Characterization of Stochastic Spiking Coherence in Coupled Neurons

Abstract

We consider a large population of globally coupled subthreshold Morris-Lecar neurons. By varying the noise intensity D, we investigate numerically stochastic spiking coherence (i.e., noise-induced coherence between neural spikings). As D passes a threshold, a transition from an incoherent to a coherent state occurs. This coherent transition is described in terms of the “thermodynamic” order parameter O, which concerns a macroscopic time-averaged fluctuation of the global potential. We note that such stochastic spiking coherence may be well visualized in terms of the raster plot of neural spikings (i.e., spatiotemporal plot of neural spikings), which is directly obtained in experiments. To quantitatively measure the degree of stochastic spiking coherence (seen in the raster plot), we introduce a new type of “spiking coherence measure,” Ms, by taking into consideration the average contribution of (microscopic) local neural spikings to the (macroscopic) global membrane potential. Hence, the spiking coherence measure may be regarded as a “statistical-mechanical” measure. Through competition between the constructive and the destructive roles of noise, stochastic spiking coherence is found to occur over a large range of intermediate noise intensities and to be well characterized in terms of the mutually complementary quantities of O and Ms. Particularly, Ms reflects the degree of stochastic spiking coherence seen in the raster plot very well.