J. Phys. Chem. B 2008, 112, 1293-1298
1293
Quantum Mechanical Calculations on Selectivity in the KcsA Channel: The Role of the Aqueous Cavity Alisher M. Kariev and Michael E. Green* Department of Chemistry, City College of the City UniVersity of New York, 160 ConVent AVenue, New York New York 10031 ReceiVed: August 27, 2007; In Final Form: October 30, 2007
We have carried out quantum calculations on selected residues at the intracellular side of the selectivity filter of the KcsA potassium channel, using the published X-ray coordinates as starting points. The calculations involved primarily the side chains of residues lining the aqueous cavity on the intracellular side of the selectivity filter, in addition to water molecules, plus a K+ or Na+ ion. The results showed unambiguously that Na+ significantly distorts the symmetry of the channel at the entrance to the selectivity filter (at the residue T75), while K+ does so to a much smaller extent. In all, three ion positions have been calculated: the S4 (lowest) position at the bottom of the selectivity filter, the top of the cavity, and the midpoint of the cavity; Na+ is trapped at the cavity top, while K+ is cosolvated by the selectivity filter carbonyl groups plus threonine hydroxyl groups so that it can traverse the filter. Only one water molecule remains in the K+ solvation shell at the upper position in the cavity; this solvation shell also contains four threonine (T75) hydroxyl oxygens and two backbone carbonyls, while Na+ is solvated by five molecules of water and one oxygen from threonine hydroxyls. T75 at the entrance to the selectivity filter has a key role in recognition of the alkali ion, and T74 has secondary importance. The energetic basis for the preferential bonding of potassium by these residues is briefly discussed, based on additional calculations. Taken together, the results suggest that Na+ would have difficulty entering the cavity, and if it did, it would not be able to enter the selectivity filter.
Introduction The selectivity filter of the voltage-gated potassium channel appears to be one of the most highly conserved protein structures in biology. There is a characteristic amino acid sequence, TVGYG, that is almost invariant (the V sometimes is replaced by another hydrophobic amino acid) from bacteria to fruit flies to vertebrates, including humans. The mechanism by which this selects potassium over sodium ion has naturally been intensively investigated. A number of simulations have suggested that the carbonyls of the backbone amino acids act to cosolvate the ion.1-3 There have been a number of experimental studies of the selectivity filter as well.4-9 More recently ab initio studies, or studies that include some ab initio calculations, have begun to appear;10,11 these latter have some serious restriction on the freedom of the side chains. Topological constraints have been invoked to explain selectivity by backbone carbonyls and water.12 There appears to have been somewhat less attention paid to the hydroxyl group of the tyrosine (T75 for the KcsA channel). It is of some interest to note that the human eag1 channel has serine in place of the tyrosine13 and is still K+ selective. Our computational result suggests that the highly conserved T at the beginning of the TVGYG sequence is central to selectivity and that this is a consequence of the hydroxyl group’s contribution to solvation of the ion. We have carried out ab initio studies on a larger part of the channel than has hitherto been done and found major differences between the solvation of Na+ and K+, with the largest part of the difference due to the hydroxyl group. However, the backbone carbonyls and the * To whom correspondence should be addressed. E-mail: green@ sci.ccny.cuny.edu. Phone: (212)650-6034. Fax: (212)650-6107.
