Stokes C L, Rinzel J
Mathematical Research Branch, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892.
Biophys J. 1993 Aug;65(2):597-607. doi: 10.1016/S0006-3495(93)81092-0.
Electrical bursting oscillations of mammalian pancreatic beta-cells are synchronous among cells within an islet. While electrical coupling among cells via gap junctions has been demonstrated, its extent and topology are unclear. The beta-cells also share an extracellular compartment in which oscillations of K+ concentration have been measured (Perez-Armendariz and Atwater, 1985). These oscillations (1-2 mM) are synchronous with the burst pattern, and apparently are caused by the oscillating voltage-dependent membrane currents: Extracellular K+ concentration (Ke) rises during the depolarized active (spiking) phase and falls during the hyperpolarized silent phase. Because raising Ke depolarizes the cell membrane by increasing the potassium reversal potential (VK), any cell in the active phase should recruit nonspiking cells into the active phase. The opposite is predicted for the silent phase. This positive feedback system might couple the cells' electrical activity and synchronize bursting. We have explored this possibility using a theoretical model for bursting of beta-cells (Sherman et al., 1988) and K+ diffusion in the extracellular space of an islet. Computer simulations demonstrate that the bursts synchronize very quickly (within one burst) without gap junctional coupling among the cells. The shape and amplitude of computed Ke oscillations resemble those seen in experiments for certain parameter ranges. The model cells synchronize with exterior cells leading, though incorporating heterogeneous cell properties can allow interior cells to lead. The model islet can also be forced to oscillate at both faster and slower frequencies using periodic pulses of higher K+ in the medium surrounding the islet. Phase plane analysis was used to understand the synchronization mechanism. The results of our model suggest that diffusion of extracellular K+ may contribute to coupling and synchronization of electrical oscillations in beta-cells within an islet.
哺乳动物胰腺β细胞的电爆发放振荡在胰岛内的细胞之间是同步的。虽然已经证明细胞间通过缝隙连接存在电耦合，但其程度和拓扑结构尚不清楚。β细胞还共享一个细胞外间隙，在其中已测量到K⁺浓度的振荡（佩雷斯 - 阿门达里兹和阿特沃特，1985年）。这些振荡（1 - 2 mM）与爆发模式同步，显然是由振荡的电压依赖性膜电流引起的：细胞外K⁺浓度（Ke）在去极化的活跃（放电）阶段升高，在超极化的静息阶段下降。由于提高Ke会通过增加钾反转电位（VK）使细胞膜去极化，任何处于活跃阶段的细胞都应将非放电细胞招募到活跃阶段。对于静息阶段则有相反的预测。这种正反馈系统可能会耦合细胞的电活动并使爆发放同步。我们使用β细胞爆发放的理论模型（谢尔曼等人，1988年）以及胰岛细胞外空间中K⁺扩散来探索这种可能性。计算机模拟表明，在细胞间没有缝隙连接耦合的情况下，爆发放能非常迅速地同步（在一次爆发放内）。对于某些参数范围，计算得到的Ke振荡的形状和幅度与实验中观察到的相似。模型细胞与外部细胞同步，外部细胞领先，不过纳入异质细胞特性可使内部细胞领先。使用围绕胰岛的培养基中更高K⁺的周期性脉冲，还可使模型胰岛以更快和更慢的频率振荡。相平面分析用于理解同步机制。我们模型的结果表明，细胞外K⁺的扩散可能有助于胰岛内β细胞电振荡的耦合和同步。
