Abstract
GnRH neurons are hypothalamic neurons that secrete gonadotropin-releasing hormone (GnRH) which stimulates the release of gonadotropins, one of the crucial hormones for sexual development, fertility and maturation. A mathematical model was built to help elucidate the mechanisms underlying electrical bursting and synchronous [Ca 2+] transients in GnRH neurons ( Lee et al., 2010). The model predicted that bursting in GnRH neurons (at least of the short-bursting type) requires the existence of a [Ca 2+]-dependent slow after-hyperpolarisation current (s I AHP-UCL), and this predicted current was found experimentally. GnRH behaviour under a wide range of conditions (inhibition of Na + channels, IP 3 receptors, [Ca 2+]-dependent K + channels, or Ca 2+ pumps, or in the presence of zero extracellular [Ca 2+]) is successfully reproduced by the model. In this paper, a simplified version of the previous model, with the same qualitative behaviour, is constructed and studied using timescale separation techniques and bifurcation analysis.
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