Institute for Neural Computation, University of California-San Diego, La Jolla, CA 92093, U.S.A.
Neural Comput. 2011 Dec;23(12):3094-124. doi: 10.1162/NECO_a_00209. Epub 2011 Sep 15.
Using the Morris-Lecar model neuron with a type II parameter set and K(+)-channel noise, we investigate the interspike interval distribution as increasing levels of applied current drive the model through a subcritical Hopf bifurcation. Our goal is to provide a quantitative description of the distributions associated with spiking as a function of applied current. The model generates bursty spiking behavior with sequences of random numbers of spikes (bursts) separated by interburst intervals of random length. This kind of spiking behavior is found in many places in the nervous system, most notably, perhaps, in stuttering inhibitory interneurons in cortex. Here we show several practical and inviting aspects of this model, combining analysis of the stochastic dynamics of the model with estimation based on simulations. We show that the parameter of the exponential tail of the interspike interval distribution is in fact continuous over the entire range of plausible applied current, regardless of the bifurcations in the phase portrait of the model. Further, we show that the spike sequence length, apparently studied for the first time here, has a geometric distribution whose associated parameter is continuous as a function of applied current over the entire input range. Hence, this model is applicable over a much wider range of applied current than has been thought.
使用具有 II 型参数集的 Morris-Lecar 模型神经元和 K(+)通道噪声，我们研究了尖峰间隔分布，因为施加的电流驱动模型通过亚临界 Hopf 分岔。我们的目标是提供与作为施加电流函数的尖峰相关的分布的定量描述。该模型产生突发的尖峰行为，其尖峰序列由随机数量的尖峰（爆发）组成，爆发之间的间隔长度随机。这种尖峰行为在神经系统的许多地方都有发现，也许在皮质中的口吃抑制性中间神经元中最为明显。在这里，我们展示了该模型的几个实际和诱人的方面，将模型的随机动力学分析与基于模拟的估计相结合。我们表明，尖峰间隔分布的指数尾部参数实际上在整个可能的施加电流范围内是连续的，无论模型的相图中的分岔如何。此外，我们表明，尖峰序列长度（显然是首次在这里研究）具有几何分布，其相关参数作为施加电流的函数在整个输入范围内是连续的。因此，与以前的想法相比，该模型适用于更广泛的施加电流范围。
