Schwalger Tilo, Droste Felix, Lindner Benjamin
Brain Mind Institute, École Polytechnique Féderale de Lausanne (EPFL) Station 15, CH-1015, Lausanne, Switzerland,
J Comput Neurosci. 2015 Aug;39(1):29-51. doi: 10.1007/s10827-015-0560-x. Epub 2015 May 5.
Nerve cells in the brain generate sequences of action potentials with a complex statistics. Theoretical attempts to understand this statistics were largely limited to the case of a temporally uncorrelated input (Poissonian shot noise) from the neurons in the surrounding network. However, the stimulation from thousands of other neurons has various sorts of temporal structure. Firstly, input spike trains are temporally correlated because their firing rates can carry complex signals and because of cell-intrinsic properties like neural refractoriness, bursting, or adaptation. Secondly, at the connections between neurons, the synapses, usage-dependent changes in the synaptic weight (short-term plasticity) further shape the correlation structure of the effective input to the cell. From the theoretical side, it is poorly understood how these correlated stimuli, so-called colored noise, affect the spike train statistics. In particular, no standard method exists to solve the associated first-passage-time problem for the interspike-interval statistics with an arbitrarily colored noise. Assuming that input fluctuations are weaker than the mean neuronal drive, we derive simple formulas for the essential interspike-interval statistics for a canonical model of a tonically firing neuron subjected to arbitrarily correlated input from the network. We verify our theory by numerical simulations for three paradigmatic situations that lead to input correlations: (i) rate-coded naturalistic stimuli in presynaptic spike trains; (ii) presynaptic refractoriness or bursting; (iii) synaptic short-term plasticity. In all cases, we find severe effects on interval statistics. Our results provide a framework for the interpretation of firing statistics measured in vivo in the brain.
大脑中的神经细胞会产生具有复杂统计特性的动作电位序列。从理论上理解这种统计特性的尝试主要局限于来自周围神经网络中神经元的时间上不相关输入（泊松散粒噪声）的情况。然而，来自数千个其他神经元的刺激具有各种时间结构。首先，输入的脉冲序列在时间上是相关的，这是因为它们的发放率可以携带复杂信号，还因为诸如神经不应期、爆发或适应性等细胞内在特性。其次，在神经元之间的连接部位，即突触处，突触权重的使用依赖性变化（短期可塑性）进一步塑造了细胞有效输入的相关结构。从理论角度来看，人们对这些相关刺激（即所谓的有色噪声）如何影响脉冲序列统计特性了解甚少。特别是，不存在解决具有任意有色噪声的脉冲间隔统计相关的首次通过时间问题的标准方法。假设输入波动比平均神经元驱动弱，我们推导出了一个简单公式，用于计算一个受到来自网络任意相关输入的持续发放神经元的典型模型的基本脉冲间隔统计特性。我们通过对导致输入相关性的三种典型情况进行数值模拟来验证我们的理论：（i）突触前脉冲序列中的速率编码自然刺激；（ii）突触前不应期或爆发；（iii）突触短期可塑性。在所有情况下，我们都发现对间隔统计有严重影响。我们的结果为解释在大脑中体内测量的发放统计特性提供了一个框架。
