The transport of water and ions through membranes formed from carbon nanotubes ranging in diameter from 6 to 11 Å is studied using molecular dynamics simulations under hydrostatic pressure and equilibrium conditions. Membranes incorporating carbon nanotubes are found to be promising candidates for water desalination using reverse osmosis, and the size and uniformity of tubes that is required to achieve a desired salt rejection is determined. By calculating the potential of mean force for ion and water translocation, we show that ions face a large energy barrier and will not pass through the narrower tubes studied ((5,5) and (6,6) “armchair” type tubes) but can pass through the wider (7,7) and (8,8) nanotubes. Water, however, faces no such impediment due to the formation of stable hydrogen bonds and crosses all of the tubes studied at very large rates. By measuring this conduction rate under a hydrostatic pressure difference, we show that membranes incorporating carbon nanotubes can, in principle, achieve a high degree of desalination at flow rates far in excess of existing membranes.

We test the validity of the mean-field approximation in Poisson-Nernst-Planck theory by contrasting its predictions with those of Brownian dynamics simulations in schematic cylindrical channels and in a realistic potassium channel. Equivalence of the two theories in bulk situations is demonstrated in a control study. In simple cylindrical channels, considerable differences are found between the two theories with regard to the concentration profiles in the channel and its conductance properties. These differences are at a maximum in narrow channels with a radius smaller than the Debye length and diminish with increasing radius. Convergence occurs when the channel radius is over 2 Debye lengths. These tests unequivocally demonstrate that the mean-field approximation in the Poisson-Nernst-Planck theory breaks down in narrow ion channels that have radii smaller than the Debye length.

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The mechanisms underlying ion transport and selectivity in calcium channels are examined using electrostatic calculations and Brownian dynamics simulations. We model the channel as a rigid structure with fixed charges in the walls, representing glutamate residues thought to be responsible for ion selectivity. Potential energy profiles obtained from multi-ion electrostatic calculations provide insights into ion permeation and many other observed features of L-type calcium channels. These qualitative explanations are confirmed by the results of Brownian dynamics simulations, which closely reproduce several experimental observations. These include the current-voltage curves, current-concentration relationship, block of monovalent currents by divalent ions, the anomalous mole fraction effect between sodium and calcium ions, attenuation of calcium current by external sodium ions, and the effects of mutating glutamate residues in the amino acid sequence.

The rapid and selective transport of Na(+) through sodium channels is essential for initiating action potentials within excitable cells. However, an understanding of how these channels discriminate between different ion types and how ions permeate the pore has remained elusive. Using the recently published crystal structure of a prokaryotic sodium channel from Arcobacter butzleri, we are able to determine the steps involved in ion transport and to pinpoint the location and likely mechanism used to discriminate between Na(+) and K(+). Na(+) conduction is shown to involve the loosely coupled "knock-on" movement of two solvated ions. Selectivity arises due to the inability of K(+) to fit between a plane of glutamate residues with the preferred solvation geometry that involves water molecules bridging between the ion and carboxylate groups. These mechanisms are different to those described for K(+) channels, highlighting the importance of developing a separate mechanistic understanding of Na(+) and Ca(2+) channels.

The transport of hydrated ions through narrow pores is important for a number of processes such as the desalination and filtration of water and the conductance of ions through biological channels. Here, molecular dynamics simulations are used to systematically examine the transport of anionic drinking water contaminants (fluoride, chloride, nitrate, and nitrite) through pores ranging in effective radius from 2.8 to 6.5 Å to elucidate the role of hydration in excluding these species during nanofiltration. Bulk hydration properties (hydrated size and coordination number) are determined for comparison with the situations inside the pores. Free energy profiles for ion transport through the pores show energy barriers depend on pore size, ion type, and membrane surface charge and that the selectivity sequence can change depending on the pore size. Ion coordination numbers along the trajectory showed that partial dehydration of the transported ion is the main contribution to the energy barriers. Ion transport is greatly hindered when the effective pore radius is smaller than the hydrated radius, as the ion has to lose some associated water molecules to enter the pore. Small energy barriers are still observed when pore sizes are larger than the hydrated radius due to re-orientation of the hydration shell or the loss of more distant water. These results demonstrate the importance of ion dehydration in transport through narrow pores, which increases the current level of mechanistic understanding of membrane-based desalination and transport in biological channels.

We show that narrow hydrophobic pores have an intrinsic ion selectivity by using single-walled carbon nanotube membranes as a model. We examined pores of radius 3.4-6.1 A, and conducted molecular dynamics simulations to show that Na+, K+, and Cl- face different free energy barriers when entering hydrophobic pores. Most of the differences result from the different dehydration energies of the ions; however, changes in the solvation shell structure in the confined nanotube interior and van der Waals interactions in the small tubes can both play a role. Molecular dynamics simulations conducted under hydrostatic pressure show that carbon nanotube membranes can act as ion sieves, with the pore radius and pressure determining which ions will permeate through the membrane. This work suggests that the intrinsic ion selectivity of biological pores of differing radii might also play a role in determining their selectivity, in addition to the more common explanations based on electrostatic effects. In addition, "hydrophobic gating" can arise in continuous water-filled pores.

Potassium channels are exquisitely selective, allowing K+ to pass across cell membranes while blocking other ion types. Here we demonstrate that the number of carbonyl oxygen atoms that surround permeating ions is the most important factor in determining ion selectivity rather than the size of the pore or the strength of the coordinating dipoles. Although the electrostatic properties of the coordinating ligands can lead to Na+ or K+ selectivity at some values of the dipole moment, no significant selectivity arises at the specific value of the dipole moment for carbonyl groups found in potassium channels when the ligands have complete freedom. Rather, we show that the main contribution to selectivity arises from slight constraints on the conformational freedom of the channel protein that limit the number of carbonyl oxygen atoms to a value better suited to K+ than Na+, despite the pore being flexible. This mechanism provides an example of a general framework for explaining ion discrimination in a range of natural and synthetic macromolecules in which selectivity is controlled by the number of coordinating ligands in addition to their dipole moment.