Abstract：
The classical Hodgkin-Huxley (HH) point-neuron model of action potential generation is four-dimensional. It consists of four ordinary differential equations describing the dynamics of the membrane potential and three gating variables associated to a transient sodium and a delayed-rectifier potassium ionic currents. Conductance-based models of HH type are higher-dimensional extensions of the classical HH model. They include a number of supplementary state variables associated with other ionic current types, and are able to describe additional phenomena such as subthreshold oscillations, mixed-mode oscillations (subthreshold oscillations interspersed with spikes), clustering and bursting. In this manuscript we discuss biophysically plausible and phenomenological reduced models that preserve the biophysical and/or dynamic description of models of HH type and the ability to produce complex phenomena, but the number of effective dimensions (state variables) is lower. We describe several representative models. We also describe systematic and heuristic methods of deriving reduced models from models of HH type.
摘要：
动作电位产生的经典Hodgkin-Huxley（HH）点神经元模型是四维的。它由四个描述膜电位动力学的常微分方程和与瞬态钠和延迟整流钾离子电流相关的三个门控变量组成。HH型的基于电导的模型是经典HH模型的高维扩展。它们包括许多与其他离子电流类型相关的补充状态变量，并且能够描述其他现象，例如亚阈值振荡，混合模式振荡(散布有尖峰的亚阈值振荡)，集群和爆裂。在本手稿中，我们讨论了生物物理上合理的和现象学的简化模型，这些模型保留了HH型模型的生物物理和/或动态描述以及产生复杂现象的能力，但有效维度（状态变量）的数量较低。我们描述了几个代表性的模型。我们还描述了从HH型模型中推导简化模型的系统和启发式方法。
