Fig 1.
An ensemble artificial neural network to improve neuronal connectivity inference.
A Schematic illustrating the developed analysis workflow to systematically compare statistically derived neuronal connectivity across inference algorithms and defined network dynamics. Empirical spike-train data (i), obtained by high-density microelectrode array (HD-MEA) recordings from primary cortical cultures, and different types of white noise (ii) were used as input to a network (iii) of leaky integrate-and-fire (LIF) neurons (300 neurons, 50:50 excitatory (E) and inhibitory (I) neurons), adopted from previous work [41]. The a priori defined structure underlying the LIF network served as the first ground truth to compare established and new connectivity-inference methods, providing a connectivity score (s) and a weight (w) for each connection (v-vi). Moreover, connectivity-inference performance was also assessed on connectivity data obtained from parallel HD-MEA/patch-clamp recordings [58]. B Schematic depicting the architecture of the ensemble artificial neural network (eANN). The eANN receives as input the connectivity score s and weight w values from multiple established inference algorithms. Then the feed-forward network is trained. Finally, the eANN outputs probability values which indicate whether the connection is excitatory, inhibitory, or if there is no connection at all.
Table 1.
Overview of connectivity inference methods and abbreviations.
Fig 2.
Reconstruction performance across algorithms, dynamics, cell types, and recording length.
A Example raster plot (upper panel) and traces of binned population activity (lower panel; the number of spikes per second and neuron) of the high-burst rate condition. B Network reconstruction obtained from a subset of the data shown in A, exemplified for the GLMCC method [40]. Red and blue squares correspond to ground-truth excitatory and inhibitory synapses. White and black circles indicate predicted true positives and false positives. C Same as B, for the results obtained with the eANN approach, which generally improved the reconstruction performance. D The mean average precision score (APS, upper panel) and Matthews correlation coefficient (MCC, lower panel), estimated across all connections, obtained from all inference algorithms and the eANN across three different dynamical regimes. Dots depict the performance obtained on three different subnetworks of the same simulation. E Connectivity reconstruction performance (APS, MCC) as a function of recording time. Results indicated an improvement for longer recordings. Results in panel E are depicted for the intermediate dynamical regime. F APS and MCC for each type of connectivity, i.e., either excitatory (E, in red), or inhibitory (I, in blue), or a combination of both types (E+I, in black). Correspondingly, the performance gains achieved by the eANN are plotted in shades of red, blue, and black. G Quality of topological feature reconstruction for the inferred network across the three dynamical regimes. In the upper panel, the relative difference between four global features (network density, average clustering, and efficiency) is shown. The panel in the middle shows average Pearson correlation coefficients for the local/nodal metrics, comparing values obtained for the ground truth and inferred networks. Black stars indicate the method that performed best. The lower panels depict the absolute difference of triplet-motif frequencies between the ground truth and the inferred networks.
Fig 3.
A SHAP values for an examplary excitatory (E) connection (top panel) and an inhibitory (I) connection (bottom panel), ranked according to their importance. The length of the arrows denotes the approximated feature contribution to the eANN output, as estimated by the SHAP method [60]. The y-axis shows the corresponding features with the feature value in brackets. Green arrows pointing to the right indicate that this feature was informative in the process of determining an E/I connection; purple arrows pointing to the left indicate the opposite. Normalized histograms plotted in light green and purple show the eANN output for connected pairs and unconnected pairs. The dashed line is the average eANN output for all connections in the dataset. B The features with the highest average SHAP values for excitatory (E, top panel) and inhibitory (I, bottom panel) connections. Red and blue bars depict the average SHAP values for excitatory and inhibitory connections; error bars represent the standard deviation, calculated over all E/I connections present in the dataset. C SHAP values as a function of feature values for the top two features depicted in panel B, namely GLMPP w, and GLMCC w; black dots indicate unconnected pairs.
Fig 4.
Validating synaptic connectivity inference with parallel HD-MEA/patch-clamp recordings.
