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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)
S. Bordin and colleagues have proposed that the depolarizing effects of acetylcholine and other muscarinic agonists on pancreatic beta-cells are mediated by a calcium release-activated current (CRAC). We support this hypothesis with additional data, and present a theoretical model which accounts for most known data on muscarinic effects. Additional(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)
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)
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)
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)
Facilitation is a transient stimulation-induced increase in synaptic response, a ubiquitous form of short-term synaptic plasticity that can regulate synaptic transmission on fast time scales. In their pioneering work, Katz and Miledi and Rahamimoff demonstrated the dependence of facilitation on presynaptic Ca(2+) influx and proposed that facilitation(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)
A novel calcium-dependent potassium current (K(slow)) that slowly activates in response to a simulated islet burst was identified recently in mouse pancreatic beta-cells (Göpel, S.O., T. Kanno, S. Barg, L. Eliasson, J. Galvanovskis, E. Renström, and P. Rorsman. 1999. J. Gen. Physiol. 114:759-769). K(slow) activation may help terminate the cyclic bursts of(More)