Multiconformation continuum electrostatics analysis of the NhaA Na+/H+ antiporter of Escherichia coli with functional implications
- *Department of Molecular Membrane Biology, Max Planck Institute of Biophysics, Max-von-Laue Strasse 3, D-60438 Frankfurt am Main, Germany; and
- †Department of Biological Chemistry, Alexander Silberman Institute of Life Sciences, Hebrew University of Jerusalem, Jerusalem 91904, Israel
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Contributed by Hartmut Michel, December 20, 2005
Abstract
Sodium proton antiporters are essential enzymes that catalyze the exchange of sodium ions for protons across biological membranes. Protonations and deprotonations of individual amino acid residues and of clusters formed by these residues play an important role in activating these enzymes and in the mechanism of transport. We have used multiconformation continuum electrostatics method to investigate the protonation states of residues in the sodium proton exchanger NhaA from Escherichia coli, the structure of which has been determined recently by x-ray crystallography. Our calculations identify four clusters of electrostatically tightly interacting residues as well as long-range interactions between residues required for activation. The importance of many of these residues has been demonstrated by the characterization of site-directed mutants. A number of residues with extreme pKa values, including several of the “pH sensor,” can only undergo protonation/deprotonation reactions subsequent to conformational changes. The results of the calculations provide valuable information on the activation of the antiporter and the role of individual amino acid residues, and provide a solid framework for further experiments.
Sodium proton antiporters, located in the cytoplasmic and organelle membranes of cells of many different origins, play an important role in homeostasis of intracellular pH, cellular Na+ content, and cell volume (1–4). NhaA is the main Na+/H+ antiporter of Escherichia coli and many other enterobacteria (5). It is inactive at pH 7 and below but is highly active at pH 8. The regulation of the activity of NhaA by pH, as well as that of other, both eukaryotic and prokaryotic Na+/H+ antiporters, requires a “pH sensor” whose change in protonation leads to conformational changes in different parts of the protein that transduce the pH signal into a change in activity. NhaA is electrogenic with a stoichiometry of two H+ exchanged for each Na+ (6).
The crystal structure of NhaA, in the down-regulated conformation found at low pH, has recently been determined at 3.45 Å resolution (7) (Fig. 1). NhaA contains 12 transmembrane segments (TMSs). A negatively charged funnel formed of TMSs II, IX, IVc (“p” and “c” stand for the periplasmic and cytoplasmic parts, respectively), and V opens to the cytoplasm and ends in the middle of the membrane at the putative ion binding site. In TMS IV and TMS XI, the helices are interrupted by extended chains that cross each other. This TMSs IV/XI assembly creates a delicately balanced electrostatic environment in the middle of the membrane. A shallow negatively charged funnel formed by TMSs II, VIII, and XIp opens to the periplasm. The two funnels point to each other but are separated by a group of densely packed hydrophobic residues forming a barrier in the acidic pH down-regulated antiporter. The pH sensor appears to be located at the cytoplasmic funnel entry and to transduce the pH signal (at alkaline pH) to the TMSs IV/XI assembly to activate the antiporter (5). On the basis of the structure, it has been proposed that binding of the charged substrates causes an electrostatic imbalance allowing for a rapid alternating access mechanism (7).
The overall architecture of the NhaA and the general distribution of internal water molecules predicted by the program grid (red balls). The 12 TMSs viewed parallel to the membrane are represented by a matrix of carbon atoms (shown in blue balls) surrounding the protein. The ion binding site is encircled. The image was prepared with vmd (53).
