Journal of Computational Neuroscience

, Volume 32, Issue 1, pp 119–136 | Cite as

A simple integrative electrophysiological model of bursting GnRH neurons

  • Dávid Csercsik
  • Imre Farkas
  • Erik Hrabovszky
  • Zsolt Liposits


In this paper a modular model of the GnRH neuron is presented. For the aim of simplicity, the currents corresponding to fast time scales and action potential generation are described by an impulsive system, while the slower currents and calcium dynamics are described by usual ordinary differential equations (ODEs). The model is able to reproduce the depolarizing afterpotentials, afterhyperpolarization, periodic bursting behavior and the corresponding calcium transients observed in the case of GnRH neurons.


Gonadotropin-releasing hormone dynamic modelling bursting 



This work was supported by the National Science Foundation of Hungary K69127, K67625, and T73002) and the Hungarian Health Research Council Fund (122/2009). The research leading to these results has received funding from the European Community’s Seventh Framework Program (FP7/ 2007-2013) under Grant Agreement 245009. The authors would like to thank Katalin Hangos for her contribution.


  1. Ábrahám, I., Han, S., Todman, M., Korach, K. & Herbison, A. (2003). Estrogen receptor beta mediates rapid estrogen actions on gonadotropin-releasing hormone neurons in vivo. Journal of Neuroscience, 23(13), 5771–5777.PubMedGoogle Scholar
  2. Bainov, D. & Simeonov, P. (Eds.). (1989). Systems With Impulse Effect Systems with impulse effect. Ellis Horwood Limited.Google Scholar
  3. Bezprozvanny, I., Watras, J. & Ehrlich, B. (1991). Bell-shaped calcium-response curves of Ins(1,4,5)–P3–and calcium gated channels from endoplasmic reticulum of cerebellum. Nature, 351, 751–754.PubMedCrossRefGoogle Scholar
  4. Caeser, M., Brown, D., Gahwiler, B. & Knopfel, T. (2006). Characterization of a calcium-dependent current generating a slow afterdepolarization of CA3 pyramidal cells in rat hippocampal slice cultures. European Journal of Neuroscience, 5, 560–569.CrossRefGoogle Scholar
  5. Campbell, R., Gaidamaka, G., Han, S. & Herbison, A. (2009). Dendro-denritic bundling and shared synapses between gonadotropin-releasing hormone neurons. Proceedings of the National Academy of Sciences of the USA, 106, 10835–10840.PubMedCrossRefGoogle Scholar
  6. Campbell, R., Han, S. & Herbison, A. (2005). Biocytin filling of adult gonadotropin-releasing hormone neurons in situ reveals extensive, spiny, dendritic processes. Endocrinology, 146, 1163–1169.PubMedCrossRefGoogle Scholar
  7. Cantrell, A. & Catterall, W. (2001). Neuromodulation of Na +  channels: An unexpected form of cellular plasticity Neuromodulation of Na +  channels: An unexpected form of cellular plasticity. Nature Reviews Neuroscience, 2, 397–407.PubMedCrossRefGoogle Scholar
  8. Charles, A., Weiner, R. & Costantin, J. (2001). CAMP modulates the excitability of immortalized hypothalamic (GT1) neurons via a cyclic nucleotide gated channel. Molecular Endocrinology, 15, 997–1009.PubMedCrossRefGoogle Scholar
  9. 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(17), 5616–5627.PubMedCrossRefGoogle Scholar
  10. Chu, Z. & Moenter, S. (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.PubMedCrossRefGoogle Scholar