water are part of the same system of hydration, and help to differentiate Na+ from K+. Lockless et al.14 have now shown that ion size is critical, by use of isothermal titration calorimetry, with confirmation from X-ray crystallography. A major finding of that study was that the atoms of the selectivity filter underwent a small conformational displacement inward as the smaller sodium ion was bound. Other ions of varying size were also studied, and the ion size relation was found to be consistent. In another key study, Varma and Rempe15 examined model systems by ab initio calculation of the position of the ions with respect to some residues of the channel; they found that the topological characteristics of the coordination state of the permeant ion played a central role. However, the way in which they truncated the selectivity filter did not allow investigation of the role of water in what we now find to be necessary detail. Noskov and Roux16 have considered the NaK channel recently reported by Shi et al.17 and proposed, based on energetics and simulations, that hydration plays a key role in selectivity. Since ion size is a major determinant of hydration, the results of Lockless et al. and of Noskov and Roux do not disagree. We have now completed an ab initio study of the amino acids near the intracellular side of the selectivity filter, including sufficient neighboring water molecules, and residues just below the entrance to the selectivity filter, to allow us to understand the solvation of the ion properly. We began with the X-ray structure of the KcsA potassium channel (1k4c structure in the Protein Data Bank) and, in the case of Na+, found some displacement of the atoms inward. This appears to be a major feature of the mode by which the selectivity filter functions. The T75 residues remain fairly close to the X-ray positions for the K+ ion but are pulled slightly inward by the larger field of
10.1021/jp076854o CCC: $40.75 © 2008 American Chemical Society Published on Web 01/05/2008
1294 J. Phys. Chem. B, Vol. 112, No. 4, 2008 the smaller Na+ ion. The displacement is sufficient to lead to a significant difference in cosolvation and a loss of symmetry. Below the selectivity filter there is part of the channel that widens out and contains more than ten water molecules, forming an aqueous cavity. Energetics of the ions in the upper cavity position (just below the selectivity filter) suggest that Na+ is at a relatively high-energy position, compared to K+; further down, the Na+ is completely unstable. K+ should more easily move into and through the cavity and be able to enter the selectivity filter. We are now able to present calculations on energy that are sufficient to allow us to see how Na+ is treated differently by the channel from K+. The energetics, as calculated below, show that there is a clear difference in how the ions would proceed in the channel; further work may add detail, but the basic differences in energy, as found in this work, are robust enough to make clear how K+ can pass through the channel, while Na+ cannot. Calculation Our calculations of the KcsA selectivity filter amino acids near the intracellular entrance of the selectivity filter include water and one ion: Na+ or K+. The amino acids that lined the central cavity and constituted the lower end of the selectivity filter, plus several from the cavity below the selectivity filter, were included, while all those that were some distance away, or whose side chains pointed away while the backbone was several angstroms distant from the central region, were omitted. Those included were: T74, T75, I100, G103, and T107. Twelve water molecules were also included. However, for K+ an additional optimization with F103 and six additional water molecules (but see below for other restrictions) was completed as a check; this calculation had a total of 439 atoms instead of the 341 atoms of the original calculation (some of these atoms were optimized, while others were frozen). A few ion-water distances changed, in two cases as much as 0.5 Å, but not enough to affect any conclusions. Thus, the F103 phenyl group and the additional six water molecules are sufficiently distant from the cavity that it is safe to neglect them, and we can therefore be confident that the system we have studied is large enough to be appropriate for the actual channel; the check did not change the conclusions. In the calculations, the outer methyl groups were frozen in the X-ray position to ensure the correct positioning of the main backbone atoms (see Figure 1 for details), while side chains and water molecules were optimized. In the supplementary calculation, the F103 plus six additional water molecules were included; all of the water plus F103 was optimized to check its position. The result showed that the side chain was more than 10 Å distant from the pore lining; hence, our initial approximation, omitting it from the computation, is reasonable for the determination of the behavior of the water, the ion, and the amino acids lining the cavity. The calculation was done at HF/ 3-21G level, a limited method; the size of the system already strains the computing resources. At this computational level, the geometry is reasonably accurate, but the absolute energy is not good enough. The correlation energy that is omitted by using HF is about 1% of the total energy, and the small basis set limits energy accuracy further. The only effect of the limited basis set on the geometry is expected to be bonds that may be slightly too short; the relative bond lengths should be approximately accurate, and the overall geometric relations will be accurate. In the optimization, 18 waters were included for both Na+ and K+ cases.
