Self-organization of in vitro neuronal assemblies drives to complex network topology

  1. Priscila C Antonello
  2. Thomas F Varley
  3. John Beggs
  4. Marimélia Porcionatto
  5. Olaf Sporns
  6. Jean Faber

  • Curated by eLife

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    Evaluation Summary:

    This manuscript is of interest to readers working on neuronal network dynamics and development. It uses an in vitro model to characterize the emergence of complex topology in neuronal circuits. The presented mathematical tools for data analysis are sophisticated and supported by numerical simulations. However, further investigation is required to delineate the specific mechanisms of network formation.

    (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 agreed to share their name with the authors.)

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Abstract

Activity-dependent self-organization plays an important role in the formation of specific and stereotyped connectivity patterns in neural circuits. By combining neuronal cultures, and tools with approaches from network neuroscience and information theory, we can study how complex network topology emerges from local neuronal interactions. We constructed effective connectivity networks using a transfer entropy analysis of spike trains recorded from rat embryo dissociated hippocampal neuron cultures between 6 and 35 days in vitro to investigate how the topology evolves during maturation. The methodology for constructing the networks considered the synapse delay and addressed the influence of firing rate and population bursts as well as spurious effects on the inference of connections. We found that the number of links in the networks grew over the course of development, shifting from a segregated to a more integrated architecture. As part of this progression, three significant aspects of complex network topology emerged. In agreement with previous in silico and in vitro studies, a small-world architecture was detected, largely due to strong clustering among neurons. Additionally, the networks developed in a modular topology, with most modules comprising nearby neurons. Finally, highly active neurons acquired topological characteristics that made them important nodes to the network and integrators of modules. These findings leverage new insights into how neuronal effective network topology relates to neuronal assembly self-organization mechanisms.

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  1. Version published to 10.7554/elife.74921 on eLife
  2. eLife

    Author Response

    Reviewer #1 (Public Review):

    Thank you for your comments. We incorporated concepts, details, and analysis to make the narrative clearer. We tested some additional computational simulations, completely silencing the inhibitory neurons, to investigate inhibition influence in the detection of communication paths. However, by silencing inhibition the firing rate of excitatory neurons increased about 70 times, which impaired the analysis given the limitations of the techniques used. Including the decrease of accuracy in the inference of connections from the spike trains with 70 times more spikes. To obtain similar results as for the empirical data the procedure to exclude spurious connections must be adjusted to be even more rigorous, but this change would make the comparison with connections inferred from actual data unfeasible. Such an increase in firing rate was not observed in our results even for stages of maturation before the excitatory-to-inhibitory GABA switch (7-8 DIV, Soriano et al., PNAS 2008) most likely due to neuron homeostatic mechanisms. We understand and agree with the need for additional models, but the inclusion of such an analysis would require a considerable modification of the pipeline and the format and interpretation of the text. Therefore, we included this issue in the discussion and make explicit the limitations of the current analyses.

    Reviewer #2 (Public Review):

    Thank you for your review and suggestions.

    (1) Once the work used a fully recorded data set, a highly recommended approach for reducing the use of animals, by using creative ways to extract different information from the same data, the study of key mechanisms behind the formation of the networks is limited. However, we used the results to leverage new insights into possible mechanisms and promote ideas to new experimental approaches. The novel contribution of this study relies on the fine-scale analysis of the formation of the information flow in neuronal assemblies. Which could be compared with neuronal firing rate and neuron’s physical location. We formulated one hypothesis related to the activation of silent synapses as a mechanism related to the phenomenon. But other alternative explanations may also be possible. However, we believe our results can help other scientists guide their research to look at synapses activation, GABAR switch, formation of effective networks in low [CA2+]E, and intrinsic neuronal mechanisms related to firing rate control.

    (2) Although in vitro experiments have their limitations, we can assume the neuronal assembly hypothesis in Hebb's postulate (Hebb, 1949, doi: 10.1126/science.1238411), that says the coactivation of neurons is what gives rise to functional neural circuits. It means that even dissociated from the brain, if neurons have retained their intrinsic properties, they will connect among them, building networks.
    However, we agree that some aims of this work were not very well described. We did not intend to infer neuronal structures from dynamics as sometimes it seems in the first version of the manuscript. In our analysis, by ‘connections’ we meant strong paths for information flow rather than actual structural connections. Synaptic pruning is a structural mechanism that could be for example related to synapses that were not activated. However, despite may exist correlations (Park & Friston, 2013, doi: 10.1126/science.1238411), we cannot directly relate it with the increase in edge density of effective connections. The self-organization of neuronal assemblies is a complex process that involves many mechanisms, and in this work, we are looking at the formation of paths of information flow.

