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Modulation of multi-timescale compound Ca-NMDA-Na oscillations in pyramidal neuron by extracellular electric fields |
| Yaqin Fan(樊亚琴)1, Meili Lu(卢梅丽)2, and Xile Wei(魏熙乐)3,† |
1 Academy of Medical Engineering and Translational Medicine, Tianjin University, Tianjin 300072, China;
2 School of Information Technology Engineering, Tianjin University of Technology and Education, Tianjin 300222, China;
3 Tianjin Key Laboratory of Process Measurement and Control, School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China |
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Abstract Evidence shows that there exist dendritic Ca$^{2+}$-spike-dependent and NMDA-spike-dependent multi-timescale compound oscillations in epileptiform activity, and the electric field (EF) plays a significant role in the propagation of compound oscillations. However, it is still unclear how the 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 first activates dendritic Ca$^{2+}$ oscillations, subsequently leading to the generation of dendritic NMDA oscillations, which together facilitate 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 modulatory influence of EF on multi-timescale neuronal compound oscillations. Additionally, our results indicate that the EF-induced depolarization at the apical dendrite causes the system equilibrium point to experience an invariant circle saddle-node bifurcation 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 experiences a subcritical Hopf bifurcation to produce Na$^{+}$ spikes. These results provide valuable insights into the mechanisms underlying the generation of epileptiform discharges in the brain, which is helpful for developing therapeutic strategies for epilepsy.
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Received: 17 July 2025
Revised: 08 September 2025
Accepted manuscript online: 18 September 2025
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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02.70.-c
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(Computational techniques; simulations)
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02.30.Oz
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(Bifurcation theory)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 62571367, 62271348, and 62171312). |
Corresponding Authors:
Xile Wei
E-mail: xilewei@tju.edu.cn
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Cite this article:
Yaqin Fan(樊亚琴), Meili Lu(卢梅丽), and Xile Wei(魏熙乐) Modulation of multi-timescale compound Ca-NMDA-Na oscillations in pyramidal neuron by extracellular electric fields 2026 Chin. Phys. B 35 060508
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