Biological Cybernetics

, Volume 109, Issue 3, pp 287–306 | Cite as

Spike-frequency adaptation of a two-compartment neuron modulated by extracellular electric fields

  • Guosheng Yi
  • Jiang Wang
  • Kai-Ming Tsang
  • Xile Wei
  • Bin Deng
  • Chunxiao Han
Original Paper


Spike-frequency adaptation has been shown to play an important role in neural coding. Based on a reduced two-compartment model, here we investigate how two common adaptation currents, i.e., voltage-sensitive potassium current (\(I_{\mathrm{M}}\)) and calcium-sensitive potassium current (\(I_{\mathrm{AHP}}\)), modulate neuronal responses to extracellular electric fields. It is shown that two adaptation mechanisms lead to distinct effects on the dynamical behavior of the neuron to electric fields. These effects depend on a neuronal morphological parameter that characterizes the ratio of soma area to total membrane area and internal coupling conductance. In the case of \(I_{\mathrm{AHP}}\) current, changing the morphological parameter switches spike initiation dynamics between saddle-node on invariant cycle bifurcation and supercritical Hopf bifurcation, whereas it only switches between subcritical and supercritical Hopf bifurcations for \(I_{\mathrm{M}}\) current. Unlike the morphological parameter, internal coupling conductance is unable to alter the bifurcation scenario for both adaptation currents. We also find that the electric field threshold for triggering neuronal steady-state firing is determined by two parameters, especially by the morphological parameter. Furthermore, the neuron with \(I_{\mathrm{AHP}}\) current generates mixed-mode oscillations through the canard phenomenon for some small values of the morphological parameter. All these results suggest that morphological properties play a critical role in field-induced effects on neuronal dynamics, which could qualitatively alter the outcome of adaptation by modulating internal current between soma and dendrite. The findings are readily testable in experiments, which could help to reveal the mechanisms underlying how the neuron responds to electric field stimulus.


Extracellular electric field Spike-frequency adaptation Two-compartment neuron Spike initiation dynamic Bifurcation Morphological parameter 



This work is supported by the National Natural Science Foundation of China under Grants 61471265, 61372010 and 61172009, and Tianjin Municipal Natural Science Foundation under Grants 12JCZDJC21100 and 13JCZDJC27900.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Guosheng Yi
    • 1
  • Jiang Wang
    • 1
  • Kai-Ming Tsang
    • 2
  • Xile Wei
    • 1
  • Bin Deng
    • 1
  • Chunxiao Han
    • 3
  1. 1.School of Electrical Engineering and AutomationTianjin UniversityTianjinChina
  2. 2.Department of Electrical EngineeringThe Hong Kong Polytechnic UniversityHong KongChina
  3. 3.School of Automation and Electrical EngineeringTianjin University of Technology and EducationTianjinChina

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