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Dynamics and function of neuronal networks are determined by their synapticconnectivity. Current experimental methods to analyze synaptic networkstructure on the cellular level, however, cover only small fractions offunctional neuronal circuits, typically without a simultaneous record ofneuronal spiking activity. Here we present a method for the reconstruction oflarge recurrent neuronal networks from thousands of parallel spike trainrecordings. We employ maximum likelihood estimation of a generalized linearmodel of the spiking activity in continuous time. For this model the pointprocess likelihood is concave, such that a global optimum of the parameters canbe obtained by gradient ascent. Previous methods, including those of the sameclass, did not allow recurrent networks of that order of magnitude to bereconstructed due to prohibitive computational cost and numericalinstabilities. We describe a minimal model that is optimized for large networksand an efficient scheme for its parallelized numerical optimization on genericcomputing clusters. For a simulated balanced random network of 1000 neurons,synaptic connectivity is recovered with a misclassification error rate of lessthan 1% under ideal conditions. We show that the error rate remains low in aseries of example cases under progressively less ideal conditions. Finally, wesuccessfully reconstruct the connectivity of a hidden synfire chain that isembedded in a random network, which requires clustering of the networkconnectivity to reveal the synfire groups. Our results demonstrate how synapticconnectivity could potentially be inferred from large-scale parallel spiketrain recordings.

Reconstruction of recurrent synaptic connectivity of thousands of neurons from simulated spiking activity