Department of Brain and Cognitive Sciences, University of Rochester, Rochester, New York, 14627, USA.
Neural Comput. 2010 Jun;22(6):1528-72. doi: 10.1162/neco.2010.06-09-1036.
Delivery of neurotransmitter produces on a synapse a current that flows through the membrane and gets transmitted into the soma of the neuron, where it is integrated. The decay time of the current depends on the synaptic receptor's type and ranges from a few (e.g., AMPA receptors) to a few hundred milliseconds (e.g., NMDA receptors). The role of the variety of synaptic timescales, several of them coexisting in the same neuron, is at present not understood. A prime question to answer is which is the effect of temporal filtering at different timescales of the incoming spike trains on the neuron's response. Here, based on our previous work on linear synaptic filtering, we build a general theory for the stationary firing response of integrate-and-fire (IF) neurons receiving stochastic inputs filtered by one, two, or multiple synaptic channels, each characterized by an arbitrary timescale. The formalism applies to arbitrary IF model neurons and arbitrary forms of input noise (i.e., not required to be gaussian or to have small amplitude), as well as to any form of synaptic filtering (linear or nonlinear). The theory determines with exact analytical expressions the firing rate of an IF neuron for long synaptic time constants using the adiabatic approach. The correlated spiking (cross-correlations function) of two neurons receiving common as well as independent sources of noise is also described. The theory is illustrated using leaky, quadratic, and noise-thresholded IF neurons. Although the adiabatic approach is exact when at least one of the synaptic timescales is long, it provides a good prediction of the firing rate even when the timescales of the synapses are comparable to that of the leak of the neuron; it is not required that the synaptic time constants are longer than the mean interspike intervals or that the noise has small variance. The distribution of the potential for general IF neurons is also characterized. Our results provide powerful analytical tools that can allow a quantitative description of the dynamics of neuronal networks with realistic synaptic dynamics.
神经递质的传递在突触处产生电流，该电流流经细胞膜并传入神经元的胞体，在那里被整合。电流的衰减时间取决于突触受体的类型，范围从几个毫秒（例如 AMPA 受体）到几百个毫秒（例如 NMDA 受体）。目前尚不清楚各种突触时程的作用，其中一些同时存在于同一个神经元中。一个首要的问题是，输入尖峰列车在不同时间尺度上的时间滤波对神经元反应的影响是什么。在这里，基于我们之前关于线性突触滤波的工作，我们为接收由一个、两个或多个突触通道过滤的随机输入的积分和点火（IF）神经元的稳态点火响应构建了一个通用理论，每个通道都具有任意的时间尺度。该形式适用于任意 IF 模型神经元和任意形式的输入噪声（即不需要是高斯噪声或具有小幅度），以及任意形式的突触滤波（线性或非线性）。该理论使用绝热方法，用精确的解析表达式确定 IF 神经元在长突触时间常数下的点火率。还描述了接收共同和独立噪声源的两个神经元的相关尖峰（互相关函数）。使用泄漏、二次和噪声阈值 IF 神经元来说明该理论。尽管当至少一个突触时间常数较长时，绝热方法是精确的，但即使当突触的时间常数与神经元的泄漏时间相当，它也能很好地预测点火率；不需要突触时间常数长于平均尖峰间隔或噪声具有小方差。还对一般 IF 神经元的势分布进行了特征描述。我们的结果提供了强大的分析工具，可以对具有现实突触动力学的神经元网络的动力学进行定量描述。
