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We describe a classification scheme for bursting oscillations which encompasses many of those found in the literature on bursting in excitable media. This is an extension of the scheme of Rinzel (in Mathematical Topics in Population Biology, Springer, Berlin, 1987), put in the context of a sequence of horizontal cuts through a two-parameter bifurcation(More)
Burst firing of dopaminergic neurons of the substantia nigra pars compacta can be induced in vitro by the glutamate agonist N-methyl-D-aspartate. It has been suggested that the interburst hyperpolarization is due to Na+ extrusion by a ouabain-sensitive pump [Johnson et al. (1992) Science 258, 665-667]. We formulate and explore a theoretical model, with a(More)
Pancreatic beta-cells exhibit bursting oscillations with a wide range of periods. Whereas periods in isolated cells are generally either a few seconds or a few minutes, in intact islets of Langerhans they are intermediate (10-60 s). We develop a mathematical model for beta-cell electrical activity capable of generating this wide range of bursting(More)
abstract A novel calcium-dependent potassium current (K slow) that slowly activates in response to a simulated islet burst was identified recently in mouse pancreatic ␤ K slow activation may help terminate the cyclic bursts of Ca 2 ϩ-dependent action potentials that drive Ca 2 ϩ influx and insulin secretion in ␤-cells. Here, we report that when [Ca 2 ϩ ] i(More)
The nucleus HVC (proper name) within the avian analog of mammal premotor cortex produces stereotyped instructions through the motor pathway leading to precise, learned vocalization by songbirds. Electrophysiological characterization of component HVC neurons is an important requirement in building a model to understand HVC function. The HVC contains three(More)
Although single-channel Ca2+ microdomains are capable of gating neurotransmitter release in some instances, it is likely that in many cases the microdomains from several open channels overlap to activate vesicle fusion. We describe a mathematical model in which transmitter release is gated by single or overlapping Ca2+ microdomains produced by the opening(More)
Insulin-secreting beta-cells, located within the pancreatic islets of Langerhans, are excitable cells that produce regular bursts of action potentials when stimulated by glucose. This system has been the focus of mathematical investigation for two decades, spawning an array of mathematical models. Recently, a new class of models has been introduced called(More)
Endocrine pituitary cells are neuronlike; they express numerous voltage-gated sodium, calcium, potassium, and chloride channels and fire action potentials spontaneously, accompanied by a rise in intracellular calcium. In some cells, spontaneous electrical activity is sufficient to drive the intracellular calcium concentration above the threshold for(More)
Prolactin (PRL) is secreted from lactotrophs of the anterior pituitary gland of rats in a unique pattern in response to uterine cervical stimulation (CS) during mating. Surges of PRL secretion occur in response to relief from hypothalamic dopaminergic inhibition and stimulation by hypothalamic releasing neurohormones. In this study, we characterized the(More)
1. We describe a model of transmitter release that is based on the finding that release can be gated during the opening of individual Ca2+ channels, suggesting that the release site can be activated by the Ca2+ domain under a single channel. In this model each release site contains four independent Ca2+ binding sites or gates with unbinding kinetics graded(More)