Homophilic wiring principles underpin neuronal network topology in vitro
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The study examines the principles according to which neurons connect to each other in the brain. The authors find that data could be best explained by the homophillic wiring principle where neurons preferentially connect to neurons within overlapping groups. The work will provide a valuable resource to the neuroscience community once analyses are standardized across various datasets included.
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Abstract
Economic efficiency has been a popular explanation for how networks self-organize within the developing nervous system. However, the precise nature of the economic negotiations governing this putative organizational principle remains unclear. Here, we address this question further by combining large-scale electrophysiological recordings, to characterize the functional connectivity of developing neuronal networks in vitro , with a generative modeling approach capable of simulating network formation. We find that the best fitting model uses a homophilic generative wiring principle in which neurons form connections to other neurons which are spatially proximal and have similar connectivity patterns to themselves. Homophilic generative models outperform more canonical models in which neurons wire depending upon their spatial proximity either alone or in combination with the extent of their local connectivity. This homophily-based mechanism for neuronal network emergence accounts for a wide range of observations that are described, but not sufficiently explained, by traditional analyses of network topology. Using rodent and human monolayer and organoid cultures, we show that homophilic generative mechanisms can accurately recapitulate the topology of emerging cellular functional connectivity, representing an important wiring principle and determining factor of neuronal network formation in vitro .
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eLife assessment
The study examines the principles according to which neurons connect to each other in the brain. The authors find that data could be best explained by the homophillic wiring principle where neurons preferentially connect to neurons within overlapping groups. The work will provide a valuable resource to the neuroscience community once analyses are standardized across various datasets included.
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Reviewer #1 (Public Review):
The authors evaluate a number of stochastic algorithms for the generation of wiring diagrams between neurons by comparing their results to tentative connectivity measured in cell cultures derived from embryonic rodent cortices. They find the best match for algorithms that include a term of homophily, i.e. preference for connections between pairs that connect to an overlapping set of neurons. The trend becomes stronger, the older the culture is (more days in vitro).
From there, they branch off to a set of related results: First, that connectivity states reached by the optimal algorithm along the way are similar to connectivity in younger cultures (fewer days in vitro). Second, that connectivity in a more densely packed network (higher plating density) differs only in terms of shorter-range connectivity and …
Reviewer #1 (Public Review):
The authors evaluate a number of stochastic algorithms for the generation of wiring diagrams between neurons by comparing their results to tentative connectivity measured in cell cultures derived from embryonic rodent cortices. They find the best match for algorithms that include a term of homophily, i.e. preference for connections between pairs that connect to an overlapping set of neurons. The trend becomes stronger, the older the culture is (more days in vitro).
From there, they branch off to a set of related results: First, that connectivity states reached by the optimal algorithm along the way are similar to connectivity in younger cultures (fewer days in vitro). Second, that connectivity in a more densely packed network (higher plating density) differs only in terms of shorter-range connectivity and even higher clustering, while other topological parameters are conserved. Third, blocking inhibition results in more unstructured functional connectivity. Fourth, results can be replicated to some degree in cultures of human neurons, but it depends on the type of cell.
The culturing and recording methods are strong and impressive. The connectivity derivation methods use established algorithms but come with one important caveat, in that they are purely based on correlation, which can lead to the addition of non-structurally present edges. While this focus on "functional connectivity" is an established method, it is important to consider how this affects the main results. One main way in which functional connectivity is likely to differ from the structural one is the presence of edges between neurons sharing common innervation, as this is likely to synchronize their spiking. As they share innervation from the same set of neurons, this type of edge is placed in accordance with a homophilic principle. In other words, this is not merely an algorithmic inaccuracy, but a potential bias directly related to the main point of the manuscript. This is not invalidating the main point, which the authors clearly state to be about the correlational, functional connectivity (and using that is established in the field). But it becomes relevant when in conclusion the functional connectivity is implicitly or explicitly equated with the structural one. Specifically, considering a long-range connection to be more costly implies an actual, structural connection to be present. Speculating that the algorithm reveals developmental principles of network formation implies that it is the actual axons and synapses forming and developing. The term "wiring" also implies structural rather than functional connectivity. One should carefully consider what the distinction means for conclusions and interpretation of results.
The main finding is that out of 13 tested algorithms to model the measured functional connectivity, one based on homophilic attachment works best, recreating with a simple principle the distributions of various topological parameters.
