Effect of Sparse Random Connectivity on the Stochastic Spiking Coherence of Inhibitory Subthreshold Neurons

We study the effect of network structure on the stochastic spiking coherence (i.e., collective coherence emerging via cooperation of noise-induced neural spikings) in an inhibitory population of subthreshold neurons (which cannot fire spontaneously without noise). Previously, stochastic spiking coherence was found to occur for the case of global coupling. However, “sparseness” of a real neural network is well known. Hence, we investigate the effect of sparse random connectivity on the stochastic spiking coherence by varying the average number of synaptic inputs per neuron Msyn. From our numerical results, stochastic spiking coherence seems to emerge if Msyn is larger than a threshold M∗ syn whose dependence on the network size N seems to be quite weak. This stochastic spiking coherence may be well visualized in a raster plot of neural spikes. For a coherent case, partially-occupied “stripes” (composed of spikes and indicating collective coherence) appear. As Msyn is decreased from N − 1 (globally-coupled case), the average occupation degree of spikes increases very slowly. On the other hand, the average pacing degree between spikes (representing the precision of spike timing) decreases slowly, but near M∗ syn its decrease becomes very rapid. This decrease in the pacing degree can also be well seen through merging of multiple peaks in the interspike interval histograms. Due to the effect of the pacing degree, the degree of stochastic spiking coherence decreases abruptly near the threshold M∗ syn.