CDF Lecture Notes on Membrane Excitability

Published: 25-09-2018| Version 1 | DOI: 10.17632/2kn5ymgwvg.1
Shimon Marom


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


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