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Biophys J. 1979 Jul;27(1):87-104. doi: 10.1016/S0006-3495(79)85204-2.
Voltage perturbation methods based upon topological concepts are used to elicit responses from the Hodgkin-Huxley (HH) nonlinear differential equations. These responses present a critical check upon the validity of the HH model for electrical activity across squid axon membrane. It is shown that when a constant current is applied such that a stable equilibrium and rhythmic firing are present, the following predictions are inherent in the HH system of equations: (a) Small instantaneous voltage perturbations to the axon given at points along its firing spike result in phase resetting curves (when new phase versus old phase is plotted) with an average slope of 1. (b) A larger voltage perturbation (from certain points along the firing spike) results in the permanent cessation of periodic firing, with membrane voltage rapidly approaching the equilibrium value. (c) A still larger perturbation yields phase resetting curves with an average slope equal to 0. These predictions, coupled with Tasaki's experimental demonstration that squid axons in excellent condition do give repetitive firing under constant current, provide a critical test of the validity of the HH model.
基于拓扑概念的电压扰动方法被用于激发霍奇金-赫胥黎（HH）非线性微分方程的响应。这些响应是对HH模型在鱿鱼轴突膜上电活动有效性的关键检验。结果表明，当施加恒定电流使得存在稳定平衡和节律性放电时，HH方程组具有以下固有预测：（a）在轴突放电尖峰沿线各点对轴突施加小的瞬时电压扰动，会导致相位重置曲线（当绘制新相位与旧相位关系时）平均斜率为1。（b）较大的电压扰动（从放电尖峰沿线某些点施加）会导致周期性放电永久停止，膜电压迅速接近平衡值。（c）更大的扰动会产生平均斜率为0的相位重置曲线。这些预测，再加上田崎的实验证明，即状态良好的鱿鱼轴突在恒定电流下确实会产生重复放电，为HH模型的有效性提供了关键检验。
