Tang Y, Stephenson J L, Othmer H G
Department of Physiology and Biophysics, Cornell University Medical College, New York, New York 10021, USA.
Biophys J. 1996 Jan;70(1):246-63. doi: 10.1016/S0006-3495(96)79567-X.
We study the models for calcium (Ca) dynamics developed in earlier studies, in each of which the key component is the kinetics of intracellular inositol-1,4,5-trisphosphate-sensitive Ca channels. After rapidly equilibrating steps are eliminated, the channel kinetics in these models are represented by a single differential equation that is linear in the state of the channel. In the reduced kinetic model, the graph of the steady-state fraction of conducting channels as a function of log10(Ca) is a bell-shaped curve. Dynamically, a step increase in inositol-1,4,5-trisphosphate induces an incremental increase in the fraction of conducting channels, whereas a step increase in Ca can either potentiate or inhibit channel activation, depending on the Ca level before and after the increase. The relationships among these models are discussed, and experimental tests to distinguish between them are given. Under certain conditions the models for intracellular calcium dynamics are reduced to the singular perturbed form epsilon dx/d tau = f(x, y, p), dy/d tau = g(x, y, p). Phase-plane analysis is applied to a generic form of these simplified models to show how different types of Ca response, such as excitability, oscillations, and a sustained elevation of Ca, can arise. The generic model can also be used to study frequency encoding of hormonal stimuli, to determine the conditions for stable traveling Ca waves, and to understand the effect of channel properties on the wave speed.
我们研究了早期研究中建立的钙（Ca）动力学模型，在每个模型中，关键成分是细胞内1,4,5-三磷酸肌醇敏感钙通道的动力学。在消除快速平衡步骤后，这些模型中的通道动力学由一个在通道状态上呈线性的单一微分方程表示。在简化的动力学模型中，导通通道稳态分数作为log10（Ca）的函数的图形是一条钟形曲线。在动态方面，1,4,5-三磷酸肌醇的阶跃增加会导致导通通道分数的增量增加，而Ca的阶跃增加根据增加前后的Ca水平可以增强或抑制通道激活。讨论了这些模型之间的关系，并给出了区分它们的实验测试。在某些条件下，细胞内钙动力学模型简化为奇异摄动形式εdx/dτ = f(x, y, p)，dy/dτ = g(x, y, p)。对这些简化模型的一般形式进行相平面分析，以展示如何产生不同类型的Ca反应，如兴奋性、振荡和Ca的持续升高。该一般模型还可用于研究激素刺激的频率编码，确定稳定传播的Ca波的条件，并理解通道特性对波速的影响。
