Research ArticleNEUROSCIENCE

Impact of modular organization on dynamical richness in cortical networks

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Science Advances  14 Nov 2018:
Vol. 4, no. 11, eaau4914
DOI: 10.1126/sciadv.aau4914
  • Fig. 1 Engineering the modularity of living cortical networks.

    (A) Confocal imaging of the polydimethylsiloxane (PDMS) stamps used for microcontact printing of the proteins. From left to right: merged, triple-bond, single-bond, and no-bond patterns. (B) Phase-contrast micrographs of cortical networks at 10 DIV. Modularity increases in the order of merged, triple-bond, single-bond, and no-bond networks. (C) A cortical network on the single-bond micropattern loaded with the fluorescence Ca indicator, Cal-520 acetoxymethyl ester (AM). Scale bar, 200 μm. (D) Fluorescence signals from a 20-min recording of the spontaneous activity of a single-bond network. Traces of eight neurons are shown, and the colors distinguish the affiliated modules. Black dots mark detected spikes. In this recording, network bursts were observed twice, in addition to 10 bursts that involved only two modules. In the third, fifth, and seventh traces (from the top), small random events were also observed, which, most probably, are sporadic action potentials. (E) The average number of network bursts per 20-min session. Note that for the no-bond network, the activity of individual modules was isolated (see fig. S4B), and an event refers to synchronized firing within each 200 μm by 200 μm island. n = 22 (merged), 21 (triple bond), 23 (single bond), and 20 (no bond). Error bars represent the SEM. (F) Distributions and cumulative distributions (inset) of IBI in the merged, triple-bond, and single-bond networks. Cum. prob., cumulative probability.

  • Fig. 2 Dynamical richness and modularity.

    (A) Computation of dynamical complexity in representative networks with gradually higher modularity, from merged to single bond. Left: Raster plot of spontaneous activity (violet) and corresponding GNA (red). Strong coherence in the merged network is revealed by the repeated network activations of size 1. Center: Matrix of pairwise CCs between neurons (i, j). The strong network coherence provides CC values close to 1. Right: Probability density functions (pdfs) of CC values rij (violet) and GNA values Γt (red-yellow). The pdfs for the merged network peak toward 1 and provide small values of ΘCC and ΘGNA, with a final dynamical richness of Θ ≅ 0.07. For the triple-bond modular network, the strong connectivity among modules facilitates integration and Θ ≅ 0.06. The single-bond modular network exhibits a much richer variability in activity patterns, with switching activations encompassing two or four modules. This variability is reflected in the GNA values and the matrix of CC values and provides broad pdfs that lead to relatively high values for both ΘCC and ΘGNA, and with Θ ≅ 0.34. (B) Distribution of GNA values for all observed concurrent neuronal activations, comparing the merged (M; 13 cultures and 345 activations), triple-bond (3-b; 13 cultures and 336 activations), and single-bond (1-b; 18 cultures and 529 activations) patterns. The cartoons on the right illustrate the relative size of the coherent activations (yellow glow). (C) Average Θ values. The single-bond pattern displays significantly higher Θ values than the merged or triple-bond ones. Merged and triple bond are not significantly different. Data are shown as means ± SEM. ***P < 0.001; **P < 0.01; n.s., not significant (two-tailed Student’s t test).

  • Fig. 3 Effective connectivity and global efficiency.

    (A) Representative effective connectivity maps for patterns with gradually higher spatial modularity. The squared contours with a dotted outline indicate the location of the spatial modules. The merged and triple-bond patterns provide highly connected, highly integrated effective networks, with G*EFF ≅ 1 and only one functional community. Provincial hubs in the triple-bond pattern facilitate the permanent functional cohesion among modules. The single-bond network exhibits a much weaker connectivity and a much lower integration capacity, with G*EFF ≅ 0.18. Its effective network is characterized by two main communities (orange and yellow areas) that extend across different modules. Provincial hubs maintain cohesion within communities, which are, in turn, linked through a kinless node. (B) Raster plot of spontaneous activity and temporal evolution of G*EFF for the same single-bond network. The graphs below show illustrative effective networks at different stages of the recording to highlight the rich functionality of the system, which switches from high integration (stages 1 and 4) to high segregation (stages 2 and 3). The values below each network indicate the number of main communities. (C) Average G*EFF values for all studied networks (merged, 13 cultures; triple bond, 13; single bond, 18). The merged and triple-bond patterns exhibit G*EFF values significantly higher than those of the single-bond patterns. The merged cultures are always integrated, the triple-bond ones are mostly integrated with rare or sporadic segregation, and the single-bond ones switch between the two scenarios. Data are shown as means ± SEM. ***P < 0.001, **P < 0.01 (two-tailed Student’s t test).

