Kang Hyuk, Han Kyungreem, Jo Junghyo, Kim Jinwoong, Choi Moo Young
Institute of Basic Science, Sungkyunkwan University, Suwon 404-746, Korea.
Front Biosci. 2008 May 1;13:6421-31. doi: 10.2741/3163.
We present mathematical models for systems of beta-cells in pancreatic islets. The first topic begins with the effects of noise and coupling strength on bursting action potentials of beta-cells. From the discussion, the regular bursts are produced by a proper amount of noise and coupling strength. Furthermore, the bursting duration and period depend on the cluster size of beta-cells. We also observe the real size of islets mostly consisting of beta-cells and obtain the size distribution of islets. In addition, we derive either log-normal or Weibull distributions of the islet sizes based on recent observation on islet growth. Islets of Langerhans are composed of several endocrine cells which interact with each other. Considering asymmetric and inhibitory interactions of these endocrine cells, we introduce a simple islet model consisting of alpha-, beta-, and delta-cells. Finally, a whole feedback model for glucose regulation is constructed, connecting the microscopic bursting mechanism and the macroscopic blood glucose regulation of the body. We analyzed these models via numerical simulations based on in vivo and in vitro experimental data.
我们提出了胰岛中β细胞系统的数学模型。第一个主题从噪声和耦合强度对β细胞爆发动作电位的影响开始。通过讨论可知，适量的噪声和耦合强度会产生规则的爆发。此外，爆发持续时间和周期取决于β细胞的簇大小。我们还观察了主要由β细胞组成的胰岛的实际大小，并获得了胰岛大小分布。此外，基于对胰岛生长的最新观察，我们推导出了胰岛大小的对数正态分布或威布尔分布。胰岛由几种相互作用的内分泌细胞组成。考虑到这些内分泌细胞的不对称和抑制性相互作用，我们引入了一个由α、β和δ细胞组成的简单胰岛模型。最后，构建了一个用于葡萄糖调节的完整反馈模型，将微观爆发机制与身体的宏观血糖调节联系起来。我们基于体内和体外实验数据，通过数值模拟对这些模型进行了分析。
