Matthews Peter B C
University Laboratory of Physiology, Parks Road, Oxford OX1 3PT, UK.
J Physiol. 2002 Oct 1;544(Pt 1):315-32. doi: 10.1113/jphysiol.2002.024984.
A new measure of excitability of tonically firing neurones termed the 'estimated potential' (EP) was tested on a model motoneurone (MN) with a voltage-dependent threshold; the threshold followed the noisy membrane potential with an exponential delay. First, the model MN's after-hyperpolarisation (AHP) was deduced from its interval histogram for tonic firing, using a recently described transform. This provided a 'distance-to-threshold' measure which underestimated the AHP's absolute size but had the same time course, thereby providing the time constant of the AHP's decay of conductance. The 'estimated potential' was then obtained from the classical 'firing index' (no. of responses/no. of stimuli) by using the estimated AHP to create a fixed threshold 'daughter' model MN to mimic its variable threshold parent and reproduce its input-output non-linearities. The EP gave a linear measure of the parent's stimulus-evoked depolarisation for firing indices up to about 60 %, corresponding to depolarisations of three to four times the noise S.D. The EP was scaled in units of voltage whose absolute value will usually be unknown for real neurones, since it depended upon the details of the parent model. The EP's virtue is that, within its range, combining stimuli gives arithmetical addition and subtraction, thereby improving on the firing index which scales sigmoidally with the input. Moreover, with weak stimuli, the EP for a given input did not change on varying the parent model's firing rate. The estimated 'distance-to-threshold' AHP did not, however, give an accurate measure of the recovery of excitability following a spike during tonic firing. Excitability then depends upon the 'survivors' trajectory' giving the mean membrane potential, relative to threshold, of those intervals which have 'survived' up to the time in question rather than upon the AHP per se; the survivors' mean is more hyperpolarised because spiking preferentially eliminates trajectories with noise-induced depolarisation.
一种称为“估计电位”（EP）的新的紧张性放电神经元兴奋性测量方法，在具有电压依赖性阈值的运动神经元（MN）模型上进行了测试；阈值以指数延迟跟随有噪声的膜电位。首先，使用最近描述的变换，从模型MN的紧张性放电间隔直方图中推导出其超极化后电位（AHP）。这提供了一种“到阈值的距离”测量方法，该方法低估了AHP的绝对大小，但具有相同的时间进程，从而提供了AHP电导衰减的时间常数。然后，通过使用估计的AHP创建一个固定阈值的“子代”模型MN，以模仿其可变阈值的亲代并再现其输入-输出非线性，从经典的“放电指数”（反应数/刺激数）中获得“估计电位”。对于高达约60%的放电指数，EP给出了亲代刺激诱发去极化的线性测量，对应于噪声标准差三到四倍的去极化。EP以电压单位进行缩放，其绝对值对于真实神经元通常是未知的，因为它取决于亲代模型的细节。EP的优点是，在其范围内，组合刺激会进行算术加法和减法，从而改进了与输入呈S形缩放的放电指数。此外，对于弱刺激，给定输入的EP在改变亲代模型的放电率时不会改变。然而，估计的“到阈值的距离”AHP并没有给出紧张性放电期间一个尖峰后兴奋性恢复的准确测量。此时的兴奋性取决于“幸存者轨迹”，即给出相对于阈值的、那些“存活”到所讨论时间的间隔的平均膜电位，而不是取决于AHP本身；幸存者的平均值更超极化，因为尖峰优先消除了由噪声诱导去极化的轨迹。
