Reduction of the Hodgkin-Huxley equations to a single-variable threshold model
Reduction of the Hodgkin-Huxley equations to a single-variable threshold model
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DOI：
10.1162/neco.1997.9.5.1015
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发表时间：
1997-07-01
影响因子：
2.9
通讯作者：
vanHemmen, JL
中科院分区：
文献类型：
--
作者：
Kistler, WM;Gerstner, W;vanHemmen, JL
通常认为，神经元是当某个变量u达到某个阈值时触发的阈值元素。在这里，我们追寻这一图景是否合理的问题，并研究霍奇金和赫胥黎的四维神经元模型作为一个具体的例子。该模型由响应核展开来近似，该响应核以单个变量膜电压的形式表示。一阶项在输入中是线性的，其核心具有初级突触后电位的典型形式。高阶核函数处理输入尖峰之间的非线性相互作用。与标准的Volterra扩展不同，内核依赖于最近输出尖峰的激发时间。特别是，包括了描述尖峰形状和典型后电位的零级核。我们的模型神经元如果由截断响应核扩展给出的膜电压超过阈值就会被激发。在具有随机输入电流的Hodgkin-Huxley模型产生的棘波序列上对该阈值模型进行了测试。我们发现，阈值模型正确预测了90%的峰值。我们的结果表明，在很好的近似下，将神经元描述为阈值元件确实是合理的。
It is generally believed that a neuron is a threshold element that fires when some variable u reaches a threshold. Here we pursue the question of whether this picture can be justified and study the four-dimensional neuron model of Hodgkin and Huxley as a concrete example. The model is approximated by a response kernel expansion in terms of a single variable, the membrane voltage. The first-order term is linear in the input and its kernel has the typical form of an elementary postsynaptic potential. Higher-order kernels take care of nonlinear interactions between input spikes. In contrast to the standard Volterra expansion, the kernels depend on the firing time of the most recent output spike. In particular, a zero-order kernel that describes the shape of the spike and the typical afterpotential is included. Our model neuron fires if the membrane voltage, given by the truncated response kernel expansion, crosses a threshold. The threshold model is tested on a spike train generated by the Hodgkin-Huxley model with a stochastic input current. We find that the threshold model predicts 90 percent of the spikes correctly. Our results show that, to good approximation, the description of a neuron as a threshold element can indeed be justified.