First, I want to clear up a potential misunderstanding caused by the naming the authors chose for the four groups of generative algorithms: While the ones labelled "clustering" are based on the clustering coefficient, they do not necessarily lead to a large value of that measure nor are they really based on the idea that connectivity is clustered. Instead, the "homophilic" ones are a form of maximizing the measure (but balanced by the distance term). To be clear, their naming is not wrong, nor needs to be changed, but it can lead to misunderstandings that I wanted to clear up. Also, this means that the principle of "homophilic wiring" is a confirmation of previous findings that neuronal connectivity features increased values of the clustering coefficient. What is novel is the valuable finding that the principle also leads to matching other topological network parameters.The main finding is based on essentially fitting a network generation algorithm by minimizing an energy function. As such, we must consider the possibility of overfitting. Here the authors provide additional validation by using measures that were not considered in the fitting (Fig 5, to a lesser degree Fig 3e), increasing the strength of the results. Also, for a given generative algorithm, only 2 wiring parameters were optimized. However, with respect to this, I was left with the impression that a different set of them was optimized for every single in-vitro network (e.g. n=6 sets for the sparse PC networks; though this was not precisely explained, I base this on the presence of distributions of wiring parameters in Fig 6c). The results would be stronger if a single set could be found for a given type of cell culture, especially if we are supposed to consider the main finding to be a universal wiring principle. At least report and discuss their variability.
Next, the strength of the finding depends on the strengths of the alternatives considered. Here, the authors selected a reasonably high number of twelve alternatives. The "degree" family places connections between nodes that are already highly connected, implementing a form of rich-club principle, which has been repeatedly found in brain networks. However, I do not understand the motivation for the "clustering" family. As mentioned above, they do not serve to increase the measure of the clustering coefficient, as the pair is likely not part of the same cluster. As inspiration, "Collective dynamics of 'small-world' networks" is cited, but I do not see the relation to the algorithm or results presented in that study. A clearly explained motivation for the alternatives (and maybe for the individual algorithms, not just the larger families) would strengthen the result.
Related to the interpretation of results, as they are presented in Fig3a, bottom left: What data points exactly go into each colored box? Specifically, into the purple box? What exactly is meant by "top performing networks across the main categories" mean? Compared with Supp Fig S4, it seems as if the authors do not select the best model out of a family and instead pool the various models that are part of the same family, albeit each with their optimized gamma and eta. Otherwise, the purple box at DIV14 in Fig3 would be identical to "degree average" at DIV14 in S4. If true, I find this problematic, as visually, the performance of one family is made to look weaker by including weak-performing models in it. I am sure one could formulate a weak-performing homophily-based rule that drives the red box up. If such pooling is done for the statistical tests in Supp Tables 3-7, this is outright misleading! (for some cases "degree average" seems not significantly worse than the homophily rules).
The next finding is related to the development of connectivity over the days in vitro. Here, the authors compare the connectivity states the network model goes through as the algorithm builds it up, to connectivity in-vitro in younger cultures. They find comparable trajectories for two global topological parameters.
Here, once again it is a strength that the authors considered additional parameters outside the ones used in fitting. However, it should be noted that the values for "global efficiency" at DIV14 (the very network that was optimized!) are clearly below the biological values plotted, weakening the generality of the previous result. This is never discussed in the text.The conclusion of the authors in this part derives from values of modularity decreasing over time in both model and data, and global efficiency increasing. The main impact of "time" in this context is the addition of more connections, and increasing edge density. And there is a known dependency between edge density and the bounds of global efficiency. I am not convinced the result is meaningful for the conclusion in this state. If one were to work backwards from the DIV14 model, randomly removing connections (with uniform probabilities): Would the resulting trajectory match DIV12, DIV10, and DIV7 equally well? If so, the trajectory resulting from the "matching" algorithm is not meaningful.
Further, the conclusion of the authors implies that connections in the cultures are formed as in the algorithm: one after another over time without pruning. This could be simply tested: How stable are individual connections in vitro over time (between DIV)?
The next finding is that at higher densities, the connections formed by the neurons still have very comparable structures, only differing in clustering and range; and that the same generative algorithm is optimal for modelling them. I think in its current state, the correlation analysis in Fig. 4a supports this conclusion only partially: Most of these correlations are not surprising. Shortest path lengths feature heavily in the calculation of small worldness and efficiency (in one case admittedly the inverse). Also for example network density has known relations with other measures. The analysis would be stronger if that was taken into account, for example showing how correlations deviate from the ones expected in an Erdos-Renyi-type network of equal sizes.
Yet, overall the results are supported by the depicted data and model fits in Supp. Fig S7. With the caveat that some of the numerical values depicted seem off:
What are the units for efficiency? Why do they take values up to 2000? Should be < 1 as in 4b. Also, what is "strength"? I assume it's supposed to be the value of STTC, but that's not supposed to be >1. Is it the sum over the edges? But at a total degree of around 40, this would imply an average STTC almost three times higher than what's reported in Fig 1i. Also, why is the degree around 40, but between 1000 and 1500 in Fig S2?
Finally, it should be mentioned that "degree average" seems (from the boxplot) to work equally well.Further, the conclusion of the "matching" algorithm equally fitting both cases would be stronger if we were informed about the wiring parameters (η and γ) resulting in both cases. That way we could understand: Is it the same algorithm fitting both cases or very different variants of the same? It is especially crucial here, because the η and γ parameters determine the interplay between the distance- and topology-dependent terms, and this is the one case where a very different set of pairwise distances (due to higher density) are tested. Does it really generalize to these new conditions?
