Figure 8. Effect of $E_{GABA}$ on SNr synchrony in a unidirectional (left) and bidirectional (right) synaptically connected two-neuron network.

(A1-A3 and B1-B3) (Top) Identification of PRC fixed points and (Bottom) histogram of the timing of synaptic inputs in the phase of neuron 2 (Input Phase) as a function of $E_{GABA}$. Recall that positive changes in phase correspond to delays. (A1,B1) $E_{GABA}=-60mV$; (A2,B2) $E_{GABA}=-55mV$; (A3,B3) $E_{GABA}=-50mV$. Black dots indicate dataset used to generate PRC in red/blue. Stable and unstable fixed points are indicated by green and white filled circles, respectively. For reference, all PRCs and fixed points are included in gray for all values of $E_{GABA}$ tested. (A4,B4) Effect of $E_{GABA}$ on SNr phase locking. Blue histograms show the distribution of synaptic inputs relative to the phase of neuron 2 (input phase) for the two network simulations for different levels of $E_{GABA}$. Green and white filled circles indicate the stable and unstable locking predicted by analysis of PRCs. Note the unstable fixed points for the lowest values of $E_{GABA}$ in the unidirectional case. (A5) In the unidirectional case, slow 1 Hz oscillations in the frequency of neuron 2 arise due to phase slipping at hyperpolarized values of $E_{GABA}$.

Figure 8—figure supplement 1. Schematic illustration of the convergence toward anti-phase locking in a birectionally coupled pair of SNr neurons.

Each vertical, deeply colored bar denotes a spike time of the cell with that color (red or blue). Following the spike time of each cell, the PRC for that cell is shown (the PRCs for $E_{GABA}=-60mV$ are used). The spike time of one cell becomes the input time to the other, target cell (‘Input’). The height of the PRC for the target cell at the arrival time of its input determines the delay (‘Delay’) until its next spike. Each pale vertical bar shows the time when that next spike would have occurred had the corresponding cell not received an input; each horizontal arrow shows how the delay due to input perturbs the cell’s actual next spike time and determines the timing of the next input to the other cell. Over successive spikes and delays, the relative phases of the cells drift, such that the cells’ spike times approach the fully anti-phase locked state, in which each cell spikes, and sends input to the other cell, half-way through each interspike interval.