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Molecular Selectivity in Aquaporin Channels Studied by the 3D- RISM Theory Saree Phongphanphanee,† Norio Yoshida,†,‡ and Fumio Hirata*,†,‡ Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki, Japan, 444-8585, and Department of Functional Molecular Science, The Graduate UniVersity for AdVanced Studies, Okazaki, Japan, 444-8585 ReceiVed: March 3, 2010; ReVised Manuscript ReceiVed: April 15, 2010
The three-deimensional distribution functions (3D-DFs) and potentials of mean force (PMFs) of small neutral molecules inside the two aquaporin channels, AQP1 and GlpF, are calculated based on the 3D-RISM theory, the statistical mechanics theory of molecular liquids, in order to investigate the permeability of those ligands through the channels. The ligands investigated are neon (Ne), carbon dioxide (CO2), nitric oxide (NO), ammonia (NH3), urea, and glycerol. Neon shows continuous distribution throughout the channel pore in AQP1 as is the case of water, although the PMF of Ne at the selective filter (SF) region is higher than that of water, indicating that the stability of molecules in the channel is determined not only by their size, but also by the charge distribution. The ligand molecules, CO2, NO, urea, and glycerol, have a large barrier in PMF at the SF region in AQP1, indicating that the channel is not permeable by those ligands. On the other hand, NH3 has only a small activation barrier, ∼2.5 kJ/mol, to be overcome. Therefore, our theory predicts that a NH3 molecule can be permeated through the AQP1 channel. In GlpF, all the ligands have negative PMF throughout the channel pore except for glycerol, which has a small barrier at the SF area, ∼2.1 kJ/mol. The barrier can be readily overcome by the thermal motion. So, our results are quite consistent with the experiments for urea and glycerol, for which the corresponding data are available. The results obtained by the 3D-RISM theory show striking differences from those obtained by the MD simulations, especially in the case of GlpF. Possible causes of the difference in the results between the two methods are discussed. Introduction The cell membrane behaves as a barrier to prevent water or other molecules from moving into and out of the cell. This constrained movement of a molecule through the membrane plays an important role for a living cell. Many trans-membrane proteins have a function to select or regulate the conduction of molecules through the membrane. Aquaporins (AQPs), known as a water channel, are membrane proteins that facilitate the passive transportation of water through a cell membrane. While the channels have high permeability close to the diffusion limit for water, they do not permeate protons or other charged particles.1-3 In addition, several members in the AQP family can conduct glycerol and urea. Considering the permeability for different species, AQPs can be categorized into two subfamilies: aquaporin, the AQPs that selectively transport water, and aquaglyceroporin, AQPs that can transport both water and glycerol.3 The AQP in some cells, such as renal tubular cells and epitheliums, no doubt plays a role as a water transport channel. On the other hand, there are aquaporins which are widely expressed in many cells, such as AQP1 in red blood cells, but their function as a water channel does not seem to be important.3 Thus, those AQPs have been considered to have other functions than water transportation. Recently, it has been reported that some AQPs can permeate uncharged molecules other than water, glycerol, and urea: for example, CO2, NO, H2O2, NH3, and arsenate.4 However, these functions of AQPs are still controversial. For example, several experimental works * To whom correspondence should be addressed. E-mail: hirata@ ims.ac.jp. Phone: +81-564-55-7257. † Institute for Molecular Science. ‡ The Graduate University for Advanced Studies.
