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 Is, and the Ca2+ -activated K+ current IKCa. Bifurcation analysis of the model shows that both modes of bursting are similar from a dynamical systems perspective despite differences in burst characteristics.

The islets of Langerhans control glucose homeostasis through secreting insulin. Glucose stimulates insulin secretion via metabolic and electrical events that increase free-calcium activity [Ca 2þ ] to trigger insulin-granule exocytosis. cAMPregulated pathways also enhancing insulin release. We previously examined how gap junctions coordinate the electrical, [Ca 2þ ] and insulin secretory response. Recent observations have shown that the cAMP is also coordinated, but the mechanisms by which this occurs are poorly understood. To examine this, we measured [Ca 2þ ] and cAMP dynamics in clusters of MIN6 b-cell line and compared results with a multicellular mathematical model of glucoseregulated [Ca 2þ ] and its interaction with cAMP. We find that [Ca 2þ ] and cAMP oscillations are both synchronized across MIN6 clusters. Cell pairs highly synchronized in [Ca 2þ ] were also highly synchronized in cAMP. Cells where cAMP and [Ca 2þ ] oscillations were robust and tightly linked correlated with highly synchronized [Ca 2þ ] and cAMP oscillations. Similar results were observed in the mathematical model that solely contained electrical coupling, supporting that synchronization [Ca 2þ ] is sufficient to promote synchronized cAMP. Optogenetic control of cAMP similarly did not generate coupled cAMP dynamics, unlike optogenetic control of [Ca 2þ ]. Upon Exendin4 stimulated cAMP synthesis, [Ca 2þ ] synchronization increased, which correlated with an increased link between [Ca 2þ ] and cAMP oscillations. This improved