  11. Conn, P. & Freeman, M. (2000). Neuroendocrinology in physiology and medicine. 999 Riverview Drive Suite 208 Totowa New Jersey 07512: Humana Press.Google Scholar
  12. Constantin, J. & Charles, A. (1999). Spontaneous action potentials initiate rhythmic intercellular calcium waves in immortalized hypothalamic (GT1-1) neurons. Journal of Neurophysiology, 82, 429–435.Google Scholar
  13. Csercsik, D., Farkas, I., Szederkényi, G., Hrabovszky, E., Liposits, Z. & Hangos, K. (2010). Hodgkin-Huxley type modelling and parameter estimation of GnRH neurons. BioSystems, 100, 198–207.PubMedCrossRefGoogle Scholar
  14. de Roux, N., Genin, E., Carel, J., Matsuda, F., Chaussain, J. & Milgrom, E. (2003). Hypogonadotropic hypogonadism due to loss of function of the KiSS1-derived peptide receptor GPR54. Proc Natl Acad Sci U S A, 100(19), 10972–10976.PubMedCrossRefGoogle Scholar
  15. DeFazio, R., Heger, S., Ojeda, S. & Moenter, S. (2002). Activation of A-type γ-aminobutyric acid receptors excites gonadotropin-releasing hormone neurons. Molecular Endocrinology, 16, 2872–2891.PubMedCrossRefGoogle Scholar
  16. DeFazio, R. & Moenter, S. (2002). Estradiol feedback alters potassium currents and firing properties of gonadotropin- releasing hormone neurons. Molecular Endocrinology, 16, 2255–2265.PubMedCrossRefGoogle Scholar
  17. Duan, W., Lee, K., Herbison, A. & Sneyd, J. (2011). A mathematical model of adult GnRH neurons in mouse brain and its bifurcation analysis. Journal of Theortical Biology, 276, 22–34.CrossRefGoogle Scholar
  18. Farkas, I., Kalló, I., Deli, L., Vida, B., Hrabovszky, E., Fekete, C., et al. (2010). Retrograde endocannabinoid signaling reduces GABAergic synaptic transmission to gonadotropin-releasing hormone neurons. Endocrinology, 151, 5818–5829.PubMedCrossRefGoogle Scholar
  19. Finch, E., Turner, T. & Goldin, S. (1991). Calcium as a coagonist of inositol 1,4,5–trisphosphate–induced calcium release. Science, 252, 443–446.PubMedCrossRefGoogle Scholar
  20. Fletcher, P. & Li, Y. (2009). An integrated model of electrical spiking, bursting, and calcium oscillations in GnRH neurons. Biophysical Journal, 96, 4514–4524.PubMedCrossRefGoogle Scholar
  21. Friedmana, A., Arens, J., Heinemann, U. & Gutnick, M. (1992). Slow depolarizing afterpotentials in neocortical neurons are sodium and calcium dependent. Neuroscience Letters, 135, 13–17.CrossRefGoogle Scholar
  22. Ghamari-Langroudi, M. & Bourque, C. (1998). Caesium blocks depolarizing after-potentials and phasic firing in rat supraoptic neurones. Journal of Physiology, 510, 165–175.PubMedCrossRefGoogle Scholar
  23. Han, S., Abraham, I. & Herbison, A. (2002). Effect of GABA on GnRH neurons switches from depolarization to hyperpolarization at puberty in the female mouse. Endocrinology, 143, 1459–1466.PubMedCrossRefGoogle Scholar
  24. Han, S., Todman, M. & Herbison, A. (2004). Endogenous GABA release inhibits the firing of adult gonadotropin-releasing hormone neurons. Endocrinology, 145, 495–499.PubMedCrossRefGoogle Scholar
  25. Heldring, N., Pike, A., Andersson, S., Matthews, J., Cheng, G., Hartman, J., et al. (2007). Estrogen receptors: how do they signal and what are their targets. Physiological Reviews, 87(3), 905–931.PubMedCrossRefGoogle Scholar
  26. Herbison, A. (2008). Estrogen positive feedback to gonadotropin-releasing hormone (GnRH) neurons in the rodent: The case for the rostral periventricular area of the third ventricle (RP3V). Brain Research Reviews, 57(2), 277–287.PubMedCrossRefGoogle Scholar
