CDF Lecture Notes on Membrane Excitability

These Mathematica® dynamic lecture notes (CDF, computational document format) focus on principles governing the generation of cellular electricity in general, and the "action potential", a pulse-like voltage wave across membranes of excitable cells (e.g. nervous system, muscles, heart, endocrine system), in particular. Cellular electrical phenomena are supported by ionic currents across membranes; so we start by describing the behaviour of ions in solution and ways by which ionic currents across membranes are realised. These include diffusion, osmosis-related ionic fluxes, and fluxes down electrochemical gradients. We then continue with dynamics of macroscopic and microscopic membrane ionic conductances and their relation to electricity. The lectures then focus on introduction to different classes of mathematical models that capture the phenomenon and mechanism of action potential generation at various timescales. A partial list of sources used: [1] B. Hille. Ion channels of excitable membranes. Sinauer, Sunderland, Mass., 3rd ed edition, 2001. [2] D. Murray. Mathematical Biology. Springer, Berlin, 1993. [3] J. J. B. Jack, D. Noble, and R. W. Tsien. Electric current flow in excitable cells. Oxford: Clarendon Press, 1975. [4] E. M. Izhikevich. Dynamical systems in neuroscience. MIT press, 2007. [5] B. Sakmann and E. Neher. Single-Channel Recording. Springer, 2009. [6] Various physiological and biophysical articles in professional journals

本套Mathematica®动态讲义采用计算文档格式（CDF，Computational Document Format），其核心内容围绕一般细胞电活动的产生原理展开，尤其聚焦于可兴奋细胞（excitable cells，如神经系统、肌肉、心脏、内分泌系统细胞）细胞膜上的脉冲样电压波——动作电位（action potential）的相关机制。细胞电现象的本质是跨膜离子电流（ionic currents across membranes），因此讲义首先讲解溶液中离子的行为，以及跨膜离子电流的实现方式，包括扩散、渗透相关的离子流，以及沿电化学梯度（electrochemical gradients）流动的离子流。随后讲义进一步讲解宏观与微观尺度下的细胞膜离子电导（ionic conductances）动力学，及其与电活动的关联。此后讲义将介绍不同类别、可在不同时间尺度上刻画动作电位产生现象与机制的数学模型。本次讲义引用的部分文献如下：
[1] B. Hille. 《可兴奋细胞膜离子通道》（Ion Channels of Excitable Membranes）. 马萨诸塞州森德兰：Sinauer出版社，第3版，2001年.
[2] D. Murray. 《数学生物学》（Mathematical Biology）. 柏林：施普林格出版社（Springer），1993年.
[3] J. J. B. Jack、D. Noble、R. W. Tsien. 《可兴奋细胞的电流流动》（Electric Current Flow in Excitable Cells）. 牛津：克拉伦登出版社（Clarendon Press），1975年.
[4] E. M. Izhikevich. 《神经科学中的动力学系统》（Dynamical Systems in Neuroscience）. MIT出版社（MIT Press），2007年.
[5] B. Sakmann、E. Neher. 《单通道记录》（Single-Channel Recording）. 施普林格出版社（Springer），2009年.
[6] 专业期刊刊载的各类生理学与生物物理学相关文章