Kariev and Green The calculations were done with the Na+ or the K+ started in each of three positions: (i) in the center of the cavity, (ii) just below the selectivity filter, and (iii) in the lowest binding site (S4) in the selectivity filter. By doing this, we looked to see whether there were local minima at these positions; although in principle “optimization” should find the global minimum, a local minimum will generally trap the system, and in this case we wish to take advantage of this fact. We found local minima in five out of six cases (although not at exactly the starting positions, especially for Na+). In the sixth case, the Na+ ion starting at the mid-cavity position, there was no local minimum, and the ion moved to the position at which it was optimized when it started at the top of the cavity. The larger K+, in contrast, was hydrated in place at the center position. Energy was obtained from single point calculations on a truncated system at the B3LYP/6-31+G** level. The truncation left 8 amino acids (T74 and T75 of each domain) plus 8 water molecules (for both Na+ and K+, for both positions for which the energy calculations were done). This gives fairly high accuracy (the method is accurate, but the truncation requires us to express caution); relative energies, and energy differences, are adequately determined. The location for the truncation is based on choosing those groups that interacted directly with the ion and those water molecules in the immediate vicinity. Atoms more than about 5 Å distant from the ion, or from one of the amino acid hydroxyl groups in the calculation, are generally omitted. We are particularly interested in differences between Na+ and K+, which are likely to be only minimally affected by distant groups that are similarly situated for either ion. Errors in Table 2 will be much smaller than the differences on which the conclusions are based. The energy includes ionprotein, ion-water, and three body (ion-protein-water) interactions. The protein was truncated at T74 plus T75 because the other amino acids did not interact nearly as strongly with the ions and could be assumed to be the same with Na+ and K+. The 10 water molecules that were dropped in going from optimization to energy calculation were also remote and should make little difference. The total number of water molecules in the computation was the same for both ions. Results The essential results are shown in Figure 1, in which two cases, with Na+ and with K+, are shown side-by-side for two positions, the upper cavity and the S4 binding site. Certain key distances are marked on the figure, but the complete set of relevant distances is given in Table 1. We will see that the energetics is such as to show a large difference between the two ions. The equations are given later in the discussion of energy. These energy differences are much greater than could be compensated by any entropic term. A. The S4 Binding Site. The Na+ ion is pulled asymmetrically to bind to two of the four T75 residues by way of their hydroxyl groups, and its distance from the neighboring oxygens is 2.6 Å, and a coordination number of seven. There are all four T75 hydroxyl oxygens (ion-oxygen distances: 2.86, 2.63, 2.84, and 3.04 Å), two peptide carbonyls (2.69 and 2.91 Å), and one water (2.91 Å). The K+ is therefore bound by all four domains, with six protein oxygens, and only one water completes the seven-member solvation shell. Four members of its solvation shell are from T75. The symmetry of
Selectivity in the KscA Channel
J. Phys. Chem. B, Vol. 112, No. 4, 2008 1295
Figure 1. (a) Potassium in the lowest selectivity filter position (S4): cutaway view, with one domain deleted for visibility. In this calculation, 20 amino acids and 12 water molecules are included (341 atoms total). F103 is not included. Note the solvation of the ion: only one water molecule is in the solvation shell, and the primary source of solvation shell oxygens are the hydroxyl group oxygens, with only one carbonyl. The asymmetry is markedly less than with Na+ (see part b). Colors: solvating water, dark blue oxygen; all other oxygens, including those from tyrosine, are red; carbon is light blue, nitrogen green, and hydrogen white; frozen atoms are black. The ion is a small red plus sign with an arrow pointing to it. (b) Na+ in the S4 position. Two waters instead of one are in the solvation shell, together with two carbonyl oxygens and two hydroxyl oxygens. Note the much greater asymmetry than in part a; the figure is rotated to center the ion. The ion is very close to two domains (one is deleted in this figure) and far from two. All arrows, colors, atoms, and deletions are as in part a. (c) K+ in the upper cavity position: again only one water is in the solvation shell, with the T75 hydroxyls providing four of the oxygens. Note that although the ion is below its previous position, the protein atoms and much of the water is not nearly as different from part a as part b is from either. The two K+ positions show a configuration much more similar than K+ is to Na+ in the same position. All arrows, colors, atoms, and deletions are as in part a. (d) Na+ in the upper cavity position: this time not only is the Na+ placed asymmetrically, but it includes 5 water molecules in its solvation shell, so that it is held back into the cavity. Only one oxygen in its solvation shell comes from a member of the selectivity filter. Nevertheless, the resemblance to part b overall is greater than to either K+ configuration. Again, all arrows, colors, atoms, and deletions are as in part a.
