The Geometry of Bursting in the Dual Oscillator Model of Pancreatic β-cells
The Geometry of Bursting in the Dual Oscillator Model of Pancreatic β-cells
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DOI：
10.1137/08074427x
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发表时间：
2009-01-01
影响因子：
2.1
通讯作者：
Sherman, Arthur
中科院分区：
文献类型：
--
作者：
Goel, Pranay;Sherman, Arthur
我们描述了一个扩展的快-慢分析的双振荡器模型（DOM）的胰腺β细胞，发生在很宽的时间尺度上，从秒到分钟的爆发振荡。这种宽的动态范围已被认为是由一个非常缓慢的代谢，可能是糖酵解，振荡器和一个更快的电振荡器，本身包含几个负反馈机制与一系列的时间尺度的相互作用。虽然高维度的慢子系统将击败一个简单的快-慢分析，我们表明，近似的几何分析，利用特定功能的DOM和叠加的分支图的组成振荡器的基础上，导致新的见解系统的功能。
We describe an extended fast-slow analysis for the dual oscillator model (DOM) for bursting oscillations in pancreatic beta-cells, which occur on a wide range of time scales, from seconds to minutes. This wide dynamic range has been suggested to result from the interactions of a very slow metabolic, possibly glycolytic, oscillator and a faster electrical oscillator, itself containing several negative feedback mechanisms with a range of time scales. Although the high dimensionality of the slow subsystem would defeat a straightforward fast-slow analysis, we show that an approximate geometrical analysis that exploits particular features of the DOM and is based on superimposing the bifurcation diagrams of the component oscillators leads to new insights into the functioning of the system.