concerning gas permeation through AQP1 have indicated that AQP1 is playing a role in the transportation of CO2 and NH3.4-9 Nakhoul and co-workers measured the intracellular pH in the AQP1 expressed in Xenopus oocytes by microelectrode, and concluded that the flux of CO2 through the membrane is increased due to permeation through the AQP1.5 Using a different technique, measuring the exchange of 18O in the cell suspension of red blood cells and the alkaline surface pH on oocytes, Enderward et al. indicated a similar result that AQP1 is responsible for CO2 passing through the cell membrane.6 However, not all works support the role of AQP1 in transportation of CO2.9,10 The study on erythrocytes in intact lung of wild type and AQP1-knockout mice shows no significant differences in CO2 permeability.10 Similarly, the NH3 permeability of AQP1 is still unclear.11,12 The potentials of mean force (PMFs) of these gas solutes in AQPs have been examined by the molecular dynamic (MD) simulation. Hub and de Groot reported the PMFs of CO2 and NH3 in AQP1 and GlpF based on the umbrella sampling technique.13 They found that the height of the free energy barrier for permeation of CO2 in AQP1 is higher than that in the lipid bilayer membrane, whereas the height of the barrier peak of NH3 in AQP1 is rather similar to that in the bilayer membrane. From those results, they have concluded that the water pore of AQP1 is not permeable by both CO2 and NH3. By using different simulation methods, or pressure induced technique and implicit ligand sampling, Wang et al. also have come to a conclusion similar to that by Hub and de Groot: CO2 cannot be permeated through the water pore.14 They also suggested that the side pore located in between AQP1 monomers might conduct the gas across the membrane. In the case of GlpF, Hub and de Groot
10.1021/jp101936y 2010 American Chemical Society Published on Web 05/24/2010
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TABLE 1: Structure and Parameter of Solvent Molecules solvent water Ne CO2 NH3 NH4+ NO urea glycerol1 and glycerol2
parameter set 30
SPC OPLS31 EMP232 Gao et al.33 Jorgensen and Gao34 Zhou et al.35 OPLS with planar structure36 OPLS with the two lowest energy conformations37,38
reported the results from the MD simulation, which shows the high barrier in PMF for both molecules. In the present paper, we apply the 3D-RISM theory, the statistical mechanical integral equation theory of molecular liquids, to study the selectivity of AQPs for nonpolar molecules.15 The 3D-RISM theory enables the calculation of the three-dimensional distributions of water as well as other solute molecules around and inside a protein in solution, which is vital information for understanding the selective binding or “recognition” of ligands by the biomolecule. Thermodynamic properties such as the partial molar volume and the solvation free energy are also obtained from the distribution functions.16-25 The physical properties obtained from the equation meet the thermodynamic limit by definition, which is a distinct advantage over the molecular simulation. Recently, the 3D-RISM theory has been successfully applied to prove water molecules and ions bound inside a cavity of protein.16-18 In this work we perform the 3D-RISM calculation to examine the distribution of inert gas, Ne, and others gases, CO2, NO and NH3, urea, and glycerol inside the pore of AQP1 and GlpF. We have selected those molecules as typical ligands for aquaporin and aquaglyceroporin subfamilies. Method of Calculations To examine the ligand distribution around and inside AQPs channel, we consider an AQP channel as a solute, and a solution around and inside the channel as a solvent. The 3D-RISM theory is applied to the solute-solvent system at the limit of infinite dilution. Details of solving the 3D-RISM equation have been described elsewhere.15,16 Here, we just present a brief sketch of the 3D-RISM calculation. To obtain the distribution function of solvent around and inside the solute channel, we begin with the calculation of the site-site pair correlation functions of the solvent systems by solving the dielectrically consistent RISM (or DRISM) equation.26,27 The correlation functions between the solvent species resulting from DRISM are used for solving the 3D-RISM equation to obtain the three-dimensional distribution functions (3D-DF) of each site of a solvent molecule, g(r). In this work, we use the KH closure for the acceleration and stability of convergence.28,29 The profiles of 1D-distribution and of potential of mean force (PMF) along the channel axis are given by averaging 3D-DF along the axis.20 The structures and parameters we have used in this calculation are summarized in Table 1.30-38 The results of ab initio optimization for the structure of glycerol in aqueous phase have shown some variety depending on the models employed.38 We chose the two lowest energy conformations for each model in thiscalculation:glycerol1 (tG′g,tG′g(Rγ))andglycerol2 (gGg′,tGg′(Rγ)). The dielectric constant for the DRISM calculation and the temperature of solvent are chosen as 78.8 and 298 K, respectively. The structures of AQP1 and GlpF are taken from 1J4N39
Figure 1. Comparison between the channels of AQP1 and GlpF; the dots demonstrate the channel surface.