the four domains is still not perfect but is much closer than for Na+. The distances from the ion to the oxygens are also larger. While the Na+-solvation bonds are in the 2.24-2.67-Å range (including the link to the T75 oxygen), the K+ links, as just noted, are 2.63-3.04 Å. In effect, the K+ ion is appreciably larger than the Na+ ion. The range of ion-ligand distances
barely overlaps. While a word of caution is required (all the bond distances may be very slightly short with a small basis set, and the cutoff between the water-K+ distances counted as solvating and neighboring is not extremely sharp), the differences between Na+ and K+ are clear and robust. (See also Table 1.)
1296 J. Phys. Chem. B, Vol. 112, No. 4, 2008
Kariev and Green
TABLE 1: Distances to Coordinating and Nearby Oxygens (Distances in Angstroms)a oxygen type
top of cavity K+
S4 position K+
S4 position K+ checkb
top of cavity Na+
S4 position Na+
Thr-75sOH Thr-75sOH Thr-75sOH Thr-75sOH Thr-75sCdO Thr-75sCdO Thr-75sCdO Thr-75sCdO water water water water water water water water
2.82 2.94 2.92 2.79 2.70 4.07 4.88 4.11 2.68 3.14 3.36 3.54 4.47 4.86 5.59 5.91
2.86 3.04 2.84 2.63 2.69 2.91 3.55 3.78 2.91 3.73 3.72 4.11 5.78 6.26 5.22 6.36
2.90 3.58 2.75 2.63 2.60 3.23 3.43 3.48 2.88 4.11 3.69 4.42 5.88 6.80 5.42 6.82
3.55 4.41 4.53 2.51 5.78 6.89 4.74 3.39 2.21 2.27 2.40 2.45 2.58 2.93 3.37 3.48
3.94 3.90 2.38 2.24 4.37 4.81 2.67 2.38 2.40 2.36 3.55 3.78 4.19 4.30 4.41 5.63
a Distances in boldface are part of the hydration sphere of the ion; the others are nearby oxygens that are not part of the inner sphere. The sCdO are the backbone carbonyls of T75, and the sOsH are the side chain hydroxyls of the same threonine. This calculation had 12 water molecules total. b Check: six additional water molecules and F103 were included in this calculation. All 18 water molecules and the F103 side chain were optimized in addition to the sidechains optimized in the earlier calculation (HF/3-21G). The oxygen positions were generally within 0.3 Å of the previous positions, at worst 0.5 Å; the six water molecules not shown had distances 8-10 Å from the K+. The F103 side chain distance was also in this range.
