Channelopathies involving acquired or genetic modifications of the delayed rectifier K⁺ channel Kv1.1 include phenotypes characterized by enhanced neuronal excitability. Affected Kv1.1 channels exhibit combinations of altered expression, voltage sensitivity, and rates of activation and deactivation. Computational modeling and analysis can reveal the potential of particular channelopathies to alter neuronal excitability. A dynamical systems approach was taken to study the excitability and underlying dynamical structure of the Hodgkin-Huxley (HH) model of neural excitation as properties of the delayed rectifier K⁺ channel were altered. Bifurcation patterns of the HH model were determined as the amplitude of steady injection current was varied simultaneously with single parameters describing the delayed rectifier rates of activation and deactivation, maximal conductance, and voltage sensitivity. Relatively modest changes in the properties of the delayed rectifier K⁺ channel analogous to what is described for its channelopathies alter the bifurcation structure of the HH model and profoundly modify excitability of the HH model. Channelopathies associated with Kv1.1 can reduce the threshold for onset of neural activity. These studies also demonstrate how pathological delayed rectifier K⁺ channels could lead to the observation of the generalized Hopf bifurcation and, perhaps, other variants of the Hopf bifurcation. The observed bifurcation patterns collectively demonstrate that properties of the nominal delayed rectifier in the HH model appear optimized to permit activation of the HH model over the broadest possible range of input currents.

涉及延迟整流器 K ⁺通道 Kv1.1 的获得性或遗传修饰的通道病包括以神经元兴奋性增强为特征的表型。受影响的 Kv1.1 通道表现出改变的表达、电压敏感性以及激活和失活率的组合。计算建模和分析可以揭示特定通道病改变神经元兴奋性的潜力。采用动态系统方法来研究作为延迟整流器 K ⁺特性的神经兴奋的霍奇金-赫胥黎 (HH) 模型的兴奋性和潜在的动态结构频道被更改。HH 模型的分叉模式被确定为稳定注入电流的幅度与描述激活和失活的延迟整流器速率、最大电导和电压灵敏度的单个参数同时变化。延迟整流器 K ⁺通道性质的相对适度变化类似于其通道病所描述的改变 HH 模型的分叉结构，并深刻地改变了 HH 模型的兴奋性。与 Kv1.1 相关的通道病可以降低神经活动开始的阈值。这些研究还证明了病理性延迟整流器 K ⁺通道可能导致对广义 Hopf 分叉的观察，也许还有 Hopf 分叉的其他变体。观察到的分叉模式共同证明了 HH 模型中标称延迟整流器的特性似乎经过优化，以允许在尽可能宽的输入电流范围内激活 HH 模型。