Relationship between threshold and bifurcations for paradoxical firing responses along with seizure induced by inhibitory stimulation

- Inhibition-induced enhancement or paradoxical response of firing was related to Hopf bifurcation instead of saddle-node bifurcation on an invariant cycle (SNIC), due to the negative threshold and rotated vector fields. In the present letter, by changing multiple parameters to adjust the vector fields, the condition for the paradoxical response and negative threshold is extended to SNIC near a co dimension-2 bifurcation appearing prior to the Hopf bifurcation, which presents a comprehensive relationship between bifurcations and threshold. Especially, the result for a special current can well explain the enhanced firing along with seizure induced by inhibitory interneuron, implying that SNIC far from the co dimension-2 bifurcation of pyramidal neuron is a potential candidate to avoid seizure.Copyright & COPY; 2023 EPLA

Automated summary

This study found that the inhibition-induced enhancement or paradoxical response of firing is related to Hopf bifurcation instead of the saddle-node bifurcation on an invariant cycle (SNIC), due to the negative threshold and rotated vector fields. By adjusting the vector fields through changing multiple parameters, the condition for the paradoxical response and negative threshold is extended to SNIC near a co dimension-2 bifurcation appearing prior to the Hopf bifurcation, which establishes a comprehensive relationship between bifurcations and threshold. The results, especially for a specific current, can effectively explain the enhanced firing and seizure induced by inhibitory interneuron, suggesting that SNIC far from the co dimension-2 bifurcation of pyramidal neuron can potentially prevent seizure.