A multi-class logistic regression algorithm to reliably infer network connectivity from cell membrane potentials

Abstract

In neuroscience, the structural connectivity matrix of synaptic weights between neurons is one of the critical factors that determine the overall function of a network of neurons. The mechanisms of signal transduction have been intensively studied at different time and spatial scales and both the cellular and molecular levels. While a better understanding and knowledge of some basic processes of information handling by neurons has been achieved, little is known about the organization and function of complex neuronal networks. Experimental methods are now available to simultaneously monitor the electrical activity of a large number of neurons in real time. The analysis of the data related to the activities of individual neurons can become a very valuable tool for the study of the dynamics and architecture of neural networks. In particular, advances in optical imaging techniques allow us to record up to thousands of neurons nowadays. However, most of the efforts have been focused on calcium signals, that lack relevant aspects of cell activity. In recent years, progresses in the field of genetically encoded voltage indicators have shown that imaging signals could be well suited to record spiking and synaptic events from a large population of neurons. Here, we present a methodology to infer the connectivity of a population of neurons from their voltage traces. At first, putative synaptic events were detected. Then, a multi-class logistic regression was used to fit the putative events to the spiking activities and a penalization term was allowed to regulate the sparseness of the inferred network. The proposed Multi-Class Logistic Regression with L1 penalization (MCLRL) was benchmarked against data obtained from in silico network simulations. MCLRL properly inferred the connectivity of all tested networks, as indicated by the Matthew correlation coefficient (MCC). Importantly, MCLRL was accomplished to reconstruct the connectivity among subgroups of neurons sampled from the network. The robustness of MCLRL to noise was also assessed and the performances remained high (MCC>0.95) even in extremely high noise conditions (>95% noisy events). Finally, we devised a procedure to determine the optimal MCLRL regularization term, which allows us to envision its application to experimental data.