Fig 1.
Synaptic input patterns applied to the detailed microcircuit model.
A: The modeled microcircuit includes 2170 input fibers grouped into 100 bundles of nearby fibers modelling thalamo-cortical afferents. B: Spike trains are prescribed to the fibers to serve as stimulus patterns. Each pattern is associated with 10 randomly selected bundles of fibers. Each repetition of a pattern activates the associated fibers with an adapting Markov process, i.e. repetitions of a pattern use the same fibers, but with different stochastic spike trains. We apply a stream of 4495 repetitions of one of 8 stimulus patterns in random order (bottom) and simulate the microcircuits response (top). Raster plot of spiking responses is sorted by the layer of the simulated neuron, with layer 1 at the top and layer 6 at the bottom C: PSTHs of the input (bottom) and population spiking response (top) for each stimulus. D: Random sampling: We sample at random offsets by randomly picking 600 neurons from all neurons within a given radius and consider their spike trains for further analysis.
Fig 2.
Analysis of volumetric samples according to the manifold hypothesis.
A: Trajectories of three components for an exemplary volumetric sample with a radius of 175μm. Responses to different stimuli are indicated in different colors (mean of 562 ± 4 (mean ± std) repetitions each). B: Mean of the most extreme value taken by individual components during a stimulus presentation, normalized as a z-score relative to the distribution over all trials and stimuli. Indicated for four random neuron populations, volumetrically sampled with a radius of 175μm. Green outline indicates the three components shown in A. C: Left: For 25 volumetric samples with radius 175μm: Negative decimal logarithm of the p-values of a test against the null hypothesis that their extreme values as in B have identical means (Kruskal test, n = 4495 stimulus repetitions). Green outlines indicate the samples shown in B. Right: Mean accuracy of a classifier of stimulus identity based on the trajectories of the 12 main components of the indicated volumetric samples (see Methods). D: Bottom: triad motif over- and underexpression in 125 volumetric samples with radii between 125 and 325 μm, relative to ER. Samples are sorted by classification accuracy (right). Top: Correlation between expression of a specific motif and classification accuracy in the samples (pearsonr).
Fig 3.
Neuron-neighborhood sampling with uncommon connectivity.
A: Neuron-neighborhood sampling: Any neuron can be a center. Its associated neighborhood comprises the center, all synaptically connected neurons, and the connections between them. We then calculate various topological parameters of the neighborhood’s connectivity. B: Blue violinplot: Distribution of various topological parameters, normalized between 0 and 1. Orange dots: Location of the champions, i.e. the 25 neighborhoods of at least 50 neurons with the highest values for a parameter. C: Frequency of triad motifs in volumetric samples with a 175μm radius relative to an Erdos-Renyi graph with the same number of nodes and edges. Grey: 25 volumetric samples; Black: their mean. D: Over- and under-expression of triad motifs in the connectivity of champion samples of various parameters, normalized with respect to mean/std of the volumetric samples.
Table 1.
Topological parameters used.
Fig 4.
Classification accuracy in champion samples.
A: Accuracy of a linear classifier to decode stimulus identity from the spike trains of the champion samples. Blue dots: Accuracies of 6-times cross validation for 25 champions (see Methods); bar and errorbars: mean and standard deviation. B: Size of champion neighborhoods against their decoding accuracy. Blue dots: individual neighborhoods; grey diamonds and errorbars: mean and standard deviation of champions of a parameter. Red markers: For the three largest classes of champions as in the legend, subsampled at 90%, 70%, 50%, 25% and 15%. C: Values of the neighborhood size average measurement (see Methods) for champion (green) and randomly picked (grey) neighborhoods against their classification accuracy. Black line: Linear fit to both; indicated in blue: residual of the fit. D: Efferent extension against the residual accuracy indicated in C for randomly picked neighborhoods. Grey dots: 1276 random neighborhoods; black line: linear fit. E: Left: Slopes of linear fits of residual accuracy against normalized values of the indicated parameter for randomly picked neighborhoods. Right: Fraction of variance of the residual accuracy that is explained by the linear models over a model that takes only the morphological type of the center into account (see Methods). Black stars indicate Bonferroni-corrected significance (***: p < 0.0001).
