Interdisciplinary Applied Mathematics

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FIGURE 13.10. An ion entering the selectivity filter of the potassium channel embedded in a lipid bilayer.

13.2.3 Transport Through Unmodified Nanotubes

Quantitative information on fundamental modes of water transport and transport rates have been obtained through carbon nanotubes of diameters of about 150 nm (Sun and Crooks, 2000). As mentioned earlier, in Chapter 11, (Hummer et al., 2001) showed by molecular dynamics simulations that water molecules enter nanotubes of as small as 8.4 A diameter even though carbon is hydrophobic. (Miller and Martin, 2002) showed experimentally that it is possible to control the rate and direction of electroosmotic flow through nanotube membranes of large diameters (120 nm). The behavior of water molecules and ions through hydrophobic carbon nanotubes is of critical importance because ion channels such as K+ channels have their selectivity filter lined with hydrophobic residues that facilitate transmembrane movement of ions and water without sticking to the side wall. However, transport of ions in these channels is stabilized by polar interactions with surrounding proteins, which is a feature that the nanotube lacks. Therefore, fundamental questions have to be answered regarding transport of ions in an electrolytic solution through nanotubes, and in this section we summarize some results.

We have performed MD simulations using a system consisting of the carbon nanotube, water, and ions using GROMACS (Lindahl et al., 2001) at a constant pressure of 1 bar and a constant temperature of 300 K. In some examples discussed below, a slab and functional (charge) groups are also used. The slab consisted of neutral atoms that mimic the interior of a hydrophobic phospholipid bilayer. The box size varied from 33 A to 75 A depending on the length and diameter of the tube and was at least twice as long as the tube length. The tube was fixed at the center of the box when there was no slab, but had limited freedom of motion when inserted into a slab that was held stationary. Periodic boundary conditions were applied in all three directions. The parameters for Lennard-Jones potentials and bonded interaction were taken from a GROMACS force field with a carbon-carbon bond length of 1.42 A. Values for the Lennard-Jones interaction parameters for the nanotube (C), and water oxygen (O) were:

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