INHIBITORY STIMULATION WITH HIGH FREQUENCY INDUCES MIXED-MODE BURSTING: COOPERATION BETWEEN DIFFERENT DYNAMICS

Identifying complex dynamics of neural bursting is helpful for understanding and treatment of brain diseases. In recent experiments, as spiking frequency of inhibitory neuron increases, the activity of excitatory pyramidal neuron is not suppressed, but is enhanced from resting state to a mixed-mode bursting, different from the common bursting which is always induced by enhanced positive effect. The bursting contains three segments: silence, burst, and depolarization block with high membrane potential and extracellular potassium ion concentration (K⁺_o), involved in multiple dynamics and associated with migraine and seizure. In the present paper, cooperation among these different dynamics underlying the counterintuitive mixed-mode bursting is studied in theoretical model. Firstly, fast-slow dynamics of inhibitory synaptic gating variable to induce strong inhibitory synaptic current is identified: The synaptic gating variable cannot decay to zero within short spiking period for high frequency, resulting in large value of gating variable and strong inhibitory synaptic current. However, low frequency spiking induces zero gating variable in most part of the long period and weak inhibitory synaptic current. Secondly, the negative threshold for the counterintuitive bursting induced by strong instead of weak inhibitory synaptic current is acquired: The strong inhibitory current can induce behavior of silent pyramidal neuron to run across a negative threshold with lower K⁺_o, resulting in the counterintuitive/uncommon mixed-mode bursting, presenting a novel theoretical explanation. Weak negative synaptic current cannot induce passage through the negative threshold. The negative threshold is compared with the well-known positive threshold with a high K⁺_o, across which the common mixed-mode bursting is induced by enhanced excitatory effect. Thirdly, the bifurcations underlying the transitions between the three segments of the mixed-mode bursting are obtained: The transitions from silence, to burst, to depolarization block, and back to silence correspond to running across the saddle-node bifurcation on an invariant cycle (SNIC), supercritical Hopf, and saddle-node bifurcation curves of the fast subsystem. Finally, the positive feedback between elevations of membrane potential, firing rate, and K⁺_o during the burst segment, which is intrinsic cause for the generation of mixed-mode bursting, is identified to be associated with the dynamics of a limit cycle locating between the SNIC and Hopf bifurcations. The results reveal the cooperation between different dynamics, which present novel mechanism of mixed-mode bursting and brain diseases and provide theoretical support to eliminate mixed-mode bursting to treat brain diseases.