Modulation of multi-timescale compound Ca-NMDA-Na oscillations in pyramidal neuron by extracellular electric fields

Evidences show that there exist dendritic Ca 2+ -spike-dependent and NMDA-spike-dependent multi-timescale compound oscillations in epileptiform activity, and electric field (EF) plays a significant role in the propagation of compound oscillations. However, it is still unclear how EF-induced spatial polarization modulates the interaction between dendritic Ca 2+ oscillations and NMDA oscillations, and subsequently influences somatic Na + spikes. To address this issue, we built a biophysical pyramidal neuron model with complex dendritic morphology, which is capable of reproducing multi-timescale neuronal oscillations observed in epileptiform discharges. By investigating the EF stimulation thresholds for triggering dendritic Ca 2+ and NMDA spikes as well as somatic Na + discharges, we found that the dendritic depolarization firstly activates dendritic Ca 2+ oscillations, subsequently leading to the generation of dendritic NMDA oscillations, which together facilitates Na + spike generation by counteracting somatic hyperpolarization. Finally, we proposed a minimal three-compartment neuronal model that successfully reproduces the Ca-NMDA-Na compound oscillations. Through singular perturbation and bifurcation analysis, we demonstrated the modulation influence of EF on multi-timescale neuronal compound oscillations. Additionally, our results pointed out that the EF-induced depolarization at apical dendrite makes the systematic equilibrium point experience invariant circle saddle-node bifurcation in order to trigger dendritic Ca 2+ oscillations. These oscillations then drive the basal dendrite to generate dendritic NMDA oscillations by experiencing a subcritical Hopf bifurcation. In this case, the soma would experience a subcritical Hopf bifurcation to produce Na + spike. These results provide valuable insights into the mechanisms underlying the generation of epileptiform discharges in the brain, which is helpful for developing the therapeutic strategies of epilepsy.