A unified model for two modes of bursting in GnRH neurons
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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.
KeywordsMathematical 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.
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Conflict of interest
The authors declare that they have no conflict of interest.
- Chen X., Sneyd J. (2014). A Computational Model of the Dendron of the GnRH Neuron. Bulletin of Mathematical Biology 904–926. doi: 10.1007/s11538-014-0052-6.
- Chu, Z., & Moenter, S. M. (2006). Physiologic regulation of a tetrodotoxin-sensitive sodium influx that mediates a slow afterdepolarization potential in gonadotropin-releasing hormone neurons: possible implications for the central regulation of fertility. Journal of Neuroscience, 26, 11961–11973. doi: 10.1523/JNEUROSCI.3171-06.2006.CrossRefPubMedGoogle Scholar
- Chu, Z., Andrade, J., Shupnik, M. A., & Moenter, S. M. (2009). Differential regulation of gonadotropin-releasing hormone neuron activity and membrane properties by acutely applied estradiol: dependence on dose and estrogen receptor subtype. Journal of Neuroscience, 29, 5616–5627. doi: 10.1523/JNEUROSCI.0352-09.2009.CrossRefPubMedPubMedCentralGoogle Scholar
- Chu, Z., Takagi, H., & Moenter, S. M. (2010). Hyperpolarization-activated currents in gonadotropin-releasing hormone (GnRH) neurons contribute to intrinsic excitability and are regulated by gonadal steroid feedback. Journal of Neuroscience, 30, 13373–13383. doi: 10.1523/JNEUROSCI.1687-10.2010.CrossRefPubMedPubMedCentralGoogle Scholar
- Hemond, P. J., O’Boyle, M. P., Roberts, C. B., et al. (2012). Simulated GABA synaptic input and L-type calcium channels form functional microdomains in hypothalamic gonadotropin-releasing hormone neurons. Journal of Neuroscience, 32, 8756–8766. doi: 10.1523/JNEUROSCI.4188-11.2012.CrossRefPubMedPubMedCentralGoogle Scholar
- LeBeau, A. P., Van Goor, F., Stojilkovic, S. S., & Sherman, A. (2000). Modeling of membrane excitability in gonadotropin-releasing hormone-secreting hypothalamic neurons regulated by Ca2 + −mobilizing and adenylyl cyclase-coupled receptors. Journal of Neuroscience, 20, 9290–9297.PubMedGoogle Scholar
- LeMasson G., Maex R. (2001). Introduction to equation solving and parameter Fitting. In E. De Schutter (Ed.), Computational neuroscience: realistic modeling for experimentalists (pp. 1–25). CRC Press.Google Scholar
- Magistretti, J., & Alonso, A. (1999). Biophysical properties and slow voltage-dependent inactivation of a sustained sodium current in entorhinal cortex layer-II principal neurons: a whole-cell and single-channel study. The Journal of General Physiology, 114, 491–509. doi: 10.1085/jgp.114.4.491.CrossRefPubMedPubMedCentralGoogle Scholar
- Miyasho, T., Takagi, H., Suzuki, H., et al. (2001). Low-threshold potassium channels and a low-threshold calcium channel regulate Ca2+ spike firing in the dendrites of cerebellar Purkinje neurons: a modeling study. Brain Research, 891, 106–115. doi: 10.1016/S0006-8993(00)03206-6.CrossRefPubMedGoogle Scholar
- Moenter, S. M., Chu, Z., & Christian, C. A. (2009). Neurobiological mechanisms underlying oestradiol negative and positive feedback regulation of gonadotrophin-releasing hormone neurones. Journal of Neuroendocrinology, 21, 327–333. doi: 10.1111/j.1365-2826.2009.01826.x.CrossRefPubMedPubMedCentralGoogle Scholar
- Pielecka-Fortuna, J., DeFazio, R. A., & Moenter, S. M. (2011). Voltage-gated potassium currents are targets of diurnal changes in estradiol feedback regulation and kisspeptin action on gonadotropin-releasing hormone neurons in mice. Biology of Reproduction, 85, 987–995. doi: 10.1095/biolreprod.111.093492.CrossRefPubMedPubMedCentralGoogle Scholar
- Roberts, C. B., O’Boyle, M. P., & Suter, K. J. (2009). Dendrites determine the contribution of after depolarization potentials (ADPs) to generation of repetitive action potentials in hypothalamic gonadotropin releasing-hormone (GnRH) neurons. Journal of Computational Neuroscience, 26, 39–53. doi: 10.1007/s10827-008-0095-5.CrossRefPubMedGoogle Scholar