.

Figure 7: Since this figure addresses the performance of the method in a larger-scale network, it may fit more naturally within the Results section rather than the Discussion.

Figure 8b: Please clarify the meaning of the parameters W = 8 and W = 32.

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Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: Yes: Drew Headley

Reviewer #2: No

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Dear Mr. Chen,

We are pleased to inform you that your manuscript 'Inferring Effective Neuronal Circuits via Network Flux Counting' has been provisionally accepted for publication in PLOS Computational Biology.

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Hugues Berry

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PLOS Computational Biology

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Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: The authors have thoroughly addressed all the issues I raised.

Reviewer #2: The authors have adequately addressed my previous concerns in the revised manuscript. I am satisfied with the revisions and recommend acceptance.

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: No

Reviewer #2: No