Abstract: 

Biology occurs in ionic solutions that are plasmas in both the physical and biological meanings of the word. Ion channels are proteins with a hole down their middle that conduct ions (spherical charges like sodium potassium, chloride, and calcium ions with different diameters ~ 0.2 nm) through a narrow tunnel of fixed charge (‘doping’) with diameter ~ 0.6 nm. Ionic channels control the movement of electric charge and current across biological membranes and so play a role in biology as significant as the role of transistors in computers: almost every process in biology is controlled by channels, one way or the other. 

Ionic channels are manipulated with the powerful techniques of molecular biology in hundreds of laboratories. Atoms (and thus charges) can be substituted a few at a time and the location of every atom can be determined in favorable cases. Ionic channels are one of the few living systems of great importance whose natural biological function can be well described by a tractable set of physically based equations. 

Ion channels can be studied by equations resembling the Poisson Drift Diffusion equations familiar in semiconductor physics — called Poisson Nernst Planck or PNP in biology, but ions and water in biology have diameters that matter, unlike the pseudo ions (holes and ‘electrons’) of semiconductor physics. Jinn-Liang Liu (Hsinchu Taiwan) and collaborators have developed a version of PNP that includes the most important consequence of diameter, namely saturation of concentration with what seems a rigorous treatment of the entropy of a mixture of water molecules and ions of different size. This is a molecular mean field theory that includes the correlations produced by finite diameter of water and ions in the mean field. A fourth order partial differential equation (pde) is used to combine second order pde’s in the near and far electric fields, and the results fit ionic properties at metal solution interfaces, in bulk solution, in ion channels–gramicidin, potassium, calcium and potassium channels–and the sodium/calcium transporter, in solutions with a range of compositions and concentrations, using only a handful of parameters. 

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