The Open Gate of the KV1.2 Channel: Quantum Calculations Show the Key Role of Hydration

Abstract

The open gate of the K_v1.2 voltage-gated potassium channel can just hold a hydrated K⁺ ion. Quantum calculations starting from the x-ray coordinates of the channel confirm this, showing little change from the x-ray coordinates for the protein. Water molecules not in the x-ray coordinates, and the ion itself, are placed by the calculation. The water molecules, including their orientation and hydrogen bonding, with and without an ion, are critical for the path of the ion, from the solution to the gate. A sequence of steps is postulated in which the potential experienced by the ion in the pore is influenced by the position of the ion. The gate structure, with and without the ion, has been optimized. The charges on the atoms and bond lengths have been calculated using natural bond orbital calculations, giving K⁺ ∼0.77 charges, rather than 1.0. The PVPV hinge sequence has been mutated in silico to PVVV (P407V in the 2A79 numbering). The water structure around the ion becomes discontinuous, separated into two sections, above and below the ion. PVPV conservation closely relates to maintaining the water structure. Finally, these results have implications concerning gating.

Introduction

Ion channels

Ion channels have been the subject of an immense literature; the major questions concerning the channels include the mode of gating (opening and closing), conduction mechanism, selectivity (Na⁺ vs. K⁺) of the channel, and the kinetic states through which the channel passes when activating and inactivating. In this work, we will discuss only conductivity and the gate itself. Neither the kinetics nor the selectivity filter is considered here. A thorough review of the literature through ∼2001 was given by Hille (1). Advances since then have been stimulated by the availability of x-ray structures, first from the laboratory of MacKinnon, who, with co-workers, has provided a structure of the prokaryotic KcsA channel (pdb: 1k4c) (2), in closed conformation, and the eukaryotic Shaker K_v1.2 channel (pdb: 2A79) (3,4), which has voltage-sensing domains, in the open conformation. The latter was extended by normal mode analysis, which included the hydrogens (pdb: 3Lut (5); the 2A79/3Lut amino acid numbering is used for the remainder of the work). Several mutually incompatible modes of gating, each involving some form of conformational change of the voltage-sensing domains, particularly its S4 transmembrane segment, have been proposed, and these have been reviewed multiple times from different points of view (e.g., see (6–8)). There is evidence that has been interpreted to favor each of these, and to rule out the others. We have offered a different point of view on gating, and discussed it in detail recently (9), and earlier (10–12). A new x-ray structure for a sodium channel suggests a very limited movement of S4, and of the pore, and is therefore far more compatible with our proposal than the standard proposals (13). In this work the primary focus is on the gate itself, rather than on the mechanism of gating. The conduction mechanism has also been the subject of multiple studies, but the question of the state of the ion in the gate, with implications for the conduction mechanism, has not been emphasized; this is the primary focus of this work.

A wide open gate would lead to serious difficulties, and contradict the x-ray data on the open state (4). An entering ion would be electrostatically pushed back from the gate by an ion in the channel cavity, which does appear in x-ray structures. Although long pores (>100 Å) have dipoles that may effectively screen ions (14), the distance between the gate and the ion in this cavity is ∼6 Å, so that no dipoles intervene. Leung (14) notes that the long pores are unlike KcsA, whose upper pore is similar to that of the channel we are principally considering, (the KcsA gate is different, but still must hold an ion). The water molecule between the ions is itself not able to do any effective screening, as it cannot orient in any position that allows both ions to be satisfied. The gate region at the bottom of the cavity increases in radius by only ∼2.5 Å, resembling that for the recently reported sodium channel (13). This allows the gate to complex the hydrated K⁺ ion, holding it in a potential minimum, so that it can push the ion in the cavity forward through the selectivity filter, rather than having the entering ion pushed backward into the solution from which it came.

Quantum calculations on ion channels

A fair amount of work has been done on quantum calculations of ion channels. In each case, a part of the channel is chosen for study, and the calculations are carried out locally. This is what we have done as well, focusing on the gate. Selectivity, for example, has been recently reviewed by Varma and others (15). Varma, Rempe, and co-workers, have written extensively on the hydration of ions in relation to selectivity: see, for example (16). Dudev and Lim (17–20) have also carried out quantum calculations on selectivity of channels. Proton wires, proton transfer, and proton tunneling, topics that are peripherally relevant here, and probably more important to gating, have been studied by Hammes-Schiffer (21,22). Bucher, Rothlisberger, and co-workers, have applied ab initio molecular dynamics (MD), (mainly Car-Parinello MD) to channels, especially but not exclusively on questions of selectivity (23,24). Extensive calculations by Hummer and co-workers on water at channel gates, water wires, and proton motion has called further attention to the importance of the hydration at the gate; most of the Hummer group work is not quantum mechanical, but it is clearly careful and informative (25,26). Voth and co-workers have applied the empirical valence bond method to water and proton transport (27); as far as we are aware there has not been an application of empirical valence bond to the type of channels we are considering. Earlier work from our group also considered proton tunneling in relation to channels (28).

This study

We have carried out optimizations (determination of the energy minimum) for the gate region of a potassium channel, K_v1.2, starting from the 2A79/3Lut x-ray structure with hydrogens added (3–5). Water has been added to that structure, and its relation to the protein and the K⁺ ion in the gate is the central finding of this work. We see the relation between the open state dimensions of the gate’s pore section, where there is a highly conserved PVPV section, and the extent of hydration. In addition to the calculations on the wild-type (WT) gate, we also calculated a PVVV mutant, finding that the continuous water column, found in the WT, broke when an ion was present. This might account for the fact that other hydrophobic mutants in that position lead to severely right-shifted channels (i.e., difficult to open, as shown by the increased depolarization required for opening). The break in hydration of the ion would be expected to severely limit conductivity, as the ion is tied into the protein at the gate. Finally, we have calculated the bond length, bond order, and charge transfer to the K⁺ ion, and the electrostatic field in the vicinity, which, taken together, allow us to get a good estimate of the way in which the ion is held at the energy minimum, with implications for conduction, and gating as well.

Results

The main new results, to our knowledge, are the optimization of the protein with water coordinates at the gate, as well as the calculation of the consequences of a mutation of the PVPV hinge sequence to PVVV (P407V in the 2A79 and 3Lut structure). The optimized configuration is shown in Fig. 1 for both the WT gate and the mutant, with and without an ion. The water rearranges, although there is very little difference in protein conformation with the ion in the gate or not; this suggests that there would be little change as the ion enters the gate. The figures have the extracellular side up, as in the usual convention.

Figure 1.

Gate configuration: Three out of four domains are shown in light blue; the fourth (front) is omitted for clarity; hydrogen bonds are inserted by gOpenMole. For parts B and D, the large red spheres are oxygen atoms of the water hydrating the K⁺ (orange spheres indicated by arrows), the smaller attached spheres are the corresponding water hydrogens. Nonhydrating waters, and all waters in parts A and C, are shown in heavy blue, protein other than P407 or V407 in light blue, P407 and V407 side chains in heavy red lines. (A) WT: Water and protein backbone are shown with no ion. The water forms a network that is roughly cylindrical, filling the space between the protein domains; and is fairly symmetric. (B) WT, ion added: Protein-protein distances are very similar, but the water is asymmetric, with an extra water molecule on one side of the ion, so that the distance to one proline is ∼6 Å, to the opposite side, 9 Å. The water structure is reoriented around the ion; the weak interactions with the protein, especially above the midpoint of the gate, are apparently of somewhat less importance. (C) The PVVV mutant (P407V) with no ion. The water column is narrower than in the WT, with the diameter of the center of the gate now down to ≈11 Å. (D) PVVV, with an ion: the ion breaks the water column, which has narrowed considerably. Three water molecules hydrate the ion above (on the pore cavity side), and two below, instead of the contiguous six water molecules in the WT case; the upper and lower groups have no hydrogen bond connections in the mutant. (There is one seemingly close water molecule shown as not hydrating, in front of the ion; this has its oxygen pointing away from the ion, at the large distance of 3.54 Å, both reasons for it not to be considered a hydrating ion.) To see this figure in color, go online.

The calculation keeps the x-ray protein structure in Fig. 1 A almost intact, albeit with the gate radius expanded 0.5 to 1 Å (hence, diameter increased up to 2 Å) compared to that in the x-ray structure (see Table 1). The atom positions thus agree with the x-ray structure (no ion case) within ∼1 Å, and the overall conformation is maintained. Table 1 shows the key distances. The confirmation calculations at a higher level showed negligible differences from the first stage calculations: see computational details section in the Supporting Material.

Table 1.

Atom pair distances (Å)

Atom pairs (P407)	X-ray	No ion, calculated	With ion, calculated
N-Na	14.27	15.61	15.44
CA–CAb	13.62	15.38	15.28
CG–CGc	12.03	13.95	14.03

^aN, Nitrogens on ring, proline.

^bC_A are the carbon atoms next to the nitrogens on the ring.

^cC_G are the carbon atoms third from the nitrogens, on the ring.

These results show no effect on the diameter of the presence of an ion. There is also some symmetry breaking in the calculation, with the two diameters at the gate not identical, whereas the x-ray structure is necessarily fourfold symmetric; we did not impose symmetry. There does not appear to be, a priori, any reason that symmetry should not be slightly broken, even with no ion. The closest amino acids to the pore pathway are the four P407s of each domain. The ion approaches one of these four P407s more closely. The distance from the ion to one nitrogen on a proline is close to 6 Å, whereas the opposite proline nitrogen is ∼9 Å distant, with an extra water molecule inserted on one side of the ion. The solvation shell is completed by the protein domain with the closest approach of the ion. An additional optimization was done from a position in which the ion was started 1 Å to the side, to test asymmetry further. The ion found a minimum position 0.83 Å off center in the plane orthogonal to the pore axis, at slightly higher energy; with the ion in the middle position of the gate (defined by average position of the proline ring nitrogens) in the PVPV case, energy equals −15989.4028 H, with the ion at middle +0.83 Å, −15989.3989 H. The difference in electronic energy is thus 0.004 H ≈ 4 k_BT, or ∼2.5 kcal (calculated using BLYP/6-31G^∗∗, and the 0.004 H difference confirmed with B3LYP/6-311G^∗∗, single point calculation on the previously optimized structure). The on-axis position appears to be the global minimum. Table 1 shows bond orders for both minima.

Charge transfer

The strong hydration of the ion is accompanied by charge transfer from the ion, mainly to the water oxygens (equivalently, electron transfer from oxygen to the ion). This also suggests that change in the hydration brought about by protonation/deprotonation of residues in the neighborhood (not necessarily immediate neighbors), plus accompanying side-chain reorientation, could disrupt hydrogen bond networks. From natural bond orbital (NBO) calculations (29), the Natural Population Analysis charge on the K⁺ ion is 0.762 (PVPV, middle), 0.759 (PVPV, middle +0.83 Å), 0.773 (PVVV). The charge has been transferred, as might be expected, largely by electron density transfer to the 4s and 4p orbitals of potassium: in the PVPV (middle) case, the 4s orbital has occupancy 0.0436, the sum of the three 4p orbitals gives 0.155, accounting for 0.199 charges; the remainder is largely in the 5s and 5p orbitals (0.029 total occupancy), leaving 0.013 for all other orbitals. Density functional theory may exaggerate the charge transfer to a small extent, but the charge transfer is clearly appreciable. For other results showing charge transfer from water to K⁺ see Soniat and Rick (30), and Varma and Rempe (31), who found slightly less charge transfer, albeit in slightly different conditions. The lesser hydration of the mutant makes little difference to the charge transfer. Failure to account for the charge transfer in a simulation will clearly give misleading results, as both electrostatics and bonding forces change; these changes are missing in classical potentials, used in most MD simulations.

The PVVV structure

The mutant P407V, illustrated in Fig. 1 part C and D, showed a very different channel. With an ion, the water structure almost collapsed: that is, the water separated into two sections that were not hydrogen bonded to each other, nor otherwise connected, and the protein distances across the gate became smaller; without an ion, the distance across dropped, although a continuous water structure through the gate survived. In the WT, the shortest diameter in the ion pathway, with no ion, is the valine V406 C–C distance of 12.14 Å. In the mutant, this distance actually gets larger (14.45 Å), but the V407–V407 shortest C–C distances are only 11.23 and 10.94 Å (slight asymmetry). This is >1 Å shorter than in the WT. The closed channel appears to have diameters of ∼8 Å (cf. KcsA). It appears that the mutant water structure collapse may be partly due to the decrease