Nonlinear Dynamics

, Volume 95, Issue 2, pp 1035–1052 | Cite as

Axonal sodium and potassium conductance density determines spiking dynamical properties of regular- and fast-spiking neurons

  • Wen Zhang
  • Boqiang Fan
  • Divyansh Agarwal
  • Tun Li
  • Yuguo YuEmail author
Original Paper


Compared with regular-spiking (RS) neurons, the action potentials (APs) of fast-spiking (FS) neurons are characterized by narrow spike durations and unusually fast decay dynamics of dV/dt process. However, quantitative measure of accurate sodium and potassium densities accounting for spike shape in the axon initial segment (AIS) where action potentials are initiated in both RS and FS cells is not well explored. Here, axonal recordings showed that the averaged axonal spike half-height duration of RS cells is significantly larger (Matlab anova1, \(p < 0.001\)) than that of FS cells. The averaged dV/dt ratio of RS cells is significantly lower (Matlab anova1, \(p < 0.001\)) than that of FS cells. We have reproduced axonal APs by cortical Hodgkin–Huxley axonal models constrained by a set of experimentally observed properties of RS and FS cells. The model predicts that sodium channel conductance \({g}_{\mathrm{Na}}\) in RS AIS is in a range of 1000–4000 pS/\(\upmu \text {m}^{2}\) and potassium channel conductance \({g}_{\mathrm{K}}\) is in a range of 30–200 pS/\(\upmu \text {m}^{2}\) in order to produce energy-efficient RS action potentials with major properties matching experimental observations of pyramidal cells. The model predicts that \({g}_{\mathrm{Na}}\) is within 1000–2500 pS/\(\upmu \text {m}^{2}\) and \({g}_{\mathrm{K}}\) ranges within 300–1000 pS/\(\upmu \text {m}^{2}\) for AIS of FS cells. The AP duration and efficiency are nonlinearly regulated by the ratio of \({g}_{\mathrm{Na}}/{g}_{\mathrm{K}}\). We performed patch-clamp recordings on both RS and FS cortical axons and observed that \({g}_{\mathrm{Na}}\) was approximately \(1620.4\pm 770\,\hbox {pS}/\upmu \text {m}^{2}\) for RS AIS and \(803.7\pm 351.5\,\hbox {pS}/\upmu \text {m}^{2}\) for FS AIS. The \({g}_{\mathrm{K}}\) was \(189.6\pm 75.8\,\hbox {pS}/\upmu \text {m}^{2}\) for the RS AIS and \(524.6\pm 281.6\,\hbox {pS}/\upmu \text {m}^{2}\) for the FS AIS. Partial drug-mediated inhibition of sodium or potassium channels significantly decreases or enlarges the AP duration and dV/dt ratio of both RS and FS cells, respectively, suggesting that sodium and potassium conductance density in cortical axons may be critical in determining the dynamical features of AP profiles in FS and RS cells.


Pyramidal cell Interneuron Action potential Sodium conductance density 



YY thanks for the support from the National Natural Science Foundation of China (81761128011, 31571070), Shanghai Science and Technology Committee support (16410722600), the program for the Professor of Special Appointment (Eastern Scholar SHH1140004) at Shanghai Institutions of Higher Learning, the Research Fund for the Doctoral Program of Higher Education of China (1322051) and Omics-based precision medicine of epilepsy entrusted by the Key Research Project of the Ministry of Science and Technology of China (Grant No. 2016YFC0904400) for their support. Thanks to Dr. Guojie Qu and Xin Fu for their help in revision.

Author Contributions

YY and WZ designed research; WZ, DA, TL and BF performed experimental recordings; YY and BF conducted computational studies; WZ, BF and YY performed data analysis; YY, WZ and DA wrote the paper. All authors reviewed the manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare no competing financial interests.

Supplementary material

11071_2018_4613_MOESM1_ESM.pdf (80 kb)
Supplementary material 1 (pdf 79 KB)


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Medical Neurobiology, School of Life Science and Human Phenome Institute, Institutes of Brain Science, Institute of Science and Technology for Brain-Inspired IntelligenceFudan UniversityShanghaiChina
  2. 2.Department of Genomics and Computational Biology, Perelman School of MedicineUniversity of PennsylvaniaPhiladelphiaUSA
  3. 3.Institute of Neuroscience and State Key Laboratory of NeuroscienceShanghai Institutes for Biological SciencesShanghaiChina

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