School of Basic Courses, Guangdong Pharmaceutical University, Guangdong, 510006 China.
Department of Dynamics and Control, Beihang University, Beijing, 100191 China.
Cogn Neurodyn. 2013 Jun;7(3):197-212. doi: 10.1007/s11571-012-9226-9. Epub 2012 Oct 25.
Based on bifurcation analysis, the synchronization behaviors of two identical pancreatic β-cells connected by electrical and chemical coupling are investigated, respectively. Various firing patterns are produced in coupled cells when a single cell exhibits tonic spiking or square-wave bursting individually, irrespectively of what the cells are connected by electrical or chemical coupling. On the one hand, cells can burst synchronously for both weak electrical and chemical coupling when an isolated cell exhibits tonic spiking itself. In particular, for electrically coupled cells, under the variation of the coupling strength there exist complex transition processes of synchronous firing patterns such as "fold/limit cycle" type of bursting, then anti-phase continuous spiking, followed by the "fold/torus" type of bursting, and finally in-phase tonic spiking. On the other hand, it is shown that when the individual cell exhibits square-wave bursting, suitable coupling strength can make the electrically coupled system generate "fold/Hopf" bursting via "fold/fold" hysteresis loop; whereas, the chemically coupled cells generate "fold/subHopf" bursting. Especially, chemically coupled bursters can exhibit inverse period-adding bursting sequence. Fast-slow dynamics analysis is applied to explore the generation mechanism of these bursting oscillations. The above analysis of bursting types and the transition may provide us with better insight into understanding the role of coupling in the dynamic behaviors of pancreatic β-cells.
基于分岔分析，研究了通过电和化学耦合连接的两个相同的胰腺β细胞的同步行为。当单个细胞单独表现出紧张性爆发或方波爆发时，在耦合细胞中会产生各种发射模式，而与细胞通过电或化学耦合连接无关。一方面，当一个孤立的细胞本身表现出紧张性爆发时，细胞可以在弱电和化学耦合下同步爆发。特别是对于电耦合细胞，在耦合强度的变化下，存在着同步发射模式的复杂转变过程，如“折叠/极限环”型爆发，然后是反相连续爆发，接着是“折叠/环面”型爆发，最后是同相紧张性爆发。另一方面，研究表明，当单个细胞表现出方波爆发时，适当的耦合强度可以使电耦合系统通过“折叠/折叠”滞后环产生“折叠/霍普夫”爆发，而化学耦合细胞则产生“折叠/亚霍普夫”爆发。特别是，化学耦合爆发器可以表现出相反的周期添加爆发序列。快慢动力学分析被应用于探究这些爆发振荡的产生机制。上述对爆发类型和转变的分析可以为我们深入了解耦合在胰腺β细胞动态行为中的作用提供更好的认识。
