Mathematical Sciences: Theories of the Open Channel

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Eisenberg 9514145 The investigator and his colleagues study the behavior of open channels in membranes, combining experiments and mathematical modeling. The starting place for a theory of open channels is a theory of electrodiffusion. It has long been known that a theory should include the phenomena of shielding or screening, whereby the ions in the ionic atmosphere in and around the channel protein help determine the potential profile of its pore, but mathematical difficulties were severe, and analysis was usually focused on the ionic atmosphere at the surface of the membrane or end of the channel and not the co- and counter-ions within the channel's pore. These difficulties have recently been overcome. The project develops PNP theory to predict the current through the channel, given its structure and distribution of fixed (i.e., permanent) charge. The project uses Poisson's equation to describe how charge on ions and the channel protein determines the electric field; and the Nernst-Planck equations to describe migration and diffusion of ions in gradients of potential and concentration. The study of open channels is an important component of biotechnology because channels have great biological importance in their role as gatekeepers to cells: they are responsible for signaling in the nervous system; they coordinate the contraction of the heart, so it can act as a pump; in general, they are receptors or effectors for many drugs and natural substances that control the life of cells. Channels are wonderful objects to study by high speed computing because they use such simple physics (diffusion) to perform important biological function. The computation of diffusion is much simpler than the computation of the quantum mechanics involved in so many enzymatic functions. Channels are also natural nanotubes and so are of importance in the emerging area of nanostructures, materials and manufacturing. Porin is particularly well suited in this regard since it is available in large quantities, it can be easily modified by the methods of biotechnology, and its structure is known in atomic detail.