and 1LDA,40 respectively, in the Brookhaven Protein Data Bank. The Amber-99 parameter set was used in this calculation for AQPs.41 In the present study, we have ignored the cell membrane and employed the rigid models of AQPs. The monomers of AQP1 and GlpF were immersed in the aqueous solutions: (1) 0.1 M Ne, (2) 1 mM CO2, (3) 10 mM NO, (4) NH4Cl at pH 7.5 (the ammonium chloride is assumed to be completely dissociated into Cl-, NH3, and NH4+, and the ratio of [NH3] and [NH4+] is set to the same condition as the case of pH 7.5), (5) 0.5 M urea, and (6) 0.5 M glycerol. The 3D-RISM equation was solved on a grid of 5123 points in a cubic supercell of 80 Å3 for AQP1 in the NH4Cl solution, and of 5123 points in a cubic supercell of 128 Å3 for GlpF in the glycerol solutions. The rather high grid resolution was required in order to ensure the accuracy of calculating PMF for those systems. We used less grid resolution, 2563 points in a cubic supercell of 128 Å3, for the other systems. Result and Discussion A. Distribution of Water in AQP1 and GlpF. Figure 1 shows the internal surfaces of both AQPs and GlpF. Apparently, GlpF has a larger channel radius at the selective filter (SF) region than AQP1. 3D-DF of water around and inside AQP1 is shown in Figure 2 with the threshold g(r) > 3, which implies that the probability of finding water molecules at the position is three times greater than that in the bulk. The figure demonstrates that the 3D-RISM theory reproduces the X-ray results for 3D-DF reasonably well. The agreement cannot be perfect, because the conditions of the systems are quite different: the X-ray results are from the cryostat measurement, and only those water molecules bound to channel sites were detected, while the 3DRISM results were obtained under ambient condition. The three-dimensional distribution functions (3D-DFs) of water inside the channels of AQP1 and GlpF are shown in the Figures 3 and 6, respectively, which are basically the same as those presented previously. Here, we just make a brief comment on our results and on those from the MD simulations. The distributions of water in both AQP1 and GlpF are similar as one can see in Figures 3 and 6; the corresponding PMFs are slightly negative throughout the channels. The finding indicates
Molecular Selectivity in Aquaporin Channels
Figure 2. Distribution of water around and inside AQP1 at criteria g > 3: the red spheres demonstrate the position of oxygens of water from the X-ray structure
that water molecules can exist in the channel at least as stable as in the bulk. The results are consistent with those from X-ray crystallography. Many papers based on X-ray crystallography have been published, in which they have reported the existence of water molecules inside the channel.39,40 The observation implies that water molecules can stay for some elongated time inside the channel, and they are at least as stable with those in the bulk. The results from the experiments as well as the 3DRISM theory are in sharp contrast with those from the MD simulations. The MD simulations have produced the large
J. Phys. Chem. B, Vol. 114, No. 23, 2010 7969 positive PMF in the channel.13 For example, the highest peaks of PMF of water in the channels estimated by Hub and de Groot were 14 and 13.5 kJ/mol for AQP1 and GlpF, respectively.13 Such behavior in PMF excludes any possibility of the water molecule existing in the channels. B. Distribution of Neutral Molecules in AQP1. Depicted in Figures 3 and 4 are 3D-DFs and PMF of water, Ne, CO2, NH3, urea, and glycerol in the AQP1 channel. Neon is a spherical molecule that has no charge distribution, and the size is slightly less than that of water. One can see from the figure that Ne has a distribution which is similar to water: both have a continuous distribution extended inside the channel. However, there is a subtle difference in the distributions around the SF region: Ne has smaller distribution compared to water. Accordingly, PMF of Ne is higher at the region compared to water (Figure 4). Since the size of Ne molecules is slightly less than that of water, Ne is expected to have a larger distribution compared to that of water at the SF region if one just considers the steric effect. The results indicate that the selectivity of ligands by AQPs is determined not only by their size but also by the charge distributions. If there is no charge distribution inside the channel, Ne should be more comfortable in the channel than in water due to the hydrophobic interactions. However, AQP1s have basically a positive electrostatic environment at the SF region, which prefers water molecules to Ne. As distinct from the case of water and Ne, 3D-DFs of CO2, NH3, and NO are not continuous and have some gaps at the SF region (Figure 3). Accordingly, PMFs of those ligands have some positive peaks at the region (Figure 4). The distribution of NH3 inside the channel is similar to that of water except for the SF region. Accordingly, the one-dimensional distribution profiles of NH3 and water showed similar overall behaviors, although the distribution function of NH3 is basically lower than
Figure 3. 3D-DFs of water, Ne, CO2, NH3, urea, and glycerol in the central pore of AQP1, g > 1.
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Figure 5. Direction of dipoles of each structure of glycerol.
Figure 4. PMFs of water, Ne, CO2, NH3, urea, and glycerol in AQP1.