The architecture of the Na+/H+ antiporter NhaA provides the basis for understanding the mechanism of Na+/H+ exchange and the unique regulation of its activity by pH. The physical separation between the pH sensor and the exchange machinery revealed by the structure entails long-range, pH-induced conformational changes for pH activation, as observed both in prokaryotic and eukaryotic antiporters (4, 8, 9). Although many aspects of the ion-translocation mechanism and pH regulation are illuminated by the NhaA structure, many subjects remain unknown: the atomic details of ligand binding, the alkaline pH-induced conformational change, the translocation mechanism, the proton pathways to the binding site, and the dynamics and energetics of these processes. The structure affords a starting point to apply in silico approaches, in particular, a study of the effect of pH on the protonation states of titratable residues in NhaA that in turn may lead to conformational changes and activation of the antiporter.
pH-dependent phenomena have been extensively modeled by using different theoretical approaches (10–12). A typical task is to compute the pKa values of ionizable groups in proteins. Conformational changes can shift pKa values of residues in proteins (13–16). It is therefore interesting to investigate the effect of pH and thus changes of protonation states on the conformational equilibria associated with pKa switching. Over the years there has been a continuous effort to develop methods for accurate pKa predictions (for review, see ref. 17). Several methods that are based on continuum electrostatics add a nonuniform protein response to charges (for review, see ref. 18). Different dielectric constants have been assigned to different regions of the protein (19) or to different amino acids (20). Several methodologies consider explicit protein motions (21, 22). Other methods simultaneously calculate ionization states of acidic and basic residues, the conformation states of surface side chains (23), hydroxyls and molecules of water (24), and polar and ionizable side chains (25).
We have investigated computationally the effect of pH values on the protonation states of titratable residues in NhaA. We used the multiconformation continuum electrostatics (mcce) method (14), which allows multiple positions of side chain rotamers, hydroxyl protons, and water protons in the calculation of the pH dependence of the ionization equilibria of titratable groups (16, 24, 25). We also studied the effect of explicit water molecules on the electrostatic interactions of surrounding residues.
The results of the study provide insight into the protein electrostatics, and identify residues and clusters of residues that change their protonation states, which may lead to conformational changes and activation of NhaA.
Results
Electrostatic Interactions Between Ionizable Residues Within NhaA.
Electrostatic interaction energies and the average protonation of all titratable residues in the NhaA Na+/H+ antiporter have been calculated. NhaA contains 61 residues including C and N termini that were considered protonatable. To identify all residues that could play a major role in affecting the pKa values of the titratable residues, we calculated mean field interaction energies of the latter residues with all other residues in the protein. The simplest model for protonation state calculations, which we denote here as “C,” is a multiple conformer where all internal cavities are filled with a high dielectric continuum (with no explicit water molecules). Clusters of strong electrostatically interacting residues have been found in other membrane proteins; for example, photosynthetic reaction centers (26–28), cytochrome c oxidase (29), and fumarate reductase (30). In NhaA antiporter, we have identified four clusters, consisting of 18 titratable groups altogether (Table 1 and Fig. 2).
Clusters of strongly electrostatically interacting ionizable groups for NhaA antiporter. Zones of negative and positive potential are colored red and blue, respectively. Four clusters of interacting residues are shown in gray, green, magenta, and yellow. Additionally, the isolated sites Lys-57 and Asp-65, and the conserved Thr-132, Arg-204, and Arg-381 are included. The figure was prepared with grasp (45).
Mean field interaction energies (in kcal/mol) of NhaA antiporter at pH 4, calculated for the model C
In the crystal structure of NhaA, residues Glu-78, Arg-81, Glu-82, Glu-252, His-253, and His-256 are located in close proximity on one side of the cytoplasmic funnel entrance of the antiporter (7). They are suggested to play a role in the pH sensor (5). The potentially negatively charged residues are thought to be well suited to attract Na+ cations into the funnel. Our electrostatic calculations show that these residues and amino acid residues Asp-133, Arg-203, His-243, Lys-249, and Arg-250 belong to a single cluster of strongly interacting residues (Table 1 and Fig. 2, shown in magenta). Because these residues are spatially close to each other, they are expected to interact via a hydrogen-bonded network that can adopt several possible configurations. The choice of the hydrogen-bonded network can have a significant impact on the results of pKa calculations (16, 24, 31, 32).