Conversely, the results relating to GABAa blocking show a case where the distances are comparable, but the topology of functional connectivity is very different. (Here again, the contrast between structural and functional connectivity could be made a bit clearer. How is correlational detection of connections affected by "bursty" activity?) The reduction in tentative inhibition following the application of the block is convincing.
The main finding is that despite of very different connectivities, the "matching" algorithm still holds best. This is adequately supported by applying the previous analyses to this case as well.
The authors then interpret the differences between blocked and control by inspection of the η and γ parameters, finding that the relative impact of the distance-based term is likely reduced, as a lower (less negative) exponent would lead to more equal values for different distances. This is a good example of inspecting the internals of a generative algorithm to understand the modeled system and is confirmed by longer edge lengths in Supp Fig. S12C.The authors further inspect the wiring probabilities used internally at each step of the algorithm and compare across conditions. They conclude from differences in the distribution of P_ij values that the GABAa-blocked network had a "more random" topology with "less specific" wiring. This is the opposite of the conclusion I would draw, given the depicted data. This may be partially because the authors do not clearly define their concept of "random" vs. "specific". I understand it to be the following: At each time step, one unconnected pair is randomly picked and connected, with probabilities proportional to P_ij, as in Akarca et al., 2021; "randomness" then refers to the entropy of that process. In that case, the "most random" or highest entropy case is given by uniform P_ij values, which would be depicted as a delta peak at 1 / n_pairs in the present plot. A flatter distribution would indicate more randomness if it was the distribution of P_ij over pairs of neurons (x-axis: pairs; y-axis P_ij). The conclusion should be clarified by the use of a mathematical definition and supported by data using that definition.
Next, the methods are repeated for various cultures of human neurons. I have no specific observations there.
In summary, while I think the most important methods are sound, and the main conclusions (reflected in the title of the paper) are supported, the analysis of more specific cases (everything from Fig 3e onwards, except for Fig 5) requires more work as in the current state their conclusions are not adequately supported.
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Reviewer #2 (Public Review):
This work presents an exhaustive study of inferred functional networks from in vitro neuronal cultures across several modalities: primary rat cultures (with varying densities and longitudinal points), and human iPSC monolayers from different cell types and organoids. The authors first estimated the functional connectivity of these networks from their spontaneous activity (recorded with high-density MEAs) and then tried to find which wiring principle could better explain the observations. By deploying generative network models (with 13 different wiring principles) they observed that models with homophilic wiring principles were systematically outperforming the other ones. This proposes a universal rule for how neurons connect, which is that they tend to connect with neurons that have many common neighbors.
One…
Reviewer #2 (Public Review):
This work presents an exhaustive study of inferred functional networks from in vitro neuronal cultures across several modalities: primary rat cultures (with varying densities and longitudinal points), and human iPSC monolayers from different cell types and organoids. The authors first estimated the functional connectivity of these networks from their spontaneous activity (recorded with high-density MEAs) and then tried to find which wiring principle could better explain the observations. By deploying generative network models (with 13 different wiring principles) they observed that models with homophilic wiring principles were systematically outperforming the other ones. This proposes a universal rule for how neurons connect, which is that they tend to connect with neurons that have many common neighbors.
One of the major strengths of this study is its scope. They analyzed sparse and dense primary rat cultures at 4 different time points during development (from 7 to 28 DIV in total) as well as with the pharmacological application of GABAA blockers; 3 different cell lines: spinal-cord motor neurons, dopaminergic neurons, and glutamatergic neurons, and organoid slices. However, the big scope of this study is also one of its weaknesses, the techniques presented here to analyze the data are used inconsistently; for some preparations, there's much more detail than in others, and the constant jump between preparations and methodologies makes the findings hard to follow.
Similarly, the number of samples used in some preparations (ranging from 6 to 12) appears to be insufficient, since the study relies on multiple comparisons across the results from 13 different generative models. In many cases, it is not possible to identify which results are significant and which aren't. Most of the methodology used in this study has been used before in the context of the human connectome project (Betzel et al, Neuroimage 2016); in there they used data from 380 total participants, which made the comparisons across all the different models much more robust.
Most previous research with generative models for neural connectivity has focused on structural connectivity. In there, the link between wiring principles, energetic costs, and network topology can be made. This study, however, focuses on functional connectivity (measured by the spike time tiling coefficient), where the link between these quantities is unclear. Although the authors highlight this point in the manuscript, the constant comparisons to structural connectivity concepts and studies often lead to confusion. A clear example of this is the section where the authors explore the effect of chronic GABAA receptor blockade. It is unclear whether the authors are trying to claim that this protocol alters the development of the structural network or only the dynamics. The former could have needed additional controls.
The authors have been diligent and thorough with their statistical testing and their claims are commensurate with that. However, given the large number of different types of results and tests being presented, it is often difficult to find the corresponding explanation in the methods.
This is valuable work for experimental and computational neuroscientists studying the development of neuronal networks and the link between structural and functional connectivity. It would greatly benefit from homogenizing the results, methods, and statistics across the different experimental preparations. The conceptual similarities and differences between structural and functional wiring principles also need to be emphasized.
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