that of water. This may be because NH3 has a slightly larger size and a smaller dipole moment than those of water. The difference of PMFs between NH3 and water at SF originates essentially from the diameter of NH3 we have used, which is slightly larger (∼0.2 Å) than that of water. The height of the peak in PMF of NH3 is 2.5 kJ/mol. This barrier in PMF is as low as the thermal energy, and is restricted in a small area. Our prediction suggests that a NH3 molecule has a possibility to overcome this barrier and to transport across the channel under appropriate osmotic conditions. The barrier peaks in PMF of NO and CO2 at the SF region exceed 15 kJ/mol, which prevent these molecules from moving across the channel. There are two factors contributing to the barrier, the steric and electrostatic effects. Since CO2 and NO are much bulkier than water, they will be sterically excluded from the narrow region of the channel. CO2 is electrostatically disfavored as well in this region, because it does not have a dipole moment. In addition, NO also has a dipole moment that is smaller than that of water. Therefore, they cannot be stable in this region. So, our results refuse those experimental results which indicate the possibility of CO2 and NO conducting through the AQP1 channel. The 3D-distributions of glycerol and urea inside the AQP1 channel depicted in Figure 3 show large gaps around the SF region, indicating that AQP1 is not permeable to these two molecules. Accordingly, the potential of mean force of the molecules shows high barrier (>20 kJ/mol) at the SF region. The results are in complete agreement with the experimental
observations which show no conductivity of those molecules in the channel. Concerning the two conformations of glycerol, glycerol1, and glycerol2, they show similar distributions and PMFs at the SF region, but are slightly different at NPA. This is due to the alignment and magnitude of the dipole moment of the molecules; the dipole moment of glycerol1 aligns lengthwise with the molecule, while that of glycerol2 aligns crosswise with the molecule (Figure 5). These directions of dipole moments of glycerol make glycerol2 more stable in the channel than glycerol1. Comparing PMFs in the present work with the results from MD (dashed line in Figure 4),13 our results for CO2, NH3, urea, and glycerol show entirely different patterns and height of the barrier peaks from those by MD. The barrier peaks are located only at the SF region in the present work, while the MD results show the barriers located other than the SF region.13 The heights of the peaks in PMF of the molecules in our study and those from the MD simulation are given in Table 2. With respect to the permeability of the channel for CO2, urea, and glycerol, the MD simulation and our method gave quantitatively the same conclusion, or “nonpermeable”. On the other hand, the two methods gave opposite conclusions for the case of NH3: it is nonpermeable by the MD simulation, while it is permeable according to our method. Since there has been no experimental consensus with respect to the permeability of AQP1 for those ligands, we do not have a solid answer to the question which is correct. Nevertheless, the results by the simulation are questionable, because the method gave results entirely opposite to the experimental observation for the case of GlpF as is discussed in the following subsection. C. Distribution of Neutral Molecules in GlpF. Compared with AQP1, GlpF has a wider pathway especially at the SF region (Figure 1). Shown in Figure 6 are 3D-DF (g(r) > 1) of CO2, NO, NH3, urea, and glycerol. As can be readily seen, the distributions are continuous throughout the channel for all the ligands studied. The density profiles and PMFs along the channel axis for all the ligands are depicted in Figure 7. All the ligands except for glycerol show PMF, which is negative throughout the channel, whereas glycerol shows positive barriers in PMF at the SF region for both conformations: glycerol1 and glycerol2. However, the barriers for both structures are not so high, 3.7 and 2.1 kJ/mol, which are comparable to the thermal energy. As we discussed above, the difference in the barrier heights between glycerol1 and glycerol2 is due to alignment and magnitude of dipole moments (Figure 5). These results indicate that all the test molecules, CO2, NO, NH3, urea, and glycerol, can be permeated through the channel, and that GlpF has less selectivity compared with AQP1. The results are in good accord with the experimental results for the case of glycerol and urea, which are known to be permeable through the channel. On the other hand, our results are just a prediction for the cases of CO2, NO, and NH3 to be confirmed by experiments. The potential of mean forces of the ligand molecules in GlpF obtained from the MD simulations shows distinctly different
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Figure 6. 3D-DFs of water, CO2, NH3, urea, and glycerol in the central pore of GlpF, g > 1.
TABLE 2: The Highest of Barrier Peaks of Each Molecule H2 O this worka Hub and de Groot13 Wang et al.42 this worka Hub and de Groot13 Jensen et al.43
x 14
CO2
NO
NH3
AQP1 (kJ/mol) >20 15 2.5 22 18
GlpF (kJ/mol) x x x 13.5 12.5
x 12.5
urea
glycerol
>20 32.5
>20 24 95b
x 29
3.7 (2.1)c 13.5 30.5
a x indicates there is no barrier potential or the PMF is negative for the entire channel. b Height of barrier peak in AQPZ. c The number in parentheses is the height of barrier peak of glycerol2.
