A major challenge in understanding spike-time dependent information encoding in the neural system is the non-linear firing response to inputs of the individual neurons. Hence, quantitative exploration of the putative mechanisms of this non-linear behavior is fundamental to formulating the theory of information transfer in the neural system. The objective of this simulation study was to evaluate and quantify the effect of slowly activating outward membrane current, on the non-linearity in the output of a one-compartment Hodgkin-Huxley styled neuron. To evaluate this effect, the peak conductance of the slow potassium channel (g_K-slow) was varied from 0% to 200% of its normal value in steps of 33%. Both cross- and iso-frequency coupling between the input and the output of the simulated neuron was computed using a generalized coherence measure, i.e., n:m coherence. With increasing g_K-slow, the amount of sub-harmonic cross-frequency coupling, where the output frequencies (1–8 Hz) are lower than the input frequencies (15–35 Hz), increased progressively whereas no change in iso-frequency coupling was observed. Power spectral and phase-space analysis of the neuronal membrane voltage vs. slow potassium channel activation variable showed that the interaction of the slow channel dynamics with the fast membrane voltage dynamics generates the observed sub-harmonic coupling. This study provides quantitative insights into the role of an important membrane mechanism i.e. the slowly activating outward current in generating non-linearities in the output of a neuron.

理解神经系统中与尖峰时间相关的信息编码的一个主要挑战是对单个神经元输入的非线性放电响应。因此，对这种非线性行为的假定机制的定量探索是制定神经系统信息传递理论的基础。这项模拟研究的目的是评估和量化缓慢激活外向膜电流对单室霍奇金-赫胥黎风格神经元输出的非线性的影响。为了评估这种效果，慢钾通道的峰值电导 ( g _K-slow ) 在其正常值的 0% 到 200% 之间变化，步长为 33%。交叉和iso模拟神经元的输入和输出之间的频率耦合是使用广义相干性度量（即n:m 相干性）计算的。随着g _{K-slow 的}增加，输出频率（1-8 Hz）低于输入频率（15-35 Hz）的次谐波交叉频率耦合量逐渐增加，而iso没有变化观察到频率耦合。神经元膜电压与慢钾通道激活变量的功率谱和相空间分析表明，慢通道动力学与快膜电压动力学的相互作用产生了观察到的次谐波耦合。这项研究提供了对重要膜机制的作用的定量见解，即缓慢激活外向电流在神经元输出中产生非线性。