Abstract
Pituitary cells of the anterior pituitary gland secrete hormones in response to patterns of electrical activity. Several types of pituitary cells produce short bursts of electrical activity which are more effective than single spikes in evoking hormone release. These bursts, called pseudo-plateau bursts, are unlike bursts studied mathematically in neurons (plateau bursting) and the standard fast-slow analysis used for plateau bursting is of limited use. Using an alternative fast-slow analysis, with one fast and two slow variables, we show that pseudo-plateau bursting is a canard-induced mixed mode oscillation. Using this technique, it is possible to determine the region of parameter space where bursting occurs as well as salient properties of the burst such as the number of spikes in the burst. The information gained from this one-fast/two-slow decomposition complements the information obtained from a two-fast/one-slow decomposition.
Highlights
Bursting is a common pattern of electrical activity in excitable cells such as neurons and many endocrine cells
Prior analysis showed that the dynamic mechanism for this type of bursting, called pseudo-plateau bursting, is significantly different from that of square-wave bursting which is common in neurons [11,12,13]
Region B consists of the folded nodes on L+, and it is the key region for the existence of mixed mode oscillations, since δ > 0 for much of this region
Summary
Bursting is a common pattern of electrical activity in excitable cells such as neurons and many endocrine cells. Prior analysis showed that the dynamic mechanism for this type of bursting, called pseudo-plateau bursting, is significantly different from that of square-wave bursting ( called plateau bursting) which is common in neurons [11,12,13] This analysis did not determine the possible number of spikes that occur during the active phase of the burst. One studies the dynamics of the fast subsystem with the slow variable treated as a slowly varying parameter [12, 15,16,17,18] This approach has been very successful for understanding plateau bursting, such as occurs in pancreatic islets [19], pre-Bötzinger neurons of the brain stem [20], trigeminal motoneurons [21] or neonatal CA3 hippocampal principal neurons [14], Fig. 1(b). The one-fast/twoslow variable analysis provides information that is not available from the standard two-fast/one-slow variable analysis in the case of pseudo-plateau bursting
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