Department of Mathematics, Florida State University, Tallahassee, Florida 32306, USA.
School of Mathematics, Monash University, Clayton, Victoria 3800, Australia.
Chaos. 2021 Oct;31(10):103128. doi: 10.1063/5.0059338.
Electrical bursting oscillations in neurons and endocrine cells are activity patterns that facilitate the secretion of neurotransmitters and hormones and have been the focus of study for several decades. Mathematical modeling has been an extremely useful tool in this effort, and the use of fast-slow analysis has made it possible to understand bursting from a dynamic perspective and to make testable predictions about changes in system parameters or the cellular environment. It is typically the case that the electrical impulses that occur during the active phase of a burst are due to stable limit cycles in the fast subsystem of equations or, in the case of so-called "pseudo-plateau bursting," canards that are induced by a folded node singularity. In this article, we show an entirely different mechanism for bursting that relies on stochastic opening and closing of a key ion channel. We demonstrate, using fast-slow analysis, how the short-lived stochastic channel openings can yield a much longer response in which single action potentials are converted into bursts of action potentials. Without this stochastic element, the system is incapable of bursting. This mechanism can describe stochastic bursting in pituitary corticotrophs, which are small cells that exhibit a great deal of noise as well as other pituitary cells, such as lactotrophs and somatotrophs that exhibit noisy bursts of electrical activity.
神经元和内分泌细胞中的电爆发振荡是一种活动模式，有助于神经递质和激素的分泌，几十年来一直是研究的焦点。数学建模在这方面是一个非常有用的工具，而快慢分析的使用使得从动态的角度理解爆发成为可能，并对系统参数或细胞环境的变化做出可测试的预测。通常情况下，爆发活跃期发生的电脉冲是由于快速子系统方程中的稳定极限环引起的，或者在所谓的“伪平台爆发”中，是由折叠节点奇点引起的鸭式飞行器。在本文中，我们展示了一种完全不同的爆发机制，它依赖于关键离子通道的随机开启和关闭。我们使用快慢分析来证明，短暂的随机通道开启如何产生更长的反应，其中单个动作电位转换为动作电位爆发。没有这种随机元素，系统就无法爆发。这种机制可以描述垂体促肾上腺皮质细胞中的随机爆发，这些小细胞表现出很大的噪声，以及其他垂体细胞，如表现出噪声爆发的电活动的催乳素细胞和生长激素细胞。
