Control of the Selectivity of the Aquaporin Water Channel Family by Global Orientational Tuning Emad Tajkhorshid, Peter Nollert, Morten Ø. Jensen, Larry J. W. Miercke, Joseph O'Connell, Robert M. Stroud, and Klaus Schulten

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Supplemental Figure 2. Integrity of the single file of water in GlpF-G, analyzed in terms of disruption frequency and average O-O distance of neighboring water molecules in the 20 Å long constriction region of the channel. The data is accumulated over the 4 ns of MD simulation. The single file is predominantly maintained during the simulations. The average O-O distances and disruption frequencies (defined as the ratio of O-O distances larger than 3.75 Å to the total number of water pairs centered at a certain z coordinate along the channel axis) are hardly above 3.5 Å and 30%, respectively.

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Supplemental Figure 3. Correlated movement of water in GlpF. Top: pair correlation between neighboring water molecules in the constriction region of the channel. Correlation is mainlly above 0.50; no anti-correlation was observed. Bottom: typical displacement trace of the water molecules in the constriction region.

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Supplemental Figure 4. One-dimensional diffusion of water along the channel axis (z) in GlpF-G. The self-diffusion was determined from the mean square displacement [{z(t)²}] of the water molecules present in the 20 Å long constriction region of GlpF.

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To improve statistics, the {z(t)²} for time interval t was calculated by averaging over multiple time origins t₀ :

where S is the number of time origins (20 in our calculations), the first being at 200 ps and consecutive origins separated by 20 ps; N(t₀ ,t) is the number of water molecules that stay in the constriction region of the channel between t₀ and t₀+ t; z_i is the z component of the center of mass of the ith water molecule. Data from all four monomers were accumulated. Linear regression from an arbitrary onset of the diffusive regime leads to an effective diffusion constant D of 0.46 ( 10^-5 cm² s^-1 for water in GlpF-G, [the diffusion constant of the TIP3P water in bulk at room temperature is about 5.2 ( 10^-5 cm² s^-1 (1, 2)].

One can deduce a mean first passage time, , from the expression = (a-b)²/2D, where (a-b) is the length of the constriction region of the channel (3). Using the obtained value for D and a-b~20 Å yields = 4.35 ns. Realizing that 8 water molecules reside in the 20 Å constriction region of the channel, the calculated diffusion constant corresponds to a flux of 1.8 ( 10⁹ s^-1. The difference to the simulated value (1.1 × 10⁹ s^-1) may be due to rate limiting steps, such as the entrance of water into the channel, which cannot be included in the calculation of a one-dimensional diffusion constant.

1. D. van der Spoel, P. J. van Maaren, H. J. C. Berendsen, J. Chem. Phys. 108, 10220 (1998).
2. M. W. Mahoney, W. L. Jorgensen, J. Chem. Phys. 114, 363 (2001).
3. A. Szabo, K. Schulten, Z. Schulten, J. Chem. Phys. 72, 4350 (1980).

Supplemental Figure 5. Fluctuations of the calculated order parameter [P₁(z), for description see Fig. 2] representing the orientation of water molecules in the two halves of the channel and in the bulk. Data is averaged over the trajectory of the 4 ns MD simulation. On the two sides of the NPA region, water molecules are restricted to orientations in which hydrogen atoms are located toward the exits. This indicates the persistence of the bipolar distribution of water molecules inside the channel and a low probability of changing the orientation of water molecules in the channel.

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