Fig 1.
In silico construction of neuronal networks with topography.
(A) Conceptual representation of a topographical network, in which a mixed population of excitatory and inhibitory neurons connect following the tracks at the bottom or at the top of a profile of height h. The axons of neurons may pass into other tracks with probabilities P1 and P2. (B) Illustrative network layout as implemented by the in silico model. Only 30 neurons are shown for clarity. Colored dots and lines illustrate the location of neuronal bodies and the excursions of their axons. The blue axon crosses from top to bottom, while the orange, red and green follow the edges of the pattern. (C) Corresponding connectivity matrix, highlighting the interconnectivity between the colored neurons. (D) Resulting network activity displayed as a rasterplot, in which each blue dot indicates the activation of a neuron (indexed along the vertical axis) along time (horizontal axis).
Table 1.
Probabilities of activity and axons crossing a PDMS border.
Table 2.
Parameter values used for simulations.
Fig 2.
Spontaneous activity in homogeneous and topographically-patterned networks.
(A) Left panel shows a fluorescence image of an in vitro neuronal network, with bright objects corresponding to active neurons. The remaining panels show examples of simulated neuronal culture layouts and connectivity. In the simulation panels, triangles correspond to excitatory and circles to inhibitory neurons. Only 25% of neurons and their connections are shown for clarity. For each simulated condition a group of neurons and their outgoing connections are highlighted to illustrate the effect of the PDMS obstacles. (B) Raster plots of the networks in (A). Each dot represents a spike of a neuron. Neurons are sorted by their position along the left-right direction, with the leftmost neuron at the bottom (0) and the rightmost neuron on the top (N). Time is represented along the horizontal axis. In the first and third columns, corresponding to the Tracks condition in experimental and simulated data respectively, the background shading separates the neurons into the different tracks. (C) Population activity (PA) plots showing the summed activity traces corresponding to the raster plots of panel B. The value ‘1’ corresponds to the full culture being active in a short time window. The red line indicates , which we use as a threshold to accept network bursts as significant (as compared to background activity) throughout the paper. Only 1-minute sections of full simulations are shown for clarity. (D) Distribution of the sizes of network bursts along development for different conditions. For each value of
, indicated along the x-axis, the peaks of the summed activity traces (see panel C) are plotted as points. The two gray-shaded plots on the left correspond to experimental results from [44]. For each axon length the peaks are plotted for the three conditions next to each other: Control (blue circles), Tracks (orange triangles) and Squares (green squares). The figure shows network burst sizes of ten independent simulation runs, each with a length of
of simulation time, for varying axon length
and for the three experimental setups shown in (A). Stars indicate significance of Mann-Whitney-Wilcoxon tests as follows: *: p < 0.05; **: p < 0.01; ***: p < 0.001. (E) Richness of network activity shown in (D) for different axon lengths and setups. Each line corresponds to a single condition: Control (blue), Tracks (orange) and Squares (green). Each dot indicates the average over 10 independent simulations runs, each with a length of
. Free simulation parameters:
,
, and in addition for panels A-C
.
Fig 3.
Front propagation in different conditions.
(A) Representative activity propagation through the neuronal cultures under different conditions. Color-coding indicates first activation time of neurons in the spatial grid point within the front. Start of the activity wave is indicated with a blue dot. (B) Spatial distribution of network burst initiation points (black dots) and its probability density function (pdf, blue-yellow colormap) for the different conditions as indicated on the left of panel (A). (C) Activity propagation velocities of each network burst for the different conditions. Stars indicate significance of Mann-Whitney-Wilcoxon tests as follows: ***: p < 0.001. (D) Network burst propagation velocities for different parameter values of the obstacle height h and noise intensity σ for the Tracks conditions. Stars indicate significance of Mann-Whitney-Wilcoxon tests as follows: *: p < 0.05; **: p < 0.01; ***: p < 0.001. (E) Barplot indicating average number of network bursts for the same parameter values as in panel (D). Gray lines indicate the standard deviation across simulation runs. Stars indicate significance of Mann-Whitney-Wilcoxon tests as follows: *: p < 0.05; **: p < 0.01; ***: p < 0.001. For each panel . For panels A-C
and
.
Fig 4.
Structural connectivity of simulated neuronal culture growth.
(A) Representative structural connectivity matrices for the three conditions. Black dots indicate that a connection exists between the neurons represented in the two axes. Neurons are ordered according to their position in the neuronal culture from left to right. (B) Distribution of connection lengths between neurons for the conditions. The gray inset shows two-sample Kolmogorov-Smirnov tests. (C) Distribution of angles between connected neurons. (D) Distribution of number of incoming connections. The gray box shows two-sample Kolmogorov-Smirnov tests. (E) Several graph-theoretical measures (from left to right: global efficiency, modularity Q, and average clustering) of the structural connectivity matrices (in color) and the values for random Erdös-Rény graphs with average in-degree matched to the average of each condition (in gray). Stars indicate significance of two-sample unpaired Student’s t-tests as follows: *: p < 0.05; **: p < 0.01; ***: p < 0.001. Significance indication below horizontal black lines indicate significance of tests across conditions. Significance indications above the gray markers indicate the significance of tests between the null distributions (indicated in gray) and the measured distributions (in color). Parameters used for all panels: and
, panels B-E contain data of 10 independently grown networks per condition.
Fig 5.
Effects of spatial anisotropy and external noise intensity on dynamics.
(A) Dynamical richness Θ as a function of obstacle height h and noise intensity σ for the Tracks condition. Data shown is averaged over three reproductions. White-circled numbers relate to highlighted plots in panel (B). By definition , but typically
. A value of
indicates dynamically rich activity. (B) Representative raster-plots of the simulation runs with parameters as marked in panel (A), illustrating the differences in activity dynamics for the different parameter values and measured dynamical richness. For all panels
. Panel A shows averaged data of 3 independent simulation runs per parameter combination.
Fig 6.
Effective connectivity analysis.
(A) Representative network maps, color-coded to indicate the functional modules that the neurons belong to, as found by estimating the effective connections of neurons using GTE and the Louvain algorithm, for different parameter values (different columns) for the Tracks condition. (B) Effective connectivity matrices as given by thresholded GTE measures, corresponding to the networks in panel (A). Neurons are ordered as Fig 4A with the leftmost neuron at index 0 and the rightmost neuron at N. (C) Receiver Operating Characteristic (ROC) curves for quantifying the resemblance between structural and effective network connectivity, for different parameter values. (D) Area Under the Curve (AUC) values of the ROC curves for a range of obstacle heights h and noise amplitudes σ. For all panels .