Recent experimental observations on seizures showed that the optogenetic activation of inhibitory interneurons cannot suppress but enhance the frequency and synchronization of spiking of excitatory pyramidal neurons, i.e., synchronized post-inhibitory rebound (PIR) spiking. This complex phenomenon presents paradoxical functions of interneurons and novel etiologies of seizures. In the present study, nonlinear mechanisms and conditions of the synchronized PIR spiking are obtained in a network model of inhibitory interneurons and excitatory pyramidal neurons. Pyramidal neurons with low spiking frequency near the bifurcation, characterized by small conductances (gh) of the hyperpolarization-activated cation (Ih) current and small applied current, are easy to generate PIR spiking. Strong optogenetic stimulation activating interneurons with high spiking frequency and inhibitory synapses with large conductances contribute to the PIR spiking. Moreover, after the optogenetic stimulation, the excitatory synaptic current from pyramidal neurons to interneurons can induce spiking of interneurons to reduce the PIR spiking. Reducing the membrane potential of interneurons can enhance the range of excitatory synaptic conductances for PIR spiking. The PIR spiking can be interpreted by complex nonlinear interactions between the hyperpolarization activation of the Ih current and membrane potential modulated by gh and inhibitory stimulation. Furthermore, higher synchronization degrees of the PIR spiking appear for the spiking with lower frequency. During the inhibitory stimulation, pyramidal neurons become silence with a small difference in membrane potential, which remains within long intervals between spikes and results in strong synchronization after stimulation. The nonlinear mechanisms and conditions of the synchronized PIR spiking are helpful for recognizing and modulating seizures.
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