Laboratory of Biological Modeling, NIDDK National Institutes of Health Bethesda, MD 20892, United States.
Department of Mathematics and Programs in Molecular Biophysics and Neuroscience, Florida State University Tallahassee, FL 32301, United States.
J Theor Biol. 2018 Nov 14;457:152-162. doi: 10.1016/j.jtbi.2018.08.029. Epub 2018 Aug 24.
Insulin-secreting pancreatic β-cells are electrically excitable cells that are unusual because their electrical activity is influenced directly by metabolism via ATP-sensitive K channels. At the same time, changes in the intracellular Caconcentration that result from the cell's electrical activity influence metabolism in several ways. Thus, there is bidirectional coupling between the electrical dynamics and the metabolic dynamics in β-cells. A mathematical model has been previously developed, called the Integrated. Oscillator Model (IOM), to highlight the bidirectional coupling involved in the oscillation mechanism. In this study, we show how this coupling can produce oscillations in β-cell activity. These oscillations have period similar to that of insulin secretion pulses observed in rats, mice, dogs, and humans, which has been shown to facilitate the action of the liver in maintaining glucose homeostasis. In a companion paper we show that the IOM can produce oscillations using two distinct mechanisms, depending on the values of electrical and metabolic parameters. In the present article, we use fast-slow analysis to understand the mechanisms underlying each of these oscillations. In particular, we show why a key variable in the glycolytic pathway generates a pulsatile time course in one type of oscillation, while it generates a sawtooth time course in the other type. The significance of these patterns is that the time course is a reflection of whether an intrinsic glycolytic oscillator is active, or whether the oscillations are a direct consequence of Ca feedback onto glycolysis.
胰岛素分泌的胰腺β细胞是电兴奋细胞，它们的电活动直接受到代谢物通过 ATP 敏感性 K 通道的影响，这使其变得不同寻常。同时，细胞电活动引起的细胞内 Ca2+浓度变化会以多种方式影响代谢。因此，β细胞中电动力学和代谢动力学之间存在双向耦合。先前已经开发出一种称为综合振荡器模型（IOM）的数学模型，以突出振荡机制中涉及的双向耦合。在这项研究中，我们展示了这种耦合如何产生β细胞活动的振荡。这些振荡的周期与在大鼠、小鼠、狗和人类中观察到的胰岛素分泌脉冲相似，这被证明有助于肝脏维持葡萄糖稳态的作用。在一篇配套论文中，我们表明 IOM 可以使用两种不同的机制产生振荡，这取决于电和代谢参数的值。在本文中，我们使用快速-缓慢分析来理解这两种振荡的机制。特别是，我们展示了为什么糖酵解途径中的一个关键变量在一种类型的振荡中产生脉冲时间过程，而在另一种类型中产生锯齿时间过程。这些模式的意义在于，时间过程反映了内在糖酵解振荡器是否活跃，或者振荡是否是 Ca 反馈对糖酵解的直接结果。