  • Fig. 4 Subquorum coherence in micropatterned cortical networks.

    (A) Relationship between the mean CC between two neighboring modules and the width of the interconnecting neurite bundle in the single-bond patterns. Each dot represents a module pair and is colored according to the result of the k-means algorithm. (B) Three-body interaction of neuronal modules. The mean CC between neurons in modules α and γ, Embedded Image, is plotted against the bundle thickness of modules α-β and β-γ. The value of Embedded Image is indicated in color, and the size of the dots is changed in proportion to the value to aid visualization. (C) Average intermodular correlation [Embedded Image] plotted against average bundle thickness [Embedded Image]. Each dot represents an individual network and is colored according to the result of the k-means algorithm. The dashed line represents a linear fit against the blue plots.

  • Fig. 5 Subquorum synchronization in in silico model networks.

    (A) Schematic representation of a modular network model. Yellow circles indicate neurons, gray lines denote the connections, and arrows indicate the direction of the connection. (B) Occurrence of network bursts (events) is shown as the average number per 20 min. A total of 300 networks were sampled per condition. The probability of a network exhibiting more than one event is shown on the counter axis. Results obtained over a wider range are shown in the inset. The dotted line indicates data obtained from networks with completely randomized connectivity with identical average node degrees. (C) Mean CC between two modules versus the number of connections between the modules (solid line). Individual data are plotted in violet. To ease visualization, we randomly displace the plots horizontally by ±0.5. (D) Raster plots of two network bursts that occurred in the same network with 26 intermodular connections. The red bar indicates the timing of an action potential. The activity is initiated in module 3 (neurons 51 to 75) and propagates to modules 2 (neurons 26 to 50) and 4 (neurons 76 to 100) and lastly to module 1 (neurons 1 to 25). (E) The mechanism of subquorum synchronization. The feedback excitation from the hidden layer nodes (orange) to the input layer nodes (blue) enhances the sparse input to each module. (F) Random rewiring of the feedback (FB) excitation to noninput layer nodes diminishes the occurrence of network bursts. A rewiring ratio of 1 corresponds to a case in which no feedback exists from the hidden layer to the input layer. The original network (rewiring ratio, 0) is a network with 26 intermodular connections, whose activity is shown in (D). Error bars represent 95% confidence intervals.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/11/eaau4914/DC1

    Fig. S1. Axon outgrowth and synapse formation of micropatterned cortical neurons.

    Fig. S2. Effect of intermodular connections on the network structure.

    Fig. S3. Average number of cells in the networks.

    Fig. S4. Analysis of network bursts.

    Fig. S5. Other complexity measures.

    Fig. S6. Role of excitatory connectivity on dynamical richness and functional organization.

    Fig. S7. Membrane potentials and synaptic conductance in model networks.

    Fig. S8. Impact of nonuniform intermodular connectivity in simulations.

    Fig. S9. Robustness of effective connectivity inference.

    Fig. S10. Dependence of global efficiency GEFF on the amount of the retained significant links.

    Movie S1. Spontaneous activity recording of a merged network.

    Movie S2. Spontaneous activity recording of a triple-bond network.

    Movie S3. Spontaneous activity recording of a single-bond network.

    Reference (41)

  • Supplementary Materials

    The PDF file includes:

    • Fig. S1. Axon outgrowth and synapse formation of micropatterned cortical neurons.
    • Fig. S2. Effect of intermodular connections on the network structure.
    • Fig. S3. Average number of cells in the networks.
    • Fig. S4. Analysis of network bursts.
    • Fig. S5. Other complexity measures.
    • Fig. S6. Role of excitatory connectivity on dynamical richness and functional organization.
    • Fig. S7. Membrane potentials and synaptic conductance in model networks.
    • Fig. S8. Impact of nonuniform intermodular connectivity in simulations.
    • Fig. S9. Robustness of effective connectivity inference.
    • Fig. S10. Dependence of global efficiency GEFF on the amount of the retained significant links.
    • Legends for movies S1 to S3.
    • Reference (41)

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). Spontaneous activity recording of a merged network.
    • Movie S2 (.mp4 format). Spontaneous activity recording of a triple-bond network.
    • Movie S3 (.mp4 format). Spontaneous activity recording of a single-bond network.

    Files in this Data Supplement:

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