TABLE 2: Interaction Energy Terms (kJ/mol); Ions in Top Cavity Position term 1 term 2
term 3
Na+ -292.0 -295.4 -377.2 (n ) 5 waters) K+ -472.0 -17.2 -32.6 (n ) 1 water) energy difference (Na+-K+) +180.0 -278.2 -344.4
B. The Upper Cavity Site. Here there is also a severe difference between the K+ and the Na+. The Na+ is drawn to two of the tyrosine oxygens, but the hydration shell is mainly water; five of the six oxygens in the Na+ shell come from water molecules and only one from threonine. K+ in contrast has two waters in its hydration shell, with two carbonyl oxygens and two hydroxyls from threonine side chains. The K+ is again close to symmetrically placed with respect to the hydroxyls at the selectivity filter entrance, although less symmetric with respect to the carbonyls. C. The Center of the Cavity. Here, there is no minimum for Na+. The ion, placed in this location, is optimized at the upper position. K+, however, is successfully hydrated by four close water molecules above the ion (approximately 2.7 Å) plus four somewhat more distant molecules below the ion (over 3.5 Å) and does stay at the center position. We do not discuss this position in detail in this paper, but the difference between Na+ and K+ is instructive. Combined with the high energy of Na+ at the upper position (which is nevertheless lower than in the center position, or the optimization would not have moved the ion from the center to the upper position), it suggests that the Na+ may have great difficulty entering the cavity at all. It is not absolutely certain that the open configuration would have the same lack of a minimum as we find in the closed position for the ion. Since the open position might allow some change in spacing between the lining residues, there is some possibility that Na+ might find itself more “comfortable”, and the minimum might exist. However, it is unlikely. We could also check the deviation from the X-ray positions that we found during optimization. The O-O distances for the T75 hydroxyls were all 3.73 Å in the X-ray structure; the four distances ranged from 3.82 to 4.38 Å after optimization for K+ in the upper cavity position and 3.63 to 4.13 Å for the K+ in the S4 position. The Figure shows that the hydroxyls twist slightly to produce this much asymmetry. For Na+ the corre-
sponding distances were 3.92-4.87 Å in the upper cavity position and 3.94-4.41 in the S4 position. The corresponding distances for the carbonyl oxygens were: for X-ray, 3.21 Å, for K+, 2.88-4.64 Å (upper cavity), 2.91-4.07 Å (S4 position), and for Na+, 2.92-4.76 Å (upper cavity) and 2.87-4.68 Å (S4). For Na+ the distortion from the 4-fold symmetry of the X-ray coordinates was more severe. The hydroxyl oxygen to carbonyl oxygen distances were 3.05 Å (X-ray), 2.90-3.19 Å (K+ upper cavity), 2.90-3.07 Å (S4), and for Na+ upper cavity 2.973.29 Å, for S4, 2.91-3.04 so that the vertical distortion was small. However, as the figures show, there is a moderate amount of twisting in the two oxygen rings in response to the presence of the ions, and the distortion is different with K+ than with Na+. The intradomain distance (carbonyl oxygen to hydroxyl oxygen) appears much less subject to distortion and the optimization gets the X-ray value within 0.15 Å in all but one Na+ case, which is off by 0.24 Å. The large Na+ deviations for the hydroxyl side chains alone are not surprising as Na+ essentially pastes itself against two domains (this is easily seen in Table 1, where the ion-oxygen distances are shown) and remains distant from the other two; this phenomenon is likely to be related to the selectivity of the filter. Because the Na+ is close to two of the oxygens, they are pulled together and thus pull apart from the other two. The interdomain symmetry breaking is smaller for K+, and the reasons for what there is are not entirely obvious; some may come from a slightly greater attraction to one wall. The largest deviations are in the upper cavity position; this position was not found in the X-ray structure, is less stable, and is therefore not a good case for comparison with the X-ray structure. (It may also be that the ion disrupts hydrogen bonds that hold the domains together at that point, but this is not established by data.) D. Energy. We do not have enough calculations to make definitive statements that determine exactly the energy of the barriers to ion motion. We have begun, and although completion will take appreciable additional work, even the limited calculations available so far help us understand the differences between Na+ and K+ in the channel. Table 2 shows the energy of the system at the upper cavity position of the ion. The energy is from single-point calculations on the truncated system (T74 and T75 are the only amino acids
Selectivity in the KscA Channel
J. Phys. Chem. B, Vol. 112, No. 4, 2008 1297