A second cluster consists of the N terminus, Asp-11, Lys-153, located on the opposite side of the cytoplasmic funnel, and His-256 (Table 1 and Fig. 2, shown in gray). A third cluster is formed by residues Tyr-112, Arg-123, Glu-124, Asp-133, Asp-163, Asp-164, Tyr-175, and Lys-300 (Table 1 and Fig. 2, shown in yellow). It includes the residues at the tip of the cytoplasmic funnel and the residues on the opposite side of the hydrophobic barrier of ion transport in the center of the membrane. The fourth cluster is formed by Tyr-38, His-39, Glu-43, and Lys-362 (Table 1 and Fig. 2, shown in green). It is located at the rim of the shallow periplasmic funnel.
The computational results summarized in Table 1 indicate that whereas Asp-133 provides a strong link between the first and the third clusters, His-256 forms a strong connection between the first and second clusters. Cys replacement of Asp-133 increases dramatically the apparent K m to sodium of the antiporter (33). The result of mcce calculations predicts that such long-range interactions between the residues located in the beginning of the funnel and those buried within the protein can have a significant effect in modulating the electrostatic potential of the antiporter.
pKa Calculations Using the Model with Implicit Water Molecules.
The pKa calculations for model “C” show that the pKa of Glu-78, Arg-81, and Glu-82 shifts to the high values 5.4, 15.4, and 10.4, respectively, from the model pKa values (Table 2). In contrast, the pKa of Glu-252 decreases to 2.7. The extreme pKa values of Arg-81, Glu-82, and Glu-252 predict that a change in the protonation states of these residues, within the normal pH range of the NhaA antiporter (6.5–8.5), can only occur if NhaA undergoes structural changes. Such structural changes could be triggered by Glu-78 with a pKa near the physiological range. Most interestingly, a pH-dependent conformational change was observed in the vicinity of these residues (5), as probed by a monoclonal antibody at the N terminus (34), and by accessibility of NhaA to trypsin at Lys-249 (35) or MIANS [2-(4′-maleimidylanilino)-naphthalene-6-sulfonic acid], a fluorescent probe bound at a Cys replacement of Glu-252 (36). This behavior reflects the pH dependence of NhaA activation (5). It has been proposed that a pH change at the pH sensor results in alteration of the protonation state at the entrance of the cytoplasmic passage, eliciting conformational changes that are transmitted to activate NhaA (7).
Calculated pKa values for titratable sites of NhaA antiporter for the different models in the presence of the implicit solvent (model CW) and in the presence of membrane layer (models CM and CMW) compared with those calculated by using the standard continuum model (C)
Analyses of the x-ray data suggest that at pH 4, whereas Asp-163 is occluded, Asp-164 is exposed to the cation passage, and that both contribute to the Na+ binding site (7). Yet, fully hydrated Na+ ions as well as water molecules cannot access the end of the funnel, where Asp-164 is positioned. Biochemical and genetic data obtained with NhaA activated at alkaline pH show that, indeed, these residues are essential for activity of NhaA (37). In our calculations, aspartic acids 163 and 164 continue to hold their protons up to a pH value of 15 or more (Table 2). These results are consistent with our assumption that in the acid-locked conformation of NhaA (pH 4), these groups remain protonated (7). Therefore, structural changes that lower their pKa values are required for activation of NhaA. The high pKa value for Asp-164 is mainly the result of the high desolvation energy term, which is not compensated by the nonpolar residues Ala-131 and Met-341, and Thr-132, surrounding Asp-164. Aspartic acid 163 is located at a distance of ≈6 Å from Asp-164 (measured between their oxygen atoms OD1 and OD2, respectively). This close interaction will mutually increase their pKa values. The side chain of Asp-163 is buried in a relatively hydrophobic pocket formed by the side chains of Ala-101, Gly-104, and Met-105, making the pKa abnormally high compared with that of a normal aspartic acid residue.
