Department of Computer Engineering, Eastern Mediterranean University, Famagusta, Via Mersin-10, Turkey.
Neural Comput. 2013 Jan;25(1):46-74. doi: 10.1162/NECO_a_00384. Epub 2012 Sep 28.
The excitability of cells is facilitated by voltage-gated ion channels. These channels accommodate a multiple number of gates individually. The possible impact of that gate multiplicity on the cell's function, specifically when the membrane area is of limited size, was investigated in the author's prior work (Güler, 2011 ). There, it was found that a nontrivially persistent correlation takes place between the transmembrane voltage fluctuations (also between the fluctuations in the gating variables) and the component of open channel fluctuations attributed to the gate multiplicity. This nontrivial phenomenon was found to be playing a major augmentative role for the elevation of excitability and spontaneous firing in small cells. In addition, the same phenomenon was found to be enhancing spike coherence significantly. Here we extend Fox and Lu's ( 1994 ) stochastic Hodgkin-Huxley equations by incorporating colored noise terms into the conductances there to obtain a formalism capable of capturing the addressed cross-correlations. Statistics of spike generation, spike coherence, firing efficiency, latency, and jitter from the articulated set of equations are found to be highly accurate in comparison with the corresponding statistics from the exact microscopic Markov simulations. This way, it is demonstrated vividly that our formulation overcomes the inherent inadequacy of the Fox and Lu equations. Finally, a recently proposed diffusion approximation method (Linaro, Storace, & Giugliano, 2011 ) is taken into consideration, and a discussion on its character is pursued.
细胞的兴奋性是由电压门控离子通道促进的。这些通道单独容纳多个门。作者之前的工作（Güler，2011）研究了这种门的多样性对细胞功能的可能影响，特别是当膜面积有限时。在那里，发现跨膜电压波动（以及门控变量之间的波动）与归因于门的多样性的开放通道波动的分量之间存在着非平凡的持久相关性。这种非平凡的现象被发现对小细胞兴奋性和自发放电的升高起着主要的增强作用。此外，还发现同样的现象显著增强了尖峰相干性。在这里，我们通过将有色噪声项纳入Fox 和 Lu（1994）的随机 Hodgkin-Huxley 方程的电导中，扩展了 Fox 和 Lu 的方程，以获得一种能够捕捉到所关注的交叉相关的形式。与从精确微观 Markov 模拟获得的相应统计数据相比，从所阐述的方程组中生成的尖峰、尖峰相干性、点火效率、潜伏期和抖动的统计数据非常准确。这样，生动地证明了我们的公式克服了 Fox 和 Lu 方程固有的不足。最后，考虑了最近提出的扩散逼近方法（Linaro、Storace 和 Giugliano，2011），并对其性质进行了探讨。
