Ion Channels, the Ultimate Multiscale Device

Prof. Bob Eisenberg
Professor of Biomathematics and Physiology
Department of Physiology & Biophysics, Rush University, Chicago IL

Proteins called ion channels are the ultimate multiscale device, the ‘nanovalves of life’ controlling most biological functions the way transistors control computers. A handful of atoms control biological function on the macroscale, so analysis must link atomic distances of 10-10m with biological distances of 1 meter. Channels are of such biological and medical importance that hundreds of scientists study them every day and thousands of talks on channels are given at (for example) the annual meeting of the Biophysical Society (USA). Channels conduct ions (spherical charges like Na+ , K+ , Ca2+ , and Cl- with diameter ~ 0.2 nm) through a narrow tunnel of permanent charge (‘doping’) with diameter ~ 0.6 nm. Channels can be studied in the tradition of physical science. PNP equations familiar in physics form an adequate initial model of current voltage relations in many types of channels under many conditions, and can be extended to describe ‘chemical’ phenomena like selectivity with some success. Variational models and methods are needed to deal with the coupling of different fields. Ionic channels are studied with the powerful techniques of molecular biology. Atoms (and thus charges) can be substituted a few at a time and the location of every atom can be determined in favorable cases. Ion channels are one of the few living systems of great importance where natural biological function can be well described by a tractable set of equations. Mathematics and mathematicians are needed to apply these equations to the hundreds of channels of biological and clinical significance.