There is increasing evidence for fine-structure in cortical connectivity. Bidirectional connectivity and motifs of 3 or more highly interconnected neurons are more prevalent than expected for an Erdös-Rényi random connectivity [1,2]. What is the effect of these excess motifs on cortical dynamics? To address this question we study the dynamics of networks of neurons randomly connected with a rule such that the probability of bidirectional connections is higher than in the pure chance case. The network consists of excitatory () and inhibitory () neurons connected with probability
Here are the connection matrices, if there is a connection from neuron in population to neuron in population and otherwise. We focus on the dynamics of such networks operating in the balanced regime .
We investigate networks of binary neurons  analytically in the limit where we first take and then , for finite . We show that both excess bidirectional connections between the cells and excess bidirectional connections between the cells slow down the fluctuations in the neuronal input. As a result, the autocorrelation of the activity decays more slowly than in the corresponding Erdös-Rényi network. In contrast, bidirectional connections between and cells decrease the decorrelation time. Remarkably, bidirectional connections between cells are more efficacious in slowing down the dynamics than those between cells. These phenomena are due to the small loops that the bidirectionallity induces in the network architecture. Together with the relatively strong synapses in balanced networks these lead to a non-negligible effective delayed self-coupling.
We also investigate the effect of
bidirectional connectivity in a balanced network
of conductance-based spiking neurons using
numerical simulations. Apart from the
connectivity, the network is similar to
that in . We show that this network behaves
qualitatively similarly to the binary network.
Furthermore, bidirectional connections between
cells or between
cells increase the Fano factor of the spike count,
while the Fano factor decreases for bidirectional
cells. We also investigate the dependence of this
effect on the synaptic time constants and study
how the spike irregularity is modified by
'sensory' stimulation of the network.
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