Fig 5.
Topological parameters in volumetric samples.
A: Two ways of calculating values for topological parameters in volumetric samples. Left: Values are calculated directly on the synaptic connectivity within the sample (blue neighborhood). Right: Generation of “synthetic” values of topological parameters that take the neighborhood structure of the sample into account: The size of the overlap of each possible neighborhood with the sample is calculated, then a weighted average of the parameter value for the N = 3 strongest overlapping neighborhoods is used (red, yellow, and green neighborhoods with relative overlaps of 3/4, 2/3, and 3/5 respectively). B: Left: Slopes of linear fits of residual accuracy against normalized parameter values that were directly calculated. Right: Fraction of variance of the residual accuracy that is explained by the linear models over a model that takes only the radius of the sample into account (see Methods). Black stars indicate Bonferroni-corrected significance (***: p < 0.0001). Shorthand parameter names see Table 1. C: Comparing directly calculated parameter values (blue) to weighted mean-based, “synthetic” values of the fourth density coefficient. D: As in B, but for synthetic values of topological parameters.
Fig 6.
Coupling coefficient and topological featurization.
A: Distribution of the coupling coefficient, as in Okun et al., 2015, of all excitatory neurons in the model. Blue: data; grey lines with errorbars: Shuffled controls that keep or shuffle mean firing rates of individual neurons. Neurons with an unexpected low coefficient are “soloists”, a high coefficient indicates a “chorister”. B: Neighborhood size against the coupling coefficient of the center for center neurons in layers 1–5 (blue) and in layer 6 (orange). Dashed lines: linear fits. C: As in B, but coupling coefficient against classification accuracy of the neighborhoods. D: Mean coupling coefficient of neurons in a volumetric sample against its residual classification accuracy, as in Fig 5C. Inset: Fraction of variance explained as in Fig 5D. E: Classification based on topological featurization: For a given neighborhood, we consider in each 10 ms time step only the subset of neurons that are firing. We then calculate the value of the Euler characteristic (EC) of the graph of connectivity between them. We classify stimulus identity based on the EC time series of 25 centers. F: Left: Results of the classification for centers randomly picked from the various morphological types in the model. Errorbar: std of cross validation. Right: Same, for the various champions. G: Mean classification accuracies using the manifold-based method against accuracies based on topological featurization. Red/blue dots: Random centers as in F; green dots as labelled. H: Accuracies as in F against the mean coupling coefficient of neurons in the neighborhoods. Errorbars: std over coupling coefficients.
Fig 7.
Feature correlation and topological featurization in volumetric samples.
A: Mean relative overlap of pairs of neighborhoods that are champions of the same parameter against the mean correlation coefficient of their Euler characteristic time series (feature correlation). B: Pairwise feature correlations of the champions of two exemplary parameters. C: Mean feature correlation of champions against their performance in feature-based classification. D1: Feature-based classification for volumetric samples can be performed using the active sub-networks of each sample in each time step, then pooling over samples. D2: Alternatively, the 25 largest neighborhoods can be found within a single volumetric sample, which are then analyzed as other neighborhood samples. E1: Mean feature correlation for volumetric samples of various radii when the technique in D1 is employed. E2: Same, when the method outlined in D2 is employed. Only data from one volumetric sample are shown. F: Feature-based classification accuracies for volumetric samples using the purely volumetric (blue) or sub-neighborhood-based (red) techniques, or a random control for sub-neighborhoods (yellow). For sub-neighborhood-based and random conditions, we pooled data from all 25 volumetric samples. Black stars indicate Bonferroni-corrected significance (volumetric vs. sub-neighborhoods: Wilcoxon rank-sum test; sub-neighborhoods vs. random: Wilcoxon signed-rank test; n.s.: not significant, *: p < 0.01, **: p < 0.001, ***: p < 0.0001). G: Feature correlation against classification accuracy for volumetric samples using the purely volumetric (blue; Pearson’s r = −0.954, p = 0.012) or sub-neighborhood-based (red; Pearson’s r = −0.811, p = 0.096) technique.
Fig 8.
Overview of the inputs into the analysis pipeline and its individual analysis steps.