title: A mathematical model of adult GnRH neurons in mouse brain and its bifurcation analysis.
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 [Ca²(+)] 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 [Ca²(+)]-dependent slow after-hyperpolarisation current (sI(AHP-UCL)), and this predicted current was found experimentally. GnRH behaviour under a wide range of conditions (inhibition of Na(+) channels, IP₃ receptors, [Ca²(+)]-dependent K(+) channels, or Ca²(+) pumps, or in the presence of zero extracellular [Ca²(+)]) 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.
authors.affiliation: Department of Mathematics, University of Auckland, Auckland 1142, New Zealand. wdua004@aucklanduni.ac.nz
authors.forename: Wen
authors.initials: W
authors.lastname: Duan
authors.forename: Kiho
authors.initials: K
authors.lastname: Lee
authors.forename: Allan E
authors.initials: AE
authors.lastname: Herbison
authors.forename: James
authors.initials: J
authors.lastname: Sneyd
mesh_terms: D000200:Action Potentials / Q000187:drug effects; D000375:Aging / Q000187:drug effects / Q000502:physiology*; D000818:Animals; D001030:Apamin / Q000494:pharmacology; D001596:Benzylamines / Q000494:pharmacology; D001896:Boron Compounds / Q000494:pharmacology; D001921:Brain / Q000166:cytology*; D002118:Calcium / Q000494:pharmacology; D003198:Computer Simulation; D005110:Extracellular Space / Q000187:drug effects / Q000378:metabolism; D007987:Gonadotropin-Releasing Hormone / Q000378:metabolism*; D007211:Indoles / Q000494:pharmacology; D051379:Mice; D008954:Models, Biological; D009474:Neurons / Q000187:drug effects / Q000502:physiology*; D011725:Pyridines / Q000494:pharmacology; D013779:Tetrodotoxin / Q000494:pharmacology
chemical_list: C549620:3-(triphenylmethylaminomethyl)pyridine; D001596:Benzylamines; D001896:Boron Compounds; D007211:Indoles; D011725:Pyridines; D001030:Apamin; D007987:Gonadotropin-Releasing Hormone; D013779:Tetrodotoxin; C109986:2-aminoethoxydiphenyl borate; D002118:Calcium; C000543:cyclopiazonic acid