A A single patched neuron on the HD-MEA, including the patch pipette. The neuron was labelled with Alexa Fluor 594 through the patch pipette; HD-MEA electrodes can be seen in the background. B Example recording of a patched neuron (lower panel, intracellular signal in blue), and some of its extracellular signals on the HD-MEA (upper panel, spikes in black); HD-MEA and patch-clamp recordings were performed in parallel and later synchronized. C The temporally aligned HD-MEA/patch-clamp signals allowed inference of the exact location of patched neurons on the HD-MEA and their electrical footprints (EFs) D. To infer the putative pre-synaptic connectivity of individual patched neurons, we first performed long-term HD-MEA baseline recordings. Next, we applied a post-processing step to match the EF of the patched cell with the EF templates obtained from the spike-sorted HD-MEA baseline recording. Panel E depicts the overlap of the EF generated during the patch session (in black), and the matched EF obtained from the spike-sorted baseline recording (in red). F HD-MEA network recording (upper panel) and simultaneous whole-cell voltage-clamp (VC) recording (lower panel). VC recordings were used to measure the excitatory/inhibitory postsynaptic currents (ePSCs/iPSCs) in the patched cell, and to link their occurrence to the extracellular activity of neurons recorded on the HD-MEA. Panel G depicts three exemplary connections of the patched cell (EF in black) to three presynaptic neurons; the EFs of these cells are depicted in light blue, orange, and purple. H IC model fit to patch-clamp recording. Spikes of identified presynaptic neurons are shown on top, aligned with the recorded currents of the patched neuron. PSCs of three units are shown as insets, with the average PSC signal depicted in black and the fitted model PSC displayed in different colors. The shaded area shows the 5–95% quantile range. I PSCs of four cells, three connected presynaptic neurons, and one unconnected neuron, are shown along with their corresponding CCGs. Note, that a high-chloride internal patch-clamp solution was used to simultaneously measure the synaptic activity of excitatory and inhibitory presynaptic cells [58]. As a result, as depicted, inhibitory input currents also have a negative polarity. On the right side of the CCG, a colored circle indicates whether the respective connectivity method found a connection or not (cross). J Panel depicts the performance of the different connectivity methods averaged over three patched neurons.
Fig 5.
Characterizing the connectivity of in vitro neuronal networks.
A Firing rate cumulative density function (CDF) of 600 spike-sorted units from HD-MEA recordings obtained from primary cortical cultures (top panel; n = 6 cultures; 100 units per network; recording duration: 1 h; culture age: DIV 14); and CDF of inter-spike interval coefficients of variation (ISI CV) for the same cultures (lower panel). B Overall distribution of eANN weights of empirical networks (in gray; values are depicted in logarithmic space) and overlaid with the corresponding distribution of eANN values inferred from surrogate networks (in yellow). The distribution of experimentally inferred values demonstrates a clear peak in the eANN weight distribution that distinguishes putative synaptic connections from unconnected pairs. C Significant eANN edges cannot exclusively be explained by the overlap across all inference methods. Panel E depicts the consensus distribution, i.e., the overlap across the six inference methods for all significant eANN edges; most eANN edges were found by five of the other methods. About 20% of edges were found by the eANN, but not by the other methods at the selected threshold (see zero bin). D Network density as a function of threshold values (corresponding to α: 0.05, 0.01, 0.005, and 0.001) across all inference methods. α threshold values were derived from surrogate connectivity estimates (temporally jittered spike trains). Network density decreased with smaller α-values, and varied significantly across methods. E Intersection of significant eANN connections with those of all other connectivity inference methods. F Inferred connectivity decayed with interneuronal distance (α = 0.01), and the likelihood of long-range connections (> 1 mm) was very low. G Example connectivity matrices for one culture inferred with all seven inference methods. H Topology of inferred in vitro networks differed significantly across inference methods (α = 0.01; filled circles: empirical data; empty circles: randomized surrogate networks). I All inference methods yielded an over-representation of triplet motifs (see Fig 2 for motif ID legend), but with slight differences across methods. Dots depict motif IDs that occurred significantly more frequently than re-wired surrogate networks (FDR corrected α of 0.001); the color indicates the relative mean difference in their occurrence. J Lower triangle (red color scale): Topological similarity, calculated by pairwise Pearson correlation coefficients across the topological metrics shown in H and I across all inference methods. Upper triangle (blue color scale): Network similarity, quantified by pairwise MCCs across all inferred adjacency matrices. Panels D-J depict network graphs thresholded with α = 0.01.