Vo Theodore, Bertram Richard, Tabak Joel, Wechselberger Martin
School of Mathematics and Statistics, University of Sydney, Sydney, NSW, Australia.
J Comput Neurosci. 2010 Jun;28(3):443-58. doi: 10.1007/s10827-010-0226-7. Epub 2010 Feb 26.
We combine bifurcation analysis with the theory of canard-induced mixed mode oscillations to investigate the dynamics of a novel form of bursting. This bursting oscillation, which arises from a model of the electrical activity of a pituitary cell, is characterized by small impulses or spikes riding on top of an elevated voltage plateau. Oscillations with these characteristics have been called "pseudo-plateau bursting". Unlike standard bursting, the subsystem of fast variables does not possess a stable branch of periodic spiking solutions, and in the case studied here the standard fast/slow analysis provides little information about the underlying dynamics. We demonstrate that the bursting is actually a canard-induced mixed mode oscillation, and use canard theory to characterize the dynamics of the oscillation. We also use bifurcation analysis of the full system of equations to extend the results of the singular analysis to the physiological regime. This demonstrates that the combination of these two analysis techniques can be a powerful tool for understanding the pseudo-plateau bursting oscillations that arise in electrically excitable pituitary cells and isolated pancreatic beta-cells.
我们将分岔分析与鸭诱导混合模式振荡理论相结合，以研究一种新型爆发形式的动力学。这种爆发振荡源自垂体细胞电活动模型，其特征是在升高的电压平台之上出现小脉冲或尖峰。具有这些特征的振荡被称为“伪平台爆发”。与标准爆发不同，快速变量子系统不具有周期尖峰解的稳定分支，并且在此处研究的情况下，标准的快/慢分析几乎无法提供有关潜在动力学的信息。我们证明这种爆发实际上是一种鸭诱导混合模式振荡，并使用鸭理论来表征振荡的动力学。我们还对方程组的完整系统进行分岔分析，将奇异分析的结果扩展到生理状态。这表明这两种分析技术的结合可以成为理解电可兴奋垂体细胞和分离的胰腺β细胞中出现的伪平台爆发振荡的有力工具。
