Journal of Computational Neuroscience

, Volume 40, Issue 3, pp 297–315 | Cite as

A unified model for two modes of bursting in GnRH neurons

  • Spencer Moran
  • Suzanne M Moenter
  • Anmar Khadra


Gonadotropin-releasing hormone (GnRH) neurons exhibit at least two intrinsic modes of action potential burst firing, referred to as parabolic and irregular bursting. Parabolic bursting is characterized by a slow wave in membrane potential that can underlie periodic clusters of action potentials with increased interspike interval at the beginning and at the end of each cluster. Irregular bursting is characterized by clusters of action potentials that are separated by varying durations of interburst intervals and a relatively stable baseline potential. Based on recent studies of isolated ionic currents, a stochastic Hodgkin-Huxley (HH)-like model for the GnRH neuron is developed to reproduce each mode of burst firing with an appropriate set of conductances. Model outcomes for bursting are in agreement with the experimental recordings in terms of interburst interval, interspike interval, active phase duration, and other quantitative properties specific to each mode of bursting. The model also shows similar outcomes in membrane potential to those seen experimentally when tetrodotoxin (TTX) is used to block action potentials during bursting, and when estradiol transitions cells exhibiting slow oscillations to irregular bursting mode in vitro. Based on the parameter values used to reproduce each mode of bursting, the model suggests that GnRH neurons can switch between the two through changes in the maximum conductance of certain ionic currents, notably the slow inward Ca2+ current I s, and the Ca2+ -activated K+ current I KCa. Bifurcation analysis of the model shows that both modes of bursting are similar from a dynamical systems perspective despite differences in burst characteristics.


Mathematical model Parabolic bursting Irregular bursting Slow oscillations Slow-fast subsystem analysis Estradiol feedback 



This work was supported by the Natural Sciences and Engineering Council of Canada (NSERC) discovery grant to AK and NIH grants R01HD34860 and R01HD41469 to SMM.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

10827_2016_598_MOESM1_ESM.pdf (633 kb)
ESM 1 (PDF 632 kb)


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Spencer Moran
    • 1
  • Suzanne M Moenter
    • 2
    • 3
    • 4
  • Anmar Khadra
    • 1
  1. 1.Department of PhysiologyMcGill UniversityMontrealCanada
  2. 2.Departments of Molecular and Integrative PhysiologyUniversity of MichiganAnn ArborUSA
  3. 3.Obstetrics and GynecologyUniversity of MichiganAnn ArborUSA
  4. 4.Internal MedicineUniversity of MichiganAnn ArborUSA

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