Influence of the Membrane Model.
We introduced a membrane model to account for the low-dielectric environment of the molecular surface that is exposed to the hydrophobic regions (Fig. 1). The presence of this low-dielectric membrane region does not shield the electrostatic interactions as strongly as the bulk water; the electrostatic interactions between the titratable sites in the protein increase even at long distances.
Our results show a remarkable increase in desolvation penalty for residues exposed to or close to the now membrane-covered part of the surface. For example, a drastic change was calculated for Arg-204; its pKa dropped by >5 ΔpK units from >12 to 7 (Table 2, model “CM”). The side chain of this residue is very close to the protein-solvent/protein-membrane interface (Fig. 2).
Predicted Water Binding Regions.
To predict the positions of putative water molecules in the interior of NhaA antiporter, we used a hydration criterion of accepting all grid waters with energies of less than −8 kcal/mol. The largest region with a favorable binding energy of −13.2 kcal/mol in the grid energy map was calculated in the internal cavity containing Lys-300 and Cys-335. After locating the energy minimum, the position of the water probe was refined and a water molecule WG385 (internal grid water molecule) was assigned to it. A second energy minimum was found in a second round by using input coordinates containing this water molecule. After four grid cycles, a total of 59 water molecules and their positions were calculated in the structure of the NhaA antiporter (Fig. 1): 6 water molecules with energies below −12 kcal/mol, 19 water molecules with energies between −12 kcal/mol and −10 kcal/mol, and 34 water molecules with interaction energies between −10 kcal/mol and −8 kcal/mol.
Few water molecules were modeled near the center of the protein, whereas large numbers were predicted to be bound at the orifices of the funnels and in the regions close to the surface (Fig. 1). grid calculations show most interesting features concerning the water distribution in the region of the potential sodium binding site, including Thr-132, Asp-133, Asp-163, and Asp-164 (7); residue Asp-163 forms a hydrogen bond toward Thr-132 via a water molecule WG416 with grid energy of −11.1 kcal/mol, and further to Asp-133. Hence, we suggest that these polar and ionizable residues as well as water molecules can contribute to the Na+ binding site of NhaA (7). This suggestion is in line with results obtained from crystal structures of other sodium-binding proteins including two Na+-pumping ATPases (38–41). These results demonstrate that small alkali-metal ions are ligated by oxygen atoms provided by water as well as main-chain carbonyl, carboxyl, or hydroxyl groups with an average coordination number of five to six.
The identification of protein-bound water molecules allows us to examine the initial hydrogen-bonded network in NhaA that, of course, would undergo changes during activation of the antiporter. Of 59 bound water molecules predicted by grid, 27 water molecules form a hydrogen-bonded network corresponding to the static structure of the protein in its inactive form. These water molecules were explicitly included in the mcce calculations and were treated in the same detail as side chains with conformations allowing rotation around the oxygen. Additionally, each water molecule has an extra conformer in bulk solvent with no interaction with protein. Regions occupied by these water molecules were treated as “protein” as far as the dielectric model is concerned, which means nearly all of the interior region was assigned a dielectric constant of 4, with only a few small interior pockets of high-dielectric continuum.
Influence of Explicit Internal Hydration.
The x-ray crystallographic analysis of NhaA at the present resolution cannot detect bound water molecules. In the “C” set of calculations the cavities were filled by delphi with a medium of a dielectric constant of 80.
