Lindner Benjamin, Longtin André, Bulsara Adi
Department of Physics, University of Ottawa, Ottawa, Canada KIN 6N5.
Neural Comput. 2003 Aug;15(8):1760-87. doi: 10.1162/08997660360675035.
We study the one-dimensional normal form of a saddle-node system under the influence of additive gaussian white noise and a static "bias current" input parameter, a model that can be looked upon as the simplest version of a type I neuron with stochastic input. This is in contrast with the numerous studies devoted to the noise-driven leaky integrate-and-fire neuron. We focus on the firing rate and coefficient of variation (CV) of the interspike interval density, for which scaling relations with respect to the input parameter and noise intensity are derived. Quadrature formulas for rate and CV are numerically evaluated and compared to numerical simulations of the system and to various approximation formulas obtained in different limiting cases of the model. We also show that caution must be used to extend these results to the Theta neuron model with multiplicative gaussian white noise. The correspondence between the first passage time statistics for the saddle-node model and the Theta neuron model is obtained only in the Stratonovich interpretation of the stochastic Theta neuron model, while previous results have focused only on the Ito interpretation. The correct Stratonovich interpretation yields CVs that are still relatively high, although smaller than in the Ito interpretation; it also produces certain qualitative differences, especially at larger noise intensities. Our analysis provides useful relations for assessing the distance to threshold and the level of synaptic noise in real type I neurons from their firing statistics. We also briefly discuss the effect of finite boundaries (finite values of threshold and reset) on the firing statistics.
我们研究了在加性高斯白噪声和静态“偏置电流”输入参数影响下鞍结系统的一维范式，该模型可视为具有随机输入的I型神经元的最简版本。这与众多关于噪声驱动的漏电积分发放神经元的研究形成对比。我们关注脉冲间隔密度的发放率和变异系数（CV），并推导了它们关于输入参数和噪声强度的标度关系。对发放率和CV的求积公式进行了数值评估，并与系统的数值模拟以及在模型不同极限情况下得到的各种近似公式进行了比较。我们还表明，将这些结果扩展到具有乘性高斯白噪声的Theta神经元模型时必须谨慎。鞍结模型和Theta神经元模型的首次通过时间统计之间的对应关系仅在随机Theta神经元模型的Stratonovich解释中得到，而先前的结果仅关注Ito解释。正确的Stratonovich解释产生的CV仍然相对较高，尽管比Ito解释中的小；它还产生了某些定性差异，尤其是在较大噪声强度时。我们的分析为从发放统计评估真实I型神经元到阈值的距离和突触噪声水平提供了有用的关系。我们还简要讨论了有限边界（阈值和重置的有限值）对发放统计的影响。