in the energy calculation) at the B3LYP/6-31+G** level. We are able to determine energy, and energy differences, by these calculations. The differences in entropy between ions cannot be calculated from QM (zero temperature) calculations. However, as we will see, the energy involved is likely to be considerably greater than the entropy term. The overall energy of an ion interacting with its surroundings can be broken into three terms
∆E ) ∆E(ion-protein) + ∆E(ion-water) + ∆E((ionprotein)-water) (1) Each term on the right-hand side corresponds to a process
First term: M+ + P f M+-P
(2a)
Second term: M+ + 8H2O f M+(H2O)8
(2b)
Third term: M+-P + n(H2O) f M+P(H2O)n
(2c)
We can then take the net process (2a) - (2b) + (2c) to get
M+(H2O)8 + P f M+P(H2O)n + (8 - n)H2O
(2d)
Eight water molecules were used in the calculation, in particular in eq 2b, because K+ is hydrated by eight water molecules in the center of the cavity. This will eventually make possible the complete determination of thermodynamic terms. To compare ions, we need to subtract the extra water that appears because n is not the same for the two ions; thus, an additional term of 8 - n waters must be added to balance eq 2d. In these equations, P, the protein, is the matrix of eq 1. M+ is either K+ or Na+, and n is the number of water molecules. It varies here, with n ) 5 for Na+ and n ) 1 for K+ for the upper cavity position. However, we can still subtract the ∆E values of Na+ and K+
∆∆E ) ∆E(Na+) - ∆E(K+)
(3)
The third term, eq 2c, is not negligible. Table 2 gives these terms for the upper cavity position, which is relevant for the case we are concerned with. The coordinates of the upper part of the system optimized at HF/3-21G level were used, as described above. The net ∆∆E(Na+-K+) ) Term1 - Term2 + Term3 ) +113.8 kJ/mol (this is the difference between ions for the sum/ difference of the terms in the last row; this corresponds to eq 2d. Table 2 suggests a seeming anomaly: the interaction of K+ with the protein matrix (Term1) is actually larger than than that of Na+. This may be a consequence of the fact that the K+ interacts with all four domains, while the Na+ interaction is primarily with only two domains. There is very limited interaction of K+ with cavity water molecules directly, although the three-body term is larger. The terms holding the Na+ ion in the upper cavity are the interactions with the water; the K+ is at lower energy by interacting with the protein. When it enters the filter, it will be relatively symmetrically cosolvated by the protein oxygens. Na+, if it entered the selectivity filter at all, could not move as it stays on the side of the filter (experimentally, it is a slight exaggeration to state that the Na+ is immobile: its permeability is of the order of 10-3 of that of K+). This is still only one point in the trajectory of the ions, so it does not give an equilibrium constant for the transfer of an ion from one position to another. To do that we need free energy, which we can only estimate at this point.
To get the free energy difference, it is necessary to include entropy; QM calculations give energy at zero Kelvin. However, the entropy difference between ions is not likely to be very important; entropy is known to be similar for K+ and Na+ in small clusters. Kebarle demonstrated this with clusters of up to six water molecules.18 With just six water molecules, the difference in entropic contribution to the free energy at 300 K is only 0.4 kJ/mol. This obviously includes a certain amount of fortuitous cancellation of terms and refers to isolated clusters. However, the K+ and Na+ entropy terms should be sufficiently similar, even here where they would not be expected to contribute to the ∆∆G for the process nearly as much as ∆∆H, which is essentially the same as ∆∆E (there is no pV term of any significance). Therefore, the largest contribution to the free energy is the energy term, which we can identify with the thermodynamic energy. The asymmetry of the Na+ result might also allow a 4-fold degeneracy (approximately), with the maximum (but unlikely) possibility of an R ln 4 term in the entropy, equivalent to a maximum of 10 kJ, still much less than the energy found. Studies of other positions of the ion will make this a more useful result. Discussion The most important results come from the Na+ and K+ ion positions relative to the hydroxyl and carbonyl oxygen atoms in the lower end of the selectivity filter. We can also see the difference in the distortion of the near-cube composed of those 8 oxygens. The Na+ ion cannot bridge the complete set of four domains and produces far more distorted complexes. K+, a larger ion, produces a much more symmetric result; furthermore K+ is “cosolvated” by many more oxygens from the protein, and many fewer from water. Competition between water and protein appears to be a fundamental theme of selectivity. We can most usefully compare our results