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. 2009 Feb;96(3):925-38.
doi: 10.1016/j.bpj.2008.09.059.

Determinants of water permeability through nanoscopic hydrophilic channels

Guillem Portella  1 , Bert L de Groot
Affiliations

Determinants of water permeability through nanoscopic hydrophilic channels

Guillem Portella et al. Biophys J. 2009 Feb.

Abstract

Naturally occurring pores show a variety of polarities and sizes that are presumably directly linked to their biological function. Many biological channels are selective toward permeants similar or smaller in size than water molecules, and therefore their pores operate in the regime of single-file water pores. Intrinsic factors affecting water permeability through such pores include the channel-membrane match, the structural stability of the channel, the channel geometry and channel-water affinity. We present an extensive molecular dynamics study on the role of the channel geometry and polarity on the water osmotic and diffusive permeability coefficients. We show that the polarity of the naturally occurring peptidic channels is close to optimal for water permeation, and that the water mobility for a wide range of channel polarities is essentially length independent. By systematically varying the geometry and polarity of model hydrophilic pores, based on the fold of gramicidin A, the water density, occupancy, and permeability are studied. Our focus is on the characterization of the transition between different permeation regimes in terms of the structure of water in the pores, the average pore occupancy and the dynamics of the permeating water molecules. We show that a general relationship between osmotic and diffusive water permeability coefficients in the single-file regime accounts for the time averaged pore occupancy, and that the dynamics of the permeating water molecules through narrow non single file channels effectively behaves like independent single-file columns.

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Figures

Figure 1
Figure 1
Top (a) and side view (a′) of the polyalanine channel p-23. The positions and alignment of the carbonyl groups is indicated by spheres (carbon atoms, green; oxygen, red). (b) Sketch of a typical simulation box, a system used to study the effect of the radius and polarity is shown. The octane molecules are drawn as sticks and the octane-like atoms connected to the pore as balls. The pore is drawn as balls. (c) Top and side view of three designed channels of different radius (from top to bottom: 0.16 nm, 0.30 nm, and 0.55 nm) and length (1.8 nm).
Figure 2
Figure 2
Normalized average water occupancy for a series of polyalanine pores as function of the dipole moment of the peptide backbone carbonyl groups. The light gray area indicates the occupancy/dipole moment in the unaltered OPLS-AA force-field. The dashed line indicates the fit to Eq. 2. A quadratic expression for the free energy was employed for the fit to the whole set of data points.
Figure 3
Figure 3
Probability distribution of the number of water molecules inside the p-27 peptidic pore for different dipole moments of peptide backbone carbonyl groups.
Figure 4
Figure 4
(a and b) Pore water occupancy as a function of the pore radius for different pore polarities. For direct comparison, the water occupancies at each radius were divided by the pore length. The horizontal dashed lines indicate multiples of 3.63 water molecules per nm, the pore occupancy for a perfectly packed single-file. The inset is a detailed view of the occupancies at small pore radius. Several representative snapshots of the water structure inside the channel are drawn, beyond the single file regime both top and side views are displayed. (c) Pore water density at different pore radius and pore polarities. The dark gray area indicates a radius smaller than the typical water molecule radius (∼0.137 nm), and the light gray area displays the minimum in the water density profile that correlates with the transition from/to the single-file regime. The vertical dashed lines mark the radii corresponding to an integer number of water molecules.
Figure 5
Figure 5
(a) Normalized radial probability density for channels of given pore radius (∼0.18 nm) at different pore polarities. As the polarity of the pore increases the maximum of the probability density is shifted toward the wall of the pore. (b) Radial distribution function g(d) (RDF) for water molecules inside the pore as a function of the effective pore radius at three different pore polarities (ch-030, ch-045, and ch-060). The red curves show the radius corresponding to the highest water density. The green, blue, and magenta curves illustrate the transition from single-file to non single-file. The starred radius indicates the radius at which the transition occurs. The solid black curve indicates the RDF at the largest pore radius studied, which has the characteristic extrema pattern of bulk water (solid curve). (c) Illustration of the transition from the single-file regime (upper channel, R = 0.23 nm) toward a double-file (lower channel, R = 0.27 nm) for the ch-045 pore polarity.
Figure 6
Figure 6
Osmotic, pf, and diffusive, pd, permeability coefficients as a function of the dipole moment of the peptide backbone carbonyl group for the three channels studied, averaged over two independent simulations for each polarity. The fitted averaged occupancy 〈θ〉 at each polarity is displayed as a continuous line. The light gray area indicates the polarity at which the permeability is the highest, correlated with intermediate backbone polarity and medium water occupancies. The dark gray indicates the dipole corresponding to the OPLS charges.
Figure 7
Figure 7
(a and b) Osmotic (upper left panel) and diffusive (lower left panel) permeability coefficients for different pore polarities as a function of the pore radius. (a′ and b′) Osmotic (upper right panel) and diffusive (lower right panel) permeability coefficients as a function of the pore water occupancy (divided by the length of the pore). The insets are detailed views of the permeability coefficients at small pore radii. The dark gray area indicates a radius smaller than the water molecule radius, and the light gray area is positioned at the transition from/to the single-file regime. The vertical dashed lines indicate radii corresponding to multiples of a water molecule radius for a and b, and multiples of 3.63 water molecules per nm in a′ and b′. Error bars are not drawn for clarity, the uncertainty is <10% of the permeability coefficient reported.
Figure 8
Figure 8
The ratio of osmotic and diffusive permeation coefficients for the set pf/pd, is linearly proportional to the averaged water occupancy in the single-file peptidic pores for any peptide backbone polarity.
Figure 9
Figure 9
(a) Ratio of osmotic permeability coefficients, pf/pd (solid lines), and averaged pore water occupancy plus one (dashed lines) as function of pore radius. Both dependent variables were normalized by the length of the pore. The inset (a′) focuses on the range of radii smaller than the diameter of a water molecule. The dark gray area indicates radius smaller the radius of a water molecules, and the light gray area indicates the transition involving the single-file regime. (b) Ratio of (〈n〉 + 1) to (pf/pd) as function of the radius. (c) Correlation between (〈n〉 + 1)/(pf/pd) and (〈n〉/L)dww, where dww is the typical water-water distance, established to 0.275 nm. Disregarding the radius where the pore presents a local minimum in the water density and radii >0.45 nm, the ratio of occupancies and permeability coefficients correctly identifies the transitions between different file regimes. The solid line indicates (〈n〉/L)dww = (〈n〉 + 1)/(pf/pd).
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