Chay T R, Rinzel J
Biophys J. 1985 Mar;47(3):357-66. doi: 10.1016/S0006-3495(85)83926-6.
We have studied periodic as well as aperiodic behavior in the self-sustained oscillations exhibited by the Hodgkin-Huxley type model of Chay, T. R., and J. Keizer (Biophys. J., 1983, 42:181-190) for the pancreatic beta-cell. Numerical solutions reveal a variety of patterns as the glucose-dependent parameter kCa is varied. These include regimes of periodic beating (continuous spiking) and bursting modes and, in the transition between these modes, aperiodic responses. Such aperiodic behavior for a nonrandom system has been called deterministic chaos and is characterized by distinguishing features found in previous studies of chaos in nonbiophysical systems and here identified for an (endogenously active) excitable membrane model. To parallel the successful analysis of chaos in other physical/chemical contexts we introduce a simplified, but quantitative, one-variable, discrete-time representation of the dynamics. It describes the evolution of intracellular calcium (which activates a potassium conductance) from one spike upstroke to the next and exhibits the various modes of behavior.
我们研究了Chay, T. R.和J. Keizer（《生物物理杂志》，1983年，42卷：181 - 190页）提出的胰腺β细胞霍奇金 - 赫胥黎型模型所表现出的自维持振荡中的周期性和非周期性行为。数值解表明，随着葡萄糖依赖参数kCa的变化会出现多种模式。这些模式包括周期性搏动（连续尖峰）和爆发模式，并且在这些模式之间的转变过程中还存在非周期性响应。对于一个非随机系统而言，这种非周期性行为被称为确定性混沌，其特征是在先前非生物物理系统的混沌研究中发现的显著特征，并且在这里被确定为一个（内源性活跃的）可兴奋膜模型的特征。为了与其他物理/化学环境中对混沌的成功分析相平行，我们引入了一种简化但定量的单变量离散时间动力学表示。它描述了从一个尖峰上升到下一个尖峰上升过程中细胞内钙（其激活钾电导）的演化，并展现出各种行为模式。