with those from the MacKinnon laboratory14 and those of Varma and Rempe.15 We have found shorter distances to the solvating oxygens of Na+ than for those of K+, and we have found that the competition between protein and water oxygen plays a key role in the solvation. In this respect we agree with Lockless et al.14 that the size of the ion is important in selectivity. That paper tested a number of ions and found a relation with apparent size, with a boundary between Na+ and K+ in the size for which the channel selects. Our result also shows that the ion size is critical in the difference between types of solvation (protein oxygens vs water). In the upper cavity position, only one water remains in the inner solvation shell, while in Na+ five water molecules occupy five of the six solvation sites. This is consistent with water having a key role in the competition for solvation that determines selectivity. The water plays a structural role in addition to its functional role. The importance of solvation is in agreement also with Noskov and Roux,16 albeit in a slightly different location and form than they had proposed. With Na+, the side chains also move in slightly, while there is no such effect with K+. The X-ray results of Lockless et al.14 show a somewhat similar effect but above, i.e., extracellular to, the region we examined (they show binding site S2 in their Figure 4). The Na+ apparently interacts strongly with the oxygens that coordinate it, pulling them in, while the greater distance and weaker interaction maintained by the K+ ion does not have this effect. The effect appears similar in X-ray and computational results. The difference between the NaK and the KcsA channel is more extracellular in the selectivity filter than the section we
1298 J. Phys. Chem. B, Vol. 112, No. 4, 2008 studied (also near S2), but apparently small changes in the lower part of the filter that may be consequent on the more extracellular change are already sufficient to affect the difference in selectivity of the two types of channel. The Role of Threonine at the Entrance to the Selecivity Filter: Since the threonine at the beginning of the TVGYG sequence is strongly conserved, it must be a necessary part of the selectivity filter, consistent with our results. Subtle differences in position of the atoms appear to contribute to their ability to solvate the ions and thus contribute to the selectivity of the channel. The ab initio calculation enables us to see how the water shares coordination of the ions and how the competition with the protein oxygens is different for the two ions. This difference is the key to the selectivity. Energy. The ∆∆G that we have discussed corresponds to the relative strength of association of Na+, compared to K+, with the protein, specifically T74 and T75, accounting for the role of water in the process. We see that Na+ is much more strongly held by water at the top of the cavity than is K+. There are two possible points that are worth investigating. The fact that the Na+ energy appears much higher at the upper cavity point than K+ energy, and Na+ does not even have a minimum at the center of the cavity, so that it must have an even higher energy there, suggests that possibly Na+ cannot even enter the cavity. The threonines thus affect the solvation of the ion in the entire cavity, possibly leading to selectivity at a much lower position in the channel. Because Na+ might be unable to enter the cavity at all, the selectivity would occur well below the filter itself. However, if a Na+ did reach the selectivity filter, it would be pulled to one side in the channel and almost certainly be too tightly bound in the lower part of the selectivity filter to progress. The possibility that the difference in solvation, leading to large energy difference for the ions further down in the cavity, pushing the selectivity below the bundle crossing, is very attractive. That way, there would be no Na+ actually in the selectivity filter, or near its entrance, positioned to interfere with the passage of a subsequent K+ ion. If the Na+ reached the selectivity filter, it is hard to see how it could be removed and, as consequence, hard to see how that channel could be saved for future function; a K+ could not pass a trapped Na+. However, at the moment it is not possible to state this with certainty. One other point should be mentioned: these calculations have begun with the closed channel configuration. While our earlier results19 suggest that the difference between closed and open states is primarily at the intracellular end, the conformational change leading to the open state may also slightly alter the behavior of water in the cavity. Summary Interaction of the ion with hydration and protein oxygens, producing cosolvation, determines the selectivity. The difference in effective ion size produces the differences in ion solvation.
