Division of Neurobiology, Department Biology II, Ludwig-Maximilians-Universität München, Planegg-Martinsried, Germany.
J Neurophysiol. 2010 Nov;104(5):2806-20. doi: 10.1152/jn.00240.2010.
Spike-frequency adaptation is a prominent aspect of neuronal dynamics that shapes a neuron's signal processing properties on timescales ranging from about 10 ms to >1 s. For integrate-and-fire model neurons spike-frequency adaptation is incorporated either as an adaptation current or as a dynamic firing threshold. Whether a physiologically observed adaptation mechanism should be modeled as an adaptation current or a dynamic threshold, however, is not known. Here we show that a dynamic threshold has a divisive effect on the onset f-I curve (the initial maximal firing rate following a step increase in an input current) measured at increasing mean threshold levels, i.e., adaptation states. In contrast, an adaptation current subtractively shifts this f-I curve to higher inputs without affecting its slope. As a consequence, an adaptation current acts essentially linearly, resulting in a high-pass filter component of the neuron's transfer function for current stimuli. With a dynamic threshold, however, the transfer function strongly depends on the input range because of the multiplicative effect on the f-I curves. Simulations of conductance-based spiking models with adaptation currents, such as afterhyperpolarization (AHP)-type, M-type, and sodium-activated potassium currents, do not show the divisive effects of a dynamic threshold, but agree with the properties of integrate-and-fire neurons with adaptation current. Notably, the effects of slow inactivation of sodium currents cannot be reproduced by either model. Our results suggest that, when lateral shifts of the onset f-I curve are seen in response to adapting inputs, adaptation should be modeled with adaptation currents and not with a dynamic threshold. In contrast, when the slope of onset f-I curves depends on the adaptation state, then adaptation should be modeled with a dynamic threshold. Further, the observation of divisively altered onset f-I curves in adapted neurons with notable variability of their spike threshold could hint to yet known biophysical mechanisms directly affecting the threshold.
峰频率适应是神经元动力学的一个突出方面，它在从大约 10 毫秒到 >1 秒的时间尺度上塑造神经元的信号处理特性。对于积分和点火模型神经元，峰频率适应可以作为适应电流或动态点火阈值来实现。然而，生理上观察到的适应机制应该建模为适应电流还是动态阈值尚不清楚。在这里，我们表明，在增加的平均阈值水平（即适应状态）下，动态阈值对起始 f-I 曲线（输入电流阶跃增加后的初始最大点火率）具有除法效应，即适应状态。相比之下，适应电流没有改变其斜率，而是将此 f-I 曲线向更高的输入值偏移。因此，适应电流实质上是线性作用的，导致神经元对电流刺激的传递函数的高通滤波器分量。然而，对于动态阈值，由于对 f-I 曲线的乘法效应，传递函数强烈依赖于输入范围。具有适应电流的基于电导的点火模型（例如后超极化（AHP）型、M 型和钠激活钾电流）的模拟不会显示动态阈值的除法效应，但与具有适应电流的积分和点火神经元的特性一致。值得注意的是，钠电流的缓慢失活效应不能用这两种模型来复制。我们的结果表明，当响应适应输入时看到起始 f-I 曲线的横向移动时，应该使用适应电流而不是动态阈值来建模适应。相反，当起始 f-I 曲线的斜率取决于适应状态时，则应该使用动态阈值来建模适应。此外，在具有明显可变点火阈值的适应神经元中观察到的除法改变的起始 f-I 曲线可能暗示着直接影响阈值的未知生物物理机制。
