Richardson Magnus J E, Gerstner Wulfram
Laboratory of Computational Neuroscience, I&C and Brain-Mind Institute, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne EPFL, Switzerland.
Neural Comput. 2005 Apr;17(4):923-47. doi: 10.1162/0899766053429444.
The subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductance-based synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.
处于活跃皮层组织中的神经元的阈下膜电压是一个波动量，其分布反映了突触前群体的放电统计特性。最近发现，基于电导的突触驱动可导致具有显著偏态的分布。本文证明，由泊松尖峰到达引起的潜在散粒噪声也会使膜分布产生偏态，但方向相反。我们使用一种微扰方法，分析散粒噪声对突触电导分布的影响，并计算由此产生的电压分布。在微扰理论的一阶近似下，电压分布是由一个捕捉偏态的前置因子调制的高斯分布。高斯分量与使用具有有效膜时间常数的基于电流的模型得出的分布相同。因此，著名的有效时间常数近似可以被视为完整的基于电导的模型的一阶解。包含偏态的高阶调制前置因子包括散粒噪声和电导波动产生的项。扩散近似忽略了这些散粒噪声效应，这意味着诸如福克 - 普朗克方程之类的解析方法或用滤波白噪声进行的模拟不能用于改进高斯近似。进一步证明，用于将理论与实验拟合的量，如电压均值和方差，对这些非高斯效应具有鲁棒性。因此，有效时间常数近似与实验相关，并提供了一个简单的解析基础，可以在此基础上添加其他相关的生物学细节。
