A stochastic differential formulation for the collective dynamics of ion channel clusters in excitable membranes is developed from the so-called “reduced strong diffusion formulation”. In this error bound optimizing reduced formulation, the potassium channel states n4 and n3, and, the sodium channel states m3h1 and m2h1 are the retained states; consequently, the formulation accommodates only four channel variables and five white noises. The accuracy of the formulation is tested over the standard deviations and autocorrelation times of the channel density fluctuations. The findings are seen to be virtually identical to the corresponding results from the exact microscopic Markov simulations. The formulation arises as the most accurate model with that structural simplicity, thus making it an important model for both analytic analyses and numerical simulations in the study of finite-sized membranes.

中文翻译：

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在误差界几乎没有增加的情况下减少离子通道簇的扩散方程

可激发膜中离子通道簇集体动力学的随机微分公式是从所谓的“减少的强扩散公式”发展而来的。在这个优化简化公式的误差界中，钾通道状态n4和n3, 和, 钠通道状态米3H1和米2H1是保留状态；因此，该公式仅包含四个通道变量和五个白噪声。公式的准确性在通道密度波动的标准偏差和自相关时间上进行测试。这些发现与精确的微观马尔可夫模拟的相应结果几乎相同。该公式是结构简单的最精确模型，因此使其成为有限尺寸膜研究中分析分析和数值模拟的重要模型。