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. 2013 Oct 8;110(41):16367-72.
doi: 10.1073/pnas.1306447110. Epub 2013 Sep 25.

Optimizing water permeability through the hourglass shape of aquaporins

Simon Gravelle  1 , Laurent Joly, François Detcheverry, Christophe Ybert, Cécile Cottin-Bizonne, Lydéric Bocquet
Affiliations

Optimizing water permeability through the hourglass shape of aquaporins

Simon Gravelle et al. Proc Natl Acad Sci U S A. .

Abstract

The ubiquitous aquaporin channels are able to conduct water across cell membranes, combining the seemingly antagonist functions of a very high selectivity with a remarkable permeability. Whereas molecular details are obvious keys to perform these tasks, the overall efficiency of transport in such nanopores is also strongly limited by viscous dissipation arising at the connection between the nanoconstriction and the nearby bulk reservoirs. In this contribution, we focus on these so-called entrance effects and specifically examine whether the characteristic hourglass shape of aquaporins may arise from a geometrical optimum for such hydrodynamic dissipation. Using a combination of finite-element calculations and analytical modeling, we show that conical entrances with suitable opening angle can indeed provide a large increase of the overall channel permeability. Moreover, the optimal opening angles that maximize the permeability are found to compare well with the angles measured in a large variety of aquaporins. This suggests that the hourglass shape of aquaporins could be the result of a natural selection process toward optimal hydrodynamic transport. Finally, in a biomimetic perspective, these results provide guidelines to design artificial nanopores with optimal performances.

Keywords: biochannels; hydrodynamic permeability; nanofluidics.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
(A) Molecular structure of human aquaporin 4 (hAQP4) obtained from the Protein Data Bank (28). (B) Profiles of two aquaporins collected from ref. . Pore dimensions were estimated using the HOLE program (29). (C) Biconical channel considered in this work. The central cylinder, where perfect slip is assumed, is connected to two truncated cones of length L, opening angle α, and with perfect or finite slip (slip length b; see text). (D) Schematic of the system used for the FE resolution of the Stokes equation (COMSOL). The channel is connected to half-spherical reservoirs (not to scale). Color represents the magnitude of fluid velocity, from blue (slow flow) to red (fast flow).
Fig. 2.
Fig. 2.
Hydrodynamic permeability K = Q/Δp of the hourglass nanochannel as a function of the opening angle α, obtained from FE calculations. K is normalized by K0 = K(α = 0). Perfect slip (b = ∞) is assumed on the cones’ inner walls. Each curve corresponds to a cone length L.
Fig. 3.
Fig. 3.
Local viscous dissipation rate D (see text) inside the nanochannel for different values of the angle α. The color scale, from blue to red, indicates increasing values of local viscous dissipation. Perfect-slip BC is imposed on the cone walls. From A to D, α = 0, 5, 10, and 25°.
Fig. 4.
Fig. 4.
(A) formula image (see text) as a function of the pore length h for a perfectly slipping cylindrical channel, obtained with FE calculations (points). The red line is a guide for the eyes. (Inset) Velocity field in the considered channel. Color represents the amplitude of the fluid velocity, from blue (slow flow) to red (fast flow). (B and C) Schematic profiles of axial velocity in a channel with no slip (NS) and perfect-slip (PS) BC. From left to right: outside far field, entry profile and inside far field.
Fig. 5.
Fig. 5.
Pore resistance R versus cone angle α for perfect slip in the cones: comparison between FE calculations (symbols) and Eq. 6 (lines). Results are presented for two pore lengths: L/a = 20 (circles and dashed line) and L/a = 5 (squares and solid line). (Inset) Optimal angle αopt, for which the resistance is minimized, as a function of cone length.
Fig. 6.
Fig. 6.
Pore resistance R versus opening angle α, for various slip lengths b in the conical regions: comparison between FE calculations (symbols) and analytical expression (lines); see text for detail. The cone length is fixed to L/a = 20.
Fig. 7.
Fig. 7.
(A) Optimal angle as a function of cone length L for various slip lengths (from top to bottom, b/a = 1, 2, 5, 10, 20): FE results (circles) and model (lines). (B) Angle α evaluated in six aquaporins (Materials and Methods). The gray shaded area corresponds to model predictions for b/a = 1–5. Data are extracted from refs. and –.
Fig. 8.
Fig. 8.
(A) Schematic of the system used to compute the cone-to-cylinder hydrodynamic resistance. (B) Cone-to-cylinder resistance Rent,cyl versus cone angle α: FE calculations (circles) and analytical approximation by a sine function (dotted line).
Fig. 9.
Fig. 9.
Profile of an aquaporin (hAQP4, ref. , dotted line) and linear curve fitting (solid lines).
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