The PING interaction.

Left panel: A schematic illustration of the PING (Pyramidal Interneuron Network Gamma) interaction. The parameters are as in Fig 1. Right panels: Nonlinear analysis of the PING rhythm. A-B) Bifurcation diagrams. The blue line, (respectively the red line), corresponds to the steady state of the inhibitory cells, (respectively the excitatory cells) while dots correspond to limit cycles. C) Stability region. D) The stimulus and corresponding raster plot of the spiking activity. E) Comparison between simulated and calculated mPRCs. The black line illustrates the analytical adjoint method while dots indicates direct perturbations of the full network. Red dots, perturbations are made on the E-cells, second row, with the blue dots, perturbations are made on the I-cells. F) PRC shape as a function of parameters obtained via the adjoint method for different values of the external current. Parameters: Ne = Ni = 5000; τe = τi = 10; τse = τsi = 1; ; Jee = 0; Jei = 15; Jii = 0; Jie = 15; ; vth = 500; vr = −500; panel A) Δe = Δi = 1; panel B) ; panel D) Δe = Δi = 1; panel E-F) Δe = Δi = 1; , direct perturbations are made with a square wave current pulse (amplitude 5, duration 0.5).