Agüera y Arcas Blaise, Fairhall Adrienne L, Bialek William
Rare Books Library, Princeton University, Princeton, NJ 08544, USA.
Neural Comput. 2003 Aug;15(8):1715-49. doi: 10.1162/08997660360675017.
A spiking neuron "computes" by transforming a complex dynamical input into a train of action potentials, or spikes. The computation performed by the neuron can be formulated as dimensional reduction, or feature detection, followed by a nonlinear decision function over the low-dimensional space. Generalizations of the reverse correlation technique with white noise input provide a numerical strategy for extracting the relevant low-dimensional features from experimental data, and information theory can be used to evaluate the quality of the low-dimensional approximation. We apply these methods to analyze the simplest biophysically realistic model neuron, the Hodgkin-Huxley (HH) model, using this system to illustrate the general methodological issues. We focus on the features in the stimulus that trigger a spike, explicitly eliminating the effects of interactions between spikes. One can approximate this triggering "feature space" as a two-dimensional linear subspace in the high-dimensional space of input histories, capturing in this way a substantial fraction of the mutual information between inputs and spike time. We find that an even better approximation, however, is to describe the relevant subspace as two dimensional but curved; in this way, we can capture 90% of the mutual information even at high time resolution. Our analysis provides a new understanding of the computational properties of the HH model. While it is common to approximate neural behavior as "integrate and fire," the HH model is not an integrator nor is it well described by a single threshold.
一个脉冲神经元通过将复杂的动态输入转化为一系列动作电位或脉冲来进行“计算”。神经元执行的计算可被表述为降维或特征检测，随后是在低维空间上的非线性决策函数。对具有白噪声输入的反向相关技术的推广提供了一种从实验数据中提取相关低维特征的数值策略，并且信息论可用于评估低维近似的质量。我们应用这些方法来分析最简单的生物物理现实模型神经元——霍奇金 - 赫胥黎（HH）模型，用这个系统来说明一般的方法学问题。我们关注触发脉冲的刺激中的特征，明确消除脉冲之间相互作用的影响。在输入历史的高维空间中，可以将这个触发“特征空间”近似为一个二维线性子空间，以这种方式捕获输入与脉冲时间之间相当一部分的互信息。然而，我们发现更好的近似是将相关子空间描述为二维但弯曲的；通过这种方式，即使在高时间分辨率下，我们也能捕获90%的互信息。我们 的分析为HH模型的计算特性提供了新的理解。虽然将神经行为近似为“积分发放”很常见，但HH模型不是一个积分器，也不能用单个阈值很好地描述。
