Decoding Neuronal Networks: A Reservoir Computing Approach for Predicting Connectivity and Functionality

TL;DR

This work introduces a reservoir-computing framework to decode electrophysiological signals from neuronal cultures and reconstruct macroscopic connectivity. By assigning each MEA electrode to an independent micro-reservoir and training only the output layer with Lasso, the model derives an Intrinsic Connectivity Matrix that captures effective, not merely functional, connections and enables prediction of localized stimulus responses. Across synthetic NEST-simulated networks and real MEA recordings, the RC approach outperforms Cross-Correlation and Transfer Entropy in connectivity mapping (AUC up to 0.94, ρ up to 0.72) and demonstrates robust spatio-temporal prediction of network dynamics, with higher accuracy when data richness and training epochs are increased. These results suggest a practical, data-driven tool for inferring mesoscale connectivity and simulating network responses, with potential applicability to high-density MEA data and broader time-series domains.

Abstract

In this study, we address the challenge of analyzing electrophysiological measurements in neuronal networks. Our computational model, based on the Reservoir Computing Network (RCN) architecture, deciphers spatio-temporal data obtained from electrophysiological measurements of neuronal cultures. By reconstructing the network structure on a macroscopic scale, we reveal the connectivity between neuronal units. Notably, our model outperforms common methods like Cross-Correlation and Transfer-Entropy in predicting the network's connectivity map. Furthermore, we experimentally validate its ability to forecast network responses to specific inputs, including localized optogenetic stimuli.

Figures (15)

• Figure 1: Description of the RC model. (a) A microscope image of amicroelectrode (diameter of 30 $\mu$m) surrounded by cultured neurons. This image illustrates how each electrophysiological measurement site samples signals from a complex circuit, whose morphology is not resolvable by simple methods. (b) An illustrative image of how the signals are intercepted by each electrode (yellow circles) from the biological neuronal network in the background. The spike trains collected at each electrode are then forming integrated signals which propagate within the network. (c) The artificial neural network (ANN) design of the RC model. It consists of three layers (input, reservoir, output) and a recurrent branch. It describes how the state of the network $\mathbf{y}$ (described by $N_{ch}$ samples of the measured signals from each electrode) is processed from time step $n$ to time step $n+1$. (d) A block diagram illustrating the sequential computational processes, including training, validation, and testing, conducted in this study.
• Figure 2: Connectivity map obtained by the RC model trained on NEST simulation data. (a), (b) Connectivity matrix (left) and connectivity graph map (right) for both the ground-truth network (a) and the the RC model (b). Color bar refers to the connection strengths (weights). The ground-truth network was simulated by a NEST simulator, producing an electrophysiological activity which was then decoded by the RC model obtaining the Intrinsic Connectivity Matrix (ICM). The nodes in the graphs represent neuronal population (or circuit) as probed by the electrodes (channels) and the edges represent their connections. Connection strengths in the RC model are deduced by the weight matrix $\mathcal{T}_0$ (Eq. \ref{['eq: intrinsic conn matrix']}). Each weight was normalized by the highest element in absolute value and color coded between -1 and 1. Note that the RC model predicted with a very high accuracy the existence of 3 uncoupled groups of nodes. In addition, the model distinguished with a high accuracy between excitatory connections (positive weights) and inhibitory (negative weights) yielding a Person correlation $\rho = 0.72$. The connectivity map in (b) displays only weights with absolute values exceeding 0.2. (c) ROC curve to which corresponds a $AUC = 0.94$. In this example, the RC model had a memory strength $\alpha = 0.5$ and a reservoir dimension $m = 50$.
• Figure 3: Connectivity map derived by the RC model from experimental data collected using a 60-electrode MEA and a mice cortical neuronal culture. The connectivity weights are normalized based on the highest absolute value within the obtained ICM model. The color code refers to the color bar on the right, scaled between -1 and 1. To enhance clarity, connections with weights below $|0.25|$ have been omitted.
• Figure 4: Connectivity retrieval performance of the various algorithms with respect to the ground-truth network. (a) Pearson correlation ($\rho$) and ROC AUC metrics as a function of the richness training data set parameter $q$ (Eq. \ref{['eq: q']}) for the RC model. Points refer to various network realizations, the lines are a fit to the data (AUC: $R^2 = 0.38$ and $\rho$: $R^2 = 0.47$), the bands refer to the 95 % confidence interval. (b) Comparison between the performances of the different algorithms evaluated on all the 51 different network realizations. RC refers to the RC model, CC to the Cross-Correlation method and TE to the Transfer Entropy method. Box plots are used to visualize the distribution of the data (minimum value, 1st quartile, median, 3rd quartile, and maximum value). Diamonds are out-layer points. To gauge the statistical relevance of the algorithm comparison, two-sided Mann-Whitney-Wilcoxon test with Bonferroni correction was applied; AUC-RC vs. AUC-CC: $U-stat. = 1820$, $p-value = 4.527\times 10^{-3}$; $\rho$-RC vs. $\rho$-CC: $U-stat. = 1864$, $p-value = 1.568\times 10^{-3}$; AUC-RC vs. AUC-TE: $U-stat. = 1993$, $p-value = 4.402\times 10^{-5}$; $\rho$-RC vs. $\rho$-TE: $U-stat. = 2417$, $p-value = 2.534\times 10^{-12}$; (c),(d) Comparison between the performances of the different algorithms as a function of the number of populations (network nodes), where each population represents a circuit of 5 neurons.
• Figure 5: Results of a response test for a specific stimulation protocol on the same network as Fig. \ref{['fig: CM example']}. The RC model was trained on NEST simulation data with a memory strength $\alpha = 0.5$ and a reservoir dimension $m=50$. A stimulus was given on the channel (node) labelled by a yellow star in the maps. (a, top panels) The amplitude response map for the ground truth network (left), the amplitude response map predicted by the RC model (centre) and the error maps for the RC model predictions as given by $\varepsilon$ (Eq. \ref{['eq: channel error']} (right). The color maps refer to the amplitudes of the channel (node) response or to the error value. (a, bottom panels) Ground truth network's channel activity map (left), RC model node activity prediction map (centre), and error map evaluated as activity prediction correctness (right). The color code is given in the inset. (b) The ROC curve.