    We add this explanation in the Results sections.

  3. eLife

    Evaluation Summary:

    This manuscript is of interest to readers working on neuronal network dynamics and development. It uses an in vitro model to characterize the emergence of complex topology in neuronal circuits. The presented mathematical tools for data analysis are sophisticated and supported by numerical simulations. However, further investigation is required to delineate the specific mechanisms of network formation.

    (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 agreed to share their name with the authors.)

  4. eLife

    Reviewer #1 (Public Review):

    In this study, Antonello et al. provide a detailed analysis of the evolution of effective connectivity along a 30-day maturation period of dissociated hippocampal networks in vitro. By using a rich repertoire of network measures and topological analyses, and linking them to neuronal activity-dependent mechanisms, the authors show that the networks gradually shift from a segregated configuration to an integrated one, with the emergence of a small-world organization, specific motifs, and modular traits that reflect the tendency of nearby neurons to interconnect. Altogether, this study substantially helps to understand in detail how neuronal circuits self-organize to shape non-random topological features that optimize the tradeoff between wiring cost and functional efficiency.

    Strengths:
    - A robust and extensive analysis of experimental neuronal activity data using tools from complex networks, accompanied with substantial statistics.
    - The inclusion of numerical simulations to validate effective connectivity inference.
    - A Discussion section that analyses in detailed the obtained results in the context of the literature, bringing to light new concepts and ideas that help to understand the richness of self-organization and the emergence of complex topologies.

    Minor weaknesses:
    - The Results are presented in a very concise manner and may be difficult to follow. Some details and small additional analysis could be incorporated here to help the reader to fully understand the results.
    - Some additional numerical simulations may be required to fully grasp some analyses and their implications.
    - Some parts of the Discussion could be extended to treat aspects that are not sufficiently clear, such as the role of inhibition or neuronal spatial distribution.

  5. eLife

    Reviewer #2 (Public Review):

    By analysing signals from hippocampal neuron cultures, the manuscript describes how so-called effective neuronal connections change during the maturation process. The authors use a range of metrices such as small-worldness and modularity to characterize these changes with an aim of understanding the underlying self-organizing mechanisms.

    Strengths. The manuscript's primary merit is that by weaving together different approaches from network neuroscience, it offers a systematic characterization of the changes of effective connections during the development process of neuron cultures.

    Weakness. I see two main weaknesses in the manuscript:
    (1) Beyond the fact that the properties of effective connections change during the maturation process, the key mechanism of how and why the networks behave in the way as described in the manuscript is unclear. In my opinion, this lack of mechanistic account of the findings does not yield new insights into understanding the development of neural networks.
    (2) The general applicability of the findings based on neuron cultures to understanding neural development in vivo is limited. For instance, this study suggests that inserting new connections is crucial for the emergence of the complex coupling architecture, which contrasts with the established in vivo finding that synaptic pruning is a principled process during neural network development.

    Because of these, it is unclear that the analysis presented in the manuscript significantly advances our understanding of developing neural networks.

  6. eLife

    Reviewer #3 (Public Review):

    Neuronal activity in the adult brain is thought to be the result of genetic, chemical, mechanical, and stimulus specific factors acting on the connections between neurons. However, how this process takes place is not completely understood. To address this problem, Antonello et al. used primary cultures of dissociated rat hippocampal neurons. Neurons in culture spontaneously form networks. In order to follow neuronal network evolution over (~30 days) time, the authors let the cultures grow on a grid of electrodes (8x8, 200µm step distance). They were, thus, able to infer network structural features from the recorded activity (using transfer entropy), to follow network topology over time, and to study how neuronal assemblies influenced network evolution. The authors found that: (i) networks showed growth in edge density for the first 21 days, and saturated thereafter; (ii) networks progressed from segregated (high clustering coefficient) to integrated (low shortest path), with five 3-motifs occurring more often than chance (labels 5, 8, 11, 12, 13); (iii) neuronal populations formed non-overlapping sub-networks made of neighboring (not necessarily adjacent) neurons; (iv) in these communities, the most active neurons could be analyzed as 'hubs' according to a scoring system based on neuron degree, connections weights, betweenness, and closeness. High scoring neurons were found to be reliable participants (integrators) of distinct sub-networks.

    The work addresses an important question for a broad audience. It adopts a clever experimental strategy. The results are clearly presented, consistently tackle the central question, and represent an advancement of our understanding. However, a number of points should be clarified or expanded (see details in the recommendations to authors).

  7. Version published to 10.1101/2021.11.17.468951v1 on bioRxiv