Dynamics and conditions for inhibitory synaptic current to induce bursting and spreading depolarization in pyramidal neurons

Enhanced activity of inhibitory neurons, which is often used to suppress behaviors of pyramidal neurons to treat brain diseases, whereas can enhance spiking to a mixed-mode bursting (MMB) in recent experiments on migraine and seizure. The MMB contains a phase with high level of membrane potential/extracellular potassium concentration ([K⁺]_o), which can propagate to form spreading depolarization (SD) wave. Different from the common view that the MMB/SD is often induced by enhanced positive effect or [K⁺]_o, in the present paper, dynamics and conditions for the uncommon MMB/SD evoked by enhanced inhibitory synaptic current are obtained in a theoretical model. Firstly, in addition to the well-known positive threshold across which the common MMB is induced by positive effect, a spiking pyramidal neuron exhibits a novel negative threshold with a low level of [K⁺]_o for the MMB. A long and strong inhibitory stimulation suppresses the spiking to silence phase via a saddle-node bifurcation on an invariant circle at first and then run across the negative threshold, triggering positive feedback to enhance membrane potential and [K⁺]_o to levels high enough, then resulting in the uncommon MMB. Secondly, in a coupling model, enhanced inhibitory effect for enhanced spiking activity of interneuron and conductance of inhibitory synapse, and enhanced spiking activity of pyramidal neuron, are favorable for the uncommon MMB. Then, reducing these activities or parameters present potential measures to prevent the MMB. Finally, in network model, the uncommon MMB of a pyramidal neuron can induce SD wave. The results present a novel theoretical explanation to the uncommon MMB/SD, counterintuitive function of the inhibitory interneuron, and potential measures to treat the diseases.