Figure 5. Phase diagrams in the presence of network heterogeneity and/or synaptic failure.

(A–D) The synchronous stationary state (sync.) corresponding to σ<5 ms is depicted as the blue region. g_a and g_b are expressed in nS and denote the values of the peak conductance g in Equation 12 for GABA_A and GABA_B, respectively. The dashed lines separating the synchronous state to the asychronous state were obtained by fitting the contour plot σ = 5 ms. The equations of the separating line are g_a = 11g_b (global, P _failure = 0.5, (B)), g_a = 14g_b (heterogeneous, P _failure = 0.0, (C) and g_a = 25g_b (heterogeneous, P _failure = 0.5, (D)). (E) spike rasterplots are indicated for a network (heterogeneous connectivity and P _failure = 0.5) with intact connections (g_a = 1 nS and g_b = 0.1 nS) and with GABA_A or GABA_B blocked. (F) Clustering of synchronized activity patterns. Two networks (A and B) of N = 100 neurons have been randomly generated with 0.5 probability of connection. At each oscillatory cycle, the network activity is represented as a binary vector in a multidimensional space (N = 100), where each dimension corresponds to the binary state of a given PN (1 if synchronized and 0 otherwise). The resolution at which synchronized neurons are determined is ε = 5 ms (see Methods). We pooled the binary data obtained at the different oscillatory cycles (extracted between 300 to 3000 ms), for the different networks (A and B) and from repeated trials (3 runs for each network). The data were projected, using logistic PCA [36], onto the first two principal components (PC). Red and blue points in the PCA plane are the projected data for networks A and B, respectively. Left is for intact networks, with GABA_A and GABA_B coupling (g_a = 1 nS and g_b = 0.1 nS). Middle and right are for GABA_A or GABA_B blocked, respectively.