Reconstructing neuronal networks from multi-electrode array recordings

The knowledge of the connectivity of in-vitro neuronal cultures can provide important insights for understanding brain networks. We present a method that estimates directed effective connectivity and synaptic weights of cortical neuronal cultures from the recordings of a multielectrode array. The neuronal culture is modelled as a dynamical system governed by a generic set of differential equations with noise. We have derived a mathematical result showing that the time-lagged cross-covariance of the dynamics is related to the equal-time cross-covariance of the dynamics via the connectivity matrix of the network. Using this relation, we reconstruct the directed effective connectivity matrix and the synaptic weights of the links with each electrode taken as a node of the network. The neuronal networks reconstructed have several interesting properties. In particular, the distributions of the average synaptic strength of the incoming and outgoing links are non-Gaussian and skewed with long tails. We show that the long-tailed distribution of the average synaptic strength of the incoming links is the underlying cause of the long-tailed distributions of spiking activity.