  27. Herbison, A., Pape, J., Simonian, S., Skynner, M. & Sim, J. (2001). Molecular and cellular properties of GnRH neurons revealed through transgenics in mouse. Molecular and Cellular Endocrinology, 185, 185–194.PubMedCrossRefGoogle Scholar
  28. Izhikevich, E. (2005). Dynamical systems in neuroscience. Camebridge, Massachusetts, London, England: The MIT Press.Google Scholar
  29. Jasoni, C., Romano, N., Constantin, S., Lee, K. & Herbison, A. (2010). Calcium dynamics in gonadotropin-releasing hormone neurons. Frontiers in Neuroendocrinology, 31, 259–269.PubMedCrossRefGoogle Scholar
  30. Kato, M., Ui-Tei, K., Watanabe, M. & Sakuma, Y. (2003). Characterization of voltage-gated calcium currents in gonadotropin-releasing hormone neurons tagged with green fluorescent protein in rats. Endocrinology, 144, 5118–5125.PubMedCrossRefGoogle Scholar
  31. Knobil, E. (1980). The neuroendocrine control of the menstrual cycle. Hormone Research, 36, 53–88.Google Scholar
  32. Krsmanovic, L., Stojilkovic, S., Merelli, F., Dufour, S., Virmani, M. & Catt, K. (1992). Calcium signaling and episodic secretion of gonadotropin-releasing hormone in hypothalamic neurons. Proceedings of the National Academy of Sciences of the USA, 89, 8462–8466.PubMedCrossRefGoogle Scholar
  33. Kuehl-Kovarik, M., Partin, K., Handa, R. & Dudek, F. (2005). Spike-dependent depolarizing afterpotentials contribute to endogenous bursting in gonadotropin releasing hormone neurons. Neuroscience, 134, 295–300.PubMedCrossRefGoogle Scholar
  34. Kuehl-Kovarik, M., Pouliot, W., Halterman, G. L. , Handa, R., Dudek, F. & Partin, K. (2002). Episodic bursting activity and response to excitatory amino acids in acutely dissociated gonadotropin-releasing hormone neurons genetically targeted with green fluorescent protein. Journal of Neuroscience, 22, 2313–2322.PubMedGoogle Scholar
  35. LeBeau, A., Goor, F. V., Stojilkovic, S. & Sherman, A. (2000). Modeling of membrane excitability in gonadotropin-releasing hormone-secreting hypothalamic neurons regulated by Ca2 + -mobilizing and adenylyl cyclase-coupled receptors. The Journal of Neuroscience, 20, 9290–9297.PubMedGoogle Scholar
  36. Lee, K., Duan, W., Sneyd, J. & Herbison, A. (2010). Two slow calcium-activated afterhyperpolarization currents control burst firing dynamics in gonadotropin-releasing hormone neurons. Journal of Neuroscience, 30, 6214–6224.PubMedCrossRefGoogle Scholar
  37. Lehman, M., Coolen, L. & Goodman, R. (2010). Minireview: Kisspeptin/neurokinin B/dynorphin (KNDy) cells of the arcuate nucleus: A central node in the control of ronadotropin-releasing hormone secretion. Endocrinology, 151, 3479–3489.PubMedCrossRefGoogle Scholar
  38. Li, Y. & Rinzel, J. (2010). Equations for InsP receptor mediated [Ca2 + ]i-oscillations derived from a detailed kinetic model: A Hodgkin-Huxley like formalism. Journal of Theoretical Biology, 166, 461–473.CrossRefGoogle Scholar
  39. Maeda, K., Ohkura, S., Uenoyama, Y., Wakabayashi, Y., Oka, Y., Tsukamura, H., et al. (2010). Neurobiological mechanisms underlying GnRH pulse generation by the hypothalamus. Brain Research, 1364, 103–115.PubMedCrossRefGoogle Scholar
