Interdisciplinary Applied Mathematics

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Selectivity of ion channels: Ion channels are highly specific filters, allowing only desired ions to go through the cell membrane. They can discriminate between size and charge of the permeant molecule. For example, potassium channels are    selective    to    potassium    but    not    sodium    even    though    the    lat

ter is smaller in diameter. The potassium channel is shown in Figure 13.9. The KcsA K+ channel is composed of four subunits, each with two transmembrane helical domains and a pore region. Recent structural imaging studies by (Doyle et al., 1998) show this three-dimensional organization in detail and have helped in understanding better the mechanism of channel selectivity (see Figure 13.10).

Engineered ion channels have been developed to function as a singlemolecule detection system (Bayley and Cremer, 2001; Woodhouse et al., 1999). In an applied potential, an ionic current is carried by the ions that bathe both sides of the lipid bilayer. When the target molecule binds to the binding site in the pore, the current is modulated. The frequency of binding reveals the concentration of the analyte, and the duration and amplitude of the events reveal its identity. Though engineered channels have significant advantages including high sensitivity, wide dynamic range, and biocompatibility, their lack of durability makes them reliable only in a lab setting. The possibility of a nanoscale device that incorporates the functionality of ion channels into artificial nanotubes and is far less complex than a biological system has    also    been    investigated. A    review    of    the    literature    shows    that

promising options for such a device that can be practically realized include gold nanotubule membranes (Kang and Martin, 2001; Li et al., 2001), ion beam etched silicon nitride membranes (Martin et al., 2001), and single carbon nanotubes.

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