Kariev and Green The exact upper limit of the advance of the Na+ in the channel remains uncertain, although the bottom of the cavity looks to be an attractive possibility for this limit. Acknowledgment. This research was performed in part using the MSCF supercomputer facility in the William R. Wiley Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the U.S. DOE, Office of Basic Energy Research, and located at PNNL. Support has been provided in part by a PSC-CUNY grant to M.E.G. References and Notes (1) Shrivastava, I. H.; Tielemann, D. P.; Biggin, P. C.; Sansom, M. S. P. K+ vs Na+ ions in a K channel selectivity filter: a simulation study. Biophys. J. 2002, 83, 633-645. (2) Capener, C. E.; Proks, P. Ashcroft, F. M.; Sansom, M. S. P. Filter flexibility in a mammalian K channel: models and simulations of Kir6.2 mutants. Biophys. J. 2003, 84, 2345-2356. (3) Sansom, M. S. P.; Shrivastava, I. H.; Bright, J. N.; Tate, J.; Capener, C. E.; Biggin, P. C. Potassium channels: structures, models, simulations. Biochem. Biophys. Acta 2002, 1565, 294-307. (4) Latorre, R. Molecular origin of ion selectivity and gating in voltage -dependent ion channels. Cienc. Cult. 1998, 50, 196-207. (5) Lu, T.; Ting, A. Y.; Mainland, J.; Jan, L. Y. Schulz, P. G.; Yang, J. Probing ion permeation and gating in K+ channel with backbone mutations in the selectivity filter. Nature Neurosci. 2001, 4, 239-246. (6) Cordero-Morales, J. F.; Cuello, L. G.; Perozo, E. Voltage-dependent gating at the KcsA selectivity filter Nature. Struct. Mol. Biol. 2006, 13, 319-322. (7) Cordero-Morales, J. F.; Cuello, L. G.; Zhao, Y.; Jogini, V. C.; Roux, D. M. B.; Perozo, E. Molecular determinants of gating at the potassiumchannel selectivity filter. Nat. Struct. Mol. Biol. 2006, 13, 311-318. (8) Thompson, J.; Begenisich, T. Two stable, conducting conformations of the selectivity filter in Shaker K+ channels. J. Gen’l. Physiol. 2005, 125, 619-629. (9) Negoda, A.; Xian, M.; Reusch, R. N. Insight into the selectivity and gating functions of Streptomyces Lividans KcsA. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 4342-4346. (10) Compoint, M.; Ramseyer, C.; Huetz, P. Ab initio investigation of the atomic charges in the KcsA channel selectivity filter. Chem. Phys. Lett. 2004, 397, 510-515. (11) Huetz, P.; Boiteux, C.; Compoint, M.; Ramseyer, C.; Girardet, C. Incidence of partial charges on ion selectivity in potassium channels. J. Chem. Phys. 2006, 124, 044703/1-044703/9. (12) Bostick, D. L.; Brooks, C. L. Selectivity in K+ channels is due to topological control of the permeant ion’s coordinated state. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 9260-9265. (13) Ju, M.; Wray, D. Molecular identification and characterization of the human eag2 potassium channel. FEBS Lett. 2002, 524, 204-210. (14) Lockless, S. W.; Zhou, M.; MacKinnon, R. Structural and thermodynamic properties of selective ion binding in a K+ channel. PLoS Biol. 2007, 5, 1079-1088. (15) Varma, S.; Rempe, S. B. Tuning ion coordination architectures to enable selective partitioning. Biophys. J. 2007, 93, 1093-1099. (16) Noskov, S. Y. R. B. Importance of hydration and dynamics on the selectivity of the KcsA and NaK channels. J. Gen’l. Physiol. 2007, 129, 135-143. (17) Shi, N.; Ye, S.; Alam, A.; Chen, L.; Jiang, Y. Atomic structure of a Na+ and K+ conducting channel. Nature 2006, 440, 570-574. (18) Kebarle, P. Ions and Ion Pairs in Organic Reactions, Mir Publishers, Moscow 1975. (19) Kariev, A. M.; Znamenskiy, V. S.; Green, M. E. Quantum mechanical calculations of charge effects on gating the KcsA channel. Biochem Biophys. Acta 2007, 1768, 1218-1229.
