Droste Felix, Lindner Benjamin
Bernstein Center for Computational Neuroscience, Haus 2, Philippstrasse 13, 10115, Berlin, Germany.
Department of Physics, Humboldt Universität zu Berlin, Newtonstr 15, 12489, Berlin, Germany.
J Comput Neurosci. 2017 Aug;43(1):81-91. doi: 10.1007/s10827-017-0649-5. Epub 2017 Jun 6.
A neuron receives input from other neurons via electrical pulses, so-called spikes. The pulse-like nature of the input is frequently neglected in analytical studies; instead, the input is usually approximated to be Gaussian. Recent experimental studies have shown, however, that an assumption underlying this approximation is often not met: Individual presynaptic spikes can have a significant effect on a neuron's dynamics. It is thus desirable to explicitly account for the pulse-like nature of neural input, i.e. consider neurons driven by a shot noise - a long-standing problem that is mathematically challenging. In this work, we exploit the fact that excitatory shot noise with exponentially distributed weights can be obtained as a limit case of dichotomous noise, a Markovian two-state process. This allows us to obtain novel exact expressions for the stationary voltage density and the moments of the interspike-interval density of general integrate-and-fire neurons driven by such an input. For the special case of leaky integrate-and-fire neurons, we also give expressions for the power spectrum and the linear response to a signal. We verify and illustrate our expressions by comparison to simulations of leaky-, quadratic- and exponential integrate-and-fire neurons.
神经元通过电脉冲（即所谓的尖峰）接收来自其他神经元的输入。在分析研究中，输入的脉冲性质常常被忽视；相反，输入通常被近似为高斯分布。然而，最近的实验研究表明，这种近似所基于的假设往往不成立：单个突触前尖峰可能对神经元的动态产生显著影响。因此，明确考虑神经输入的脉冲性质是很有必要的，即考虑由散粒噪声驱动的神经元——这是一个长期存在且在数学上具有挑战性的问题。在这项工作中，我们利用这样一个事实：具有指数分布权重的兴奋性散粒噪声可以作为二分噪声（一种马尔可夫二态过程）的极限情况得到。这使我们能够得到由这种输入驱动的一般积分发放神经元的平稳电压密度和峰峰间隔密度矩的新的精确表达式。对于漏电积分发放神经元的特殊情况，我们还给出了功率谱和对信号的线性响应的表达式。我们通过与漏电、二次和指数积分发放神经元的模拟结果进行比较，来验证和说明我们的表达式。