  40. Mayer, M. (1984). A calcium-activated chloride current generates the after-depolarization of rat sensory neurones in culture. Journal of Physiology, 364, 217–239.Google Scholar
  41. Moenter, S. & DeFazio, R. (2005). Endogenous γ-aminobutyric acid can excite gonadotropin-releasing hormone neurons. Endocrinology, 146, 5374–5379.PubMedCrossRefGoogle Scholar
  42. Morita, K. & Barret, E. (1989). Calcium dependent depolarizations originating in lizard motor nerve terminals. The Journal of Neuroscience, 9, 3359–3369.PubMedGoogle Scholar
  43. Navarro, V., Gottsch, M., Chavkin, C., Okamura, H., Clifton, D. & Steiner, R. (2009). Regulation of gonadotropin-releasing hormone secretion by Kisspeptin/Dynorphin/Neurokinin B neurons in the arcuate nucleus of the mouse. The Journal of Neuroscience, 29, 11859–11866.PubMedCrossRefGoogle Scholar
  44. Nunemaker, C., DeFazio, R. & Moenter, S. (2003). Calcium current subtypes in GnRH neurons. Biology of Reproduction, 69, 1914–1922.PubMedCrossRefGoogle Scholar
  45. Parker, I. & Ivorra, I. (1990). Inhibition by [Ca2 + ]i by inositol trisphosphate-mediated [Ca2 + ]i liberation: A possible mechanism for oscillatory release of Ca2 + . Proceedings of the National Academy of Sciences of the USA, 87, 260–264.PubMedCrossRefGoogle Scholar
  46. Petersen, S., Ottem, E. & Carpenter, C. (2003). Direct and indirect regulation of gonadotropin-releasing hormone neurons by estradiol. Biol Reprod, 69(6), 1771–1778.PubMedCrossRefGoogle Scholar
  47. Rance, N., Krajewski, S., Smith, M., Cholanian, M. & Dacks, P. (2010). Neurokinin B and the hypothalamic regulation of reproduction. Brain Research, 1364, 116–128.PubMedCrossRefGoogle Scholar
  48. Roberts, C., Best, J. & Suter, K. (2006). Dendritic processing of excitatory synaptic input in hypothalamic gonadotropin releasing-hormone neurons. Endocrinology, 147, 1545–1555.PubMedCrossRefGoogle Scholar
  49. Roberts, C., Campbell, R., Herbison, A. & Suter, K. (2008). Dendritic action potential initiation in hypothalamic gonadotropoin-releasing hormone neurons. Endocrinology, 149, 3355–3360.PubMedCrossRefGoogle Scholar
  50. Roberts, C., Hemond, P. & Suter, K. (2008). Synaptic integration in hypothalamic gonadotropin releasing hormone (GnRH) neurons. Neuroscience, 254, 1337–1351.CrossRefGoogle Scholar
  51. Roberts, C., O’Boyle, M. & Suter, K. (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.PubMedCrossRefGoogle Scholar
  52. Seminara, S., Messager, S., Chatzidaki, E., Thresher, R., Acierno, J. J., Shagoury, J., et al. (2003). The GPR54 gene as a regulator of puberty. New England Journal of Medicine, 349(17), 1614–1627.PubMedCrossRefGoogle Scholar
  53. Semple, R., Achermann, J., Ellery, J., Farooqi, I., Karet, F., Stanhope, R., et al. (2005). Two novel missense mutations in g protein-coupled receptor 54 in a patient with hypogonadotropic hypogonadism. Journal of Clinical Endocrinology and Metabolism, 90(3), 1849–1855.PubMedCrossRefGoogle Scholar
  54. Sim, J., Skynner, M. & Herbison, A. (2001). Heterogeneity in the basic membrane properties of postnatal gonadotropin-releasing hormone neurons in the mouse. The Journal of Neuroscience, 21, 1067–1075.PubMedGoogle Scholar
  55. Spergel, D., Krüth, U., Hanley, D., Sprengel, R. & Seeburg, P. (1999). Gaba- and glutamate-activated channels in green fluorescent protein-tagged gonadotropin-releasing hormone neurons in transgenic mice. The Journal of Neuroscience, 19, 2037–2050.PubMedGoogle Scholar