patterns from our results: PMFs of NH3 and urea from MD have large positive values throughout the channel, while those of CO2 and glycerol has some negative regions. In any case, the barriers in PMF at the SF region are so high and large for all four ligands examined (see also Table 2) it seems impossible for them to overcome the barrier in order to be permeated through the channel. This raises a serious question about the results from MD simulations, because the experimental observation indicates that GlpF can conduct glycerol and urea pretty well.44 (Actually, the name “glyceroporin” came from that function of the channel.) At this point, the readers may wonder why and how such a striking difference between the results from the two methods emerged, and why we think our results are more faithful to the nature. (In fact, one of the reviewers of the paper has requested the authors to make comments on such questions.) It is very unlikely that the difference in the potential parameters employed in MD and 3D-RISM caused the qualitative difference in the results from the two methods, because the parameter sets
employed in the two methods are standard ones which have reproduced the experimental data equally well in other problems in biophysics. We also do not think that the rigid structure of protein employed in our study caused the trouble, because taking account for the structural flexibility will lower the potential of mean force of ligands inside the channel rather than increasing it. The question can be put in a slightly different manner, that is, “why the molecular simulation failed to describe the experimental phenomena even in a qualitative manner”, since the results from the 3D-RISM theory are consistent with the experimental or intuitional observations. Of course, we do not have a definite answer to the question, because the simulation has not been done by ourselves. All we can do is to express our own view on how we see the problem. We presume that the trouble in the simulation results originates mainly from the insufficient sampling of the configuration space of the ligand molecules in the channel, and that it is caused by the choice of order parameters the authors of the paper have made in the umbrella sampling.13 They have defined an order parameter or a reaction coordinate onto which all other degrees of freedom are projected, that is the position of a tagged atom in ligand molecules along the channel axis. However, just one order parameter is not sufficient to sample the configuration space of the ligands, because the molecules under concern have orientational degrees of freedom. Let us consider an extreme example in which the gating region is quite narrow so that only a ligand molecule with a particular orientation can get through. In such a situation, the ligand molecule should find the particular orientation only by “chance” during the natural evolution of the simulation, because there is no force or “umbrella” put along the degrees of freedom. The chance for finding the right orientation might not be so great
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Phongphanphanee et al. investigated are neon (Ne), carbon dioxide (CO2), nitric oxide (NO), ammonia (NH3), urea, and glycerol. Neon shows continuous distribution throughout the channel pore in AQP1 as is the case of water, although PMF of Ne at the selective filter (SF) region is higher than that of water, indicating that the stability of molecules in the channel is determined not only by their size, but also by the charge distribution. The ligand molecules, CO2, NO, urea, and glycerol, have a large barrier in PMF at the SF region in AQP1, indicating that the channel is not permeable by those ligands. On the other hand, NH3 has only a small activation barrier, ∼2.5 kJ/mol, to be overcome. Therefore, our theory predicts that a NH3 molecule can permeate through the AQP1 channel. In GlpF, all the ligands have negative PMF throughout the channel except for glycerol, which has a small barrier at the SF area, ∼2.1 kJ/mol. The barrier can be readily overcome by the thermal motion. So, our results are quite consistent with the experiments for urea and glycerol, for which the corresponding data are available. In sharp contrast to our results, PMFs for CO2, NH3, urea, and glycerol in both AQP1 and GlpF, obtained from the molecular dynamics simulation, have exhibited large positive values throughout or somewhere in the channel, predicting that both AQP1 and GlpF are not permeable by those ligands. The prediction is absolutely in failure, because GlpF is known to permeate glycerol. Acknowledgment. This work was supported by the Grantin-Aid for Scientific Research on Innovative Areas “Molecular Science of Fluctuations toward Biological Functions” from the MEXT in Japan. We are also grateful to Next Generation Integrated Nanoscience Simulation Software, the project of the ministry. Molecular graphics images were produced with the UCSF Chimera package.45
Figure 7. PMFs of water, Ne, CO2, NH3, urea, and glycerol in GlpF.
for the simulation with the ordinary time steps. The chance becomes even less if the orientation is confined due to some reasons, for example, due to hydrogen bonds with residues in the channel. If the chance for the ligand to find the right orientation is low, the probability distribution of finding the ligand atom in the position across the narrow region will become low. In other words, the potential of mean force will become high. We believe that a more or less similar situation is taking place in the molecular simulation. In a sense, the 3D-RISM method adopts the same order parameter with the molecular simulation, that is, the position of a particular atom in a ligand molecule, onto which all other degrees of freedom are projected. However, in sharp contrast to the simulation, the 3D-RISM method samples the entire configuration space of the ligand molecules, including their orientations inside the channel, by means of analytical integrations over the space. There is no concern about the insufficient sampling of the configuration space or the “non-Ergordig trap”, which is notorious in the molecular simulation. Conclusion The three-dimensional distribution function (3D-DFs) and potentials of mean force (PMFs) of small neutral molecules inside the two aquaporin channels, AQP1 and GlpF, were calculated based on the 3D-RISM theory, the statistical mechanics theory of molecular liquids, in order to investigate the permeability of those ligands through the channels. The ligands
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