Thresholds and plateaus in the Hodgkin-Huxley nerve equations.
Thresholds and plateaus in the Hodgkin-Huxley nerve equations.
复制标题
DOI：
10.1085/jgp.43.5.867
复制
发表时间：
1960-05
期刊：
影响因子：
--
通讯作者：
FITZHUGH R
中科院分区：
文献类型：
--
作者：
FITZHUGH R
用相空间方法和模拟计算机分析了鱿鱼巨轴突膜的Hodgkin-Huxley非线性微分方程组。V为膜电位，m为Na+激活，h为Na+失活，n为K+激活。V和m相对于h和n变化很快。当h和n保持不变时，简化方程组的(V，m)相平面有三个奇点：一个稳定的休止点、一个阈值鞍点和一个稳定的激发点。当允许h和n变化时，恢复和不稳定是由运动引起的，随后阈值和激发点消失。N的时间常数乘以100或更多，h的时间常数乘以三分之一，再现了Tasaki和Hagiwara用四乙基铵获得的实验平台动作电位，包括平台持续时间的取消和不稳定现象。正如这些作者在真实轴突中发现的那样，这些方程瞬时有两种稳定状态。由于理论膜电导曲线与实验膜电导曲线有很大差异，还需要对四乙基铵离子流进行进一步的实验分析，以确定是否可以推广Hodgkin-Huxley模型来完全解释这些实验。
Phase space methods and an analog computer are used to analyze the Hodgkin-Huxley non-linear differential equations for the squid giant axon membrane. V is the membrane potential, m the Na+ activation, h the Na+ inactivation, and n the K+ activation. V and m change rapidly, relative to h and n. The (V, m) phase plane of a reduced system of equations, with h and n held constant at their resting values, has three singular points: a stable resting point, a threshold saddle point, and a stable excited point. When h and n are allowed to vary, recovery and refractoriness result from the movement with subsequent disappearance of the threshold and excited points. Multiplying the time constant of n by 100 or more, and that of h by one-third, reproduces the experimental plateau action potentials obtained with tetraethylammonium by Tasaki and Hagiwara, including the phenomena of abolition and of refractoriness of the plateau duration. The equations have, transiently, two stable states, as found in the real axon by these authors. Since the theoretical membrane conductance curves differ significantly from the experimental ones, further experimental analysis of ionic currents with tetraethylammonium is needed to decide whether the Hodgkin-Huxley model can be generalized to explain these experiments completely.
登录
查看更多内容
影响因子：
5.5
作者：
FATT, P;GINSBORG, BL
通讯作者：
GINSBORG, BL
影响因子：
5.5
作者：
DODGE, FA;FRANKENHAEUSER, B
通讯作者：
FRANKENHAEUSER, B
影响因子：
3.8
作者：
SPYROPOULOS, CS
通讯作者：
SPYROPOULOS, CS
DOI：
10.1085/jgp.40.6.859
发表时间：
1957-07-20
期刊：
The Journal of general physiology
影响因子：
--
作者：
TASAKI I;HAGIWAR AS
通讯作者：
HAGIWAR AS
DOI：
10.1137/0107037
发表时间：
1959-01-01
期刊：
JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS
影响因子：
--
作者：
FITZHUGH, R;ANTOSIEWICZ, HA
通讯作者：
ANTOSIEWICZ, HA