  56. Stojilkovic, S., Krsmanovic, L., Spergel, D. & Catt, K. (1994). GnRH neurons: Intrinsic pulsatility and receptor-mediated regulation. Trends in Endocrinology and Metabolism, 5, 201–209.PubMedCrossRefGoogle Scholar
  57. Suter, K. (2004). Control of firing by small (s)-γ-amino-3-hydroxy-5-methylisoxazolepropionic acid-like inputs in hypothalamic gonadotropin releasing-hormone (GnRH) neurons. Neuroscience, 128, 443–450.PubMedCrossRefGoogle Scholar
  58. Suter, K., Song, W., Sampson, T., Wuarin, J., Saunders, J., Dudek, F., et al. (2000). Genetic targeting of green fluorescent protein to gonadotropin-releasing hormone neurons: Characterization of whole-cell electrophysiological properties and morphology. Endocrinology, 141, 412–419.PubMedCrossRefGoogle Scholar
  59. Teruyama, R. & Armstrong, W. (2007). Calcium-dependent fast depolarizing afterpotentials in vasopressin neurons in the rat supraoptic nucleus. Journal of Neurophysiology, 98, 2612–2621.PubMedCrossRefGoogle Scholar
  60. Van Goor, F., LeBeau, A., Krsmanovic, L., Sherman, A., Catt, K. & Stojilkovic, S. (2000). Amplitude-dependent spike-broadening and enhanced Ca2 +  signaling in GnRH-secreting neurons. Biophysical Journal, 79, 1310–1323.PubMedCrossRefGoogle Scholar
  61. Verkhratsky, A. (2005). Physiology and pathophysiology of the calcium store in the endoplasmic reticulum of neurons. Physiological Reviews, 85, 201–279.PubMedCrossRefGoogle Scholar
  62. Vitalis, E., Costantin, J., Tsai, P., Sakakibara, H., Paruthiyil, S., Iiri, T., et al. (2000). Role of the cAMP signaling pathway in the regulation of gonadotropin-releasing hormone secretion in GT1 cells. Proceedings of the National Academy of Sciences of the United States of America, 97, 1861–1866.PubMedCrossRefGoogle Scholar
  63. Watanabe, M., Sakuma, Y. & Kato, M. (2004). High expression of the R-type voltage-gated Ca 2 +  channel and its involvement in Ca 2 + -dependent gonadotropin-releasing hormone release in GT1-7 cells. Endocrinology, 145, 2375–2388.PubMedCrossRefGoogle Scholar
  64. Watanabe, M., Sakuma, Y. & Kato, M. (2009). GABAA receptors mediate excitation in adult rat GnRH neurons. Biology of Reproduction, 81, 327–332.PubMedCrossRefGoogle Scholar
  65. Wintermantel, T., Campbell, R., Porteous, R., Bock, D., Grone, H., Todman, M. et al. (2006). Definition of estrogen receptor pathway critical for estrogen positive feedback to gonadotropin-releasing hormone neurons and fertility. Neuron, 52(2), 271–280.PubMedCrossRefGoogle Scholar
  66. Yin, C., Ishii, H., Tanaka, N., Sakuma, Y. & Kato, M. (2008). Activation of A-type γ-amino butyric acid receptors excites gonadotrophin-releasing hormone neurones isolated from adult rats. Journal of Neuroendocrinology, 20, 566–575.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Dávid Csercsik
    • 1
  • Imre Farkas
    • 2
  • Erik Hrabovszky
    • 2
  • Zsolt Liposits
    • 2
    • 3
  1. 1.Process Control Research Group, Computer and Automation Research InstituteHungarian Academy of SciencesBudapestHungary
  2. 2.Department of Endocrine Neurobiology, Institute of Experimental MedicineHungarian Academy of SciencesBudapestHungary
  3. 3.Faculty of Information TechnologyPázmány Péter Catholic UniversityBudapestHungary

Personalised recommendations