Overall, the results of the multiconformer calculation with explicit water and membrane model, denoted as “CMW,” are very similar to the results without explicit water (model “CM”). However, importantly, the inclusion of water molecules significantly alters the titration behavior of several individually titratable sites, shifting the calculated pKa values by >1 pH unit (Table 2). These residues are Glu-82 (1.2 pH units), Glu-124 (−2.5 pH units), Tyr-175 (0.7 pH units), and Tyr-261 (0.9 pH units). All of these residues form hydrogen bonds with water molecules, explicitly included in the model. Several titratable residues, including Glu-82, have two water molecules as potential hydrogen bonding partners of which only one can participate in the formation of a hydrogen bond to the neighboring titratable residue. These results indicate that including a particular water molecule in the pKa calculations most significantly affects the titration behavior of residues with which a water molecule is in hydrogen bond contact. Hence, internal waters can effectively modulate the pKa values of buried residues in NhaA.
The most significant shift of a pKa value was observed for residue Lys-300 (−2.6 pH units) from 5.8 (when water molecules are modeled implicitly) to 3.2 (when water molecules are modeled explicitly; see Theory and Methods); the HZ1 atom of Lys-300 is in a distance of 2.1 Å from the OH2 atom of a water molecule. The calculations using this model predict a pH-dependent relocation of a proton between the water molecule and Lys-300, and they suggest that the buried Lys-300 is in contact with internal waters even though these are not seen crystallographically. In support of the calculations, we have recently demonstrated accessibility to N-ethylmaleimide of Cys replacements in helix X around Lys-300 (L. Kozachkov and E.P., unpublished work).
We observed a hydrogen-bonded network between residues Asp-163 and Lys-300 via four explicit water molecules (Fig. 1). It therefore seems plausible that Lys-300 forms a hydrogen-bonded network with Asp-163 upon a reorientation of its side chain. Accordingly, the side chain of Lys-300 has a high Debye–Hückel B-factor. Lysine residue 300 has been proposed to provide charge compensation for the partial negative charge at the C-terminal of helix XIc and of helix IVp of the TMS IV/XI assembly (7). However, it cannot be excluded that an unresolved sodium ion takes this role, as it is the case in a bacterial homologue of a Na+/Cl−-dependent neurotransmitter transporter (42).
In the x-ray crystallographic model obtained at pH 4, Asp-65 is located at the tip of the shallow periplasmic funnel, 16 Å away from Asp-164 (7) (Fig. 2), and the OD1 atom of Asp-65 is located ≈3.1 Å away from the NZ atom of Lys-57 (loop I–II) (Fig. 3 A). The importance of the residues Lys-57 and Asp-65 for the activity of NhaA has recently been demonstrated by site-directed mutagenesis: replacement of Asp-65 by Cys increased dramatically the K m of NhaA for Na+; Cys replacement of Lys-57 reduced the resistance of the cells to Na+ (K. Herz and E.P., unpublished work). Notably, Asp-65 and Lys-57 do not belong to any cluster of strongly interacting residues (Table 1) and form an isolated charge pair. However, our calculations show most interesting interactions between these two residues. The calculations predict that at pH 4, Asp-65 interacts with Lys-57 with an energy of −2.4 kcal/mol. Because Lys-57 is not a buried residue, its side chain should have conformational flexibility. Thus, in contrast to its position in the x-ray structure, the side chain of Lys-57 faces the periplasm at pH 4 (Fig. 3 B), when Asp-65 becomes protonated. This discrepancy between crystallographic and calculated positions of the side chain of Lys-57 could be explained by the fact that in the crystal structure of NhaA, this residue is located at the periplasmic interface of the two monomers, present in the asymmetric unit in opposite orientation. We suggest that during formation of the artificial dimer, Lys-57 is pushed to its observed position in the x-ray structure (Fig. 3 A).
Position of occupied conformers of interacting residues Lys-57 and Asp-65 of the crystal structure of NhaA (A) (distance between atoms shown in angstroms), calculated at pH 4 (B) and pH 8 (C). The figure was prepared with vmd (53).
The intrinsic pKa of Asp-65 (5.8) is higher than that of the other aspartate residues in the protein, excluding Asp-133, Asp-163, and Asp-164. This pKa may be due to either a proximity to a negative charge in the protein or to a hydrophobic environment. The latter alternative is most likely because in the crystal structure Asp-65 is located at the tip of the periplasmic funnel surrounded by nonpolar residues of helices II, IVp, and XIp and is not in proximity to negatively charged residues. Our calculations show that the deprotonation of Asp-65 at pH 8 is accompanied by a conformational reorientation of this residue into the direction of the ion binding site/cytoplasm (Fig. 3 C) and by a formation of hydrogen bond with water molecule WG419 with a hydrogen bond distance of 2.7 Å. Therefore, at pH 8, the position of the side chain of Lys-57 will be oriented to the direction of Asp-65, as calculated (Fig. 3 C).
Concluding Remarks
Results from mcce calculations are presented for a transporter protein, the sodium/proton antiporter NhaA of E. coli.
Using a continuum dielectric model and finite difference technique, we analyzed the electrostatic interactions in the NhaA structure in its closed conformation. Four clusters, consisting of 18 titratable groups altogether, have been identified. The residues of the clusters are responsible for the electrostatic properties of NhaA and for the structural changes upon activation by raising the pH. Two clusters are located at the cytoplasmic side of the molecule, one at the periplasmic side and one in the center. Most interestingly, based on functional analysis of mutants, a similar arrangement of polar conserved residues has recently been suggested for Vc-NhaD, a Vibrio cholerae antiporter that is not homologous to Ec-NhaA and of which the structure is not known (43). It is suggested that this cross-membrane arrangement of polar residues in antiporter molecules facilitates the access of the ionic substrates to the central group, their binding and their transport.
The extreme pKa values of the clustered residues, which form the pH sensor of NhaA, suggest no change in the protonation state of these residues within the physiological pH range, unless the NhaA structure alters. Glu-78 with pKa near the physiological range is suggested to trigger such pH-dependent structural change. Long-range interactions between the pH sensor and Asp-133 have a significant effect on the electrostatic potential of the antiporter.
Analysis of the x-ray data suggests that Asp-163 and Asp-164 contribute to the Na+ binding site. Biochemical data obtained with NhaA activated at alkaline pH show that these conserved residues are essential for the activity of the antiporter. Our calculations with continuum dielectric model predict that aspartic acids 163 and 164 continue to hold their protons in the acid-locked conformation of NhaA. The protons can only be released upon a structural change.
The identification of protein-bound water molecules by using the grid method allows us to examine the initial hydrogen-bonded network of NhaA. The inclusion of water molecules alters the pKa values of several individual titratable residues. The most significant change of a pKa value was found for Lys-300.
The deprotonation of Asp-65 at pH 8 is accompanied by a conformational reorientation of its side chain to the cytoplasmic side. Furthermore, analysis of the results indicated that Lys-57 and Asp-65, whose functional importance has been demonstrated by site-directed mutagenesis, form an isolated charge pair.
This study provides clues for future analyses of the mechanism of activation and transport as well as for the interpretation or design of experimental work.
Theory and Methods
Coordinates.
The atomic model was derived from crystallographic data obtained under cryo-conditions of the sodium proton antiporter (NhaA Na+/H+ antiporter) from E. coli at 3.45 Å resolution (Protein Data Bank entry 1ZCD) (7). NhaA consists of 388 amino acid residues with the N and C termini exposed to the cytoplasm. The structural model comprises residues 9–384, which are arranged in 12 TMSs (7). Na+ ions and water molecules could not be identified at the available resolution. The N- and C-termini residues were modeled by using the charmm software package (Version c28b2) (44).
Continuum Electrostatics.
mcce has been used to investigate the pH dependence of protein electrochemistry. mcce (Version 2.0) is a hybrid method combining continuum electrostatics with molecular mechanics (14, 24). This method adds explicit conformers for polar and ionizable side chains, the cofactor, and buried water molecules. The preselection of conformers attempts to create as many good choices as possible without including positions, which will never be selected during the Monte Carlo sampling, because badly chosen conformers will not be part of a low-energy microstate (16, 30).
The interior dielectric constant of the protein was set to 4, and the solvent dielectric constant was set to 80 with an ionic strength of 150 mM. The molecular surface of the protein as the boundary between high- and low-dielectric media was defined by a solvent probe of radius 1.4 Å (29). The protein backbone and nonpolar side chains were fixed. Hydrogens were added to the structure after creating side-chain rotamers.
The program delphi (45) was used to calculate the electrostatic potential of the protein by solving the Poisson–Boltzmann equation with PARSE (parameters of solvation energies) atomic charges and radii (46). Monte Carlo sampling yielded the conformer occupancies in a Boltzmann distribution of states as a function of pH. Conformation and ionization degrees of freedom were simultaneously relaxed to low-energy states. A more detailed description of the mcce method is given in ref. 16. Groups of residues with strong pairwise electrostatic interactions (more than ±1 kcal/mol) and interdependent ionization states (for two or more residues) are referred to as clusters.
Because it has been shown that the low dielectric environment provided by the membrane helps to magnify the stabilizing effect of the pore helices in the KcsA potassium channel (47), we included a membrane model that shields the membrane-exposed protein surface from the solvent. The membrane boundaries were estimated from the distribution of tryptophan and tyrosine residues (48). The hydrophobic part of the membrane was represented by a lattice of carbon atoms that are 3 Å apart and form a 27-Å-thick layer.
grid.
To place water molecules explicitly in the antiporter, we used the program grid (Molecular Discovery) (49). grid was run with a water probe over the protein to identify possible water binding sites. grid energies lower than −8 kcal/mol with explicit formation of two hydrogen bonds were suggested as a criterion for positioning internal water molecules in previous studies on cytochrome P450cam (50) and on cytochrome c oxidase from Paracoccus denitrificans (51). The grid procedure was repeated four times keeping all previously located water molecules until no suitable deep-energy minimum (lower than −8 kcal/mol) was found any longer, indicating that all cavities were fully solvated for the chosen energy criteria (52).
Computational Details.
Four different mcce simulations were carried out (i) for protein with implicit modeling of solvent (C), (ii) for protein with implicit modeling of solvent embedded into a membrane (CM), (iii) for protein with ordered explicit water molecules from grid calculations (CW), and (iv) for protein with explicit water molecules from grid calculations embedded into a membrane (CMW). grid modeling was done on a one-processor DEC Alpha machine, and mcce and delphi calculations were performed on a one-processor Linux machine.
It is important to consider possible methodological uncertainties of our results such as the protein’s dielectric constant, the representation of the membrane, the level of internal hydration of the protein, and the low resolution of x-ray structure. Computed pKa values can be very sensitive to the positioning of protons on titratable groups (19, 54).
Acknowledgments
We thank Prof. Volkhard Helms and Dr. Stephen Marino for critical reading of the manuscript, and Lena Kozachkov and Katia Herz for sharing unpublished results. E.O. thanks Barbara Schiller for computational support. This work was supported by the Deutsche Forschungsgemeinschaft (SFB 472), the Fonds der Chemischen Industrie, the Max-Planck-Gesellschaft, the German–Israeli Foundation for Scientific Research and Development (H.M. and E.P.), and the Israeli Science Foundation (E.P.).
Footnotes
- ‡To whom correspondence may be addressed. E-mail: etana{at}vms.huji.ac.il or hartmut.michel{at}mpibp-frankfurt.mpg.de
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Author contributions: H.M. designed research; E.O. performed research; E.O., C.H., E.S., and E.P. analyzed data; and E.O., E.S., E.P., and H.M. wrote the paper.
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Conflict of interest statement: No conflicts declared.
- Abbreviation:
- TMS,
- transmembrane segment.
- © 2006 by The National Academy of Sciences of the USA