Directed effective connectivity and synaptic weights of in vitro neuronal cultures revealed from high-density multielectrode array recordings

Studying connectivity of neuronal cultures can provide insights for understanding brain networks but it is challenging to reveal neuronal connectivity from measurements. We apply a novel method that uses a theoretical relation between the time-lagged cross-covariance and the equal-time cross-covariance to reveal directed effective connectivity and synaptic weights of cortical neuron cultures at different days in vitro from multielectrode array recordings. Using a stochastic leaky-integrate-and-fire model, we show that the simulated spiking activity of the reconstructed networks can well capture the measured network bursts. The neuronal networks are found to be highly nonrandom with an over-representation of bidirectionally connections as compared to a random network of the same connection probability, with the fraction of inhibitory nodes comparable to the measured fractions of inhibitory neurons in various cortical regions in monkey, and have small-world topology with basic network measures comparable to those of the nematode C. elegans chemical synaptic network. Our analyses further reveal that (i) the excitatory and inhibitory incoming degrees have bimodal distributions the excitatory and inhibitory incoming degrees have bimodal distributions, which are that distributions that have been indicated to be optimal against both random failures and attacks in undirected networks; (ii) the distribution of the physical length of excitatory incoming links has two peaks indicating that excitatory signal is transmitted at two spatial scales, one localized to nearest nodes and the other spatially extended to nodes millimeters away, and the shortest links are mostly excitatory towards excitatory nodes and have larger synaptic weights on average; (iii) the average incoming and outgoing synaptic strength is non-Gaussian with long tails and, in particular, the distribution of outgoing synaptic strength of excitatory nodes with excitatory incoming synaptic strength is lognormal, similar to the measured excitatory postsynaptic potential in rat cortex. Author summary To understand how the brain processes signal and carries out its function, it is useful to know the connectivity of the underlying neuronal circuits. For large-scale neuronal networks, it is difficult to measure connectivity directly using electron microscopy techniques and methods that can estimate connectivity from electrophysiological recordings are thus highly desirable. Existing methods focus mainly on estimating functional connectivity, which is defined by statistical dependencies between neuronal activities but the relevant direct casual interactions are captured by effective connectivity. Here we apply a novel covariance-relation based method to estimate the directed effective connectivity and synaptic weights of cortical neuron cultures from recordings of multielectrode array of over 4000 electrodes taken at different days in vitro. The neuronal networks are found to be nonrandom, small-world, excitation/inhibition balanced as measured in monkey cortex, and with feeder hubs. Our analyses further suggest some form of specialisation of nodes in receiving excitatory and inhibitory signals and the transmission of excitatory signals at two spatial scales, one localized to nearest nodes and the other spatially extended to nodes millimeters away, and reveal that the distributions of the average incoming and outgoing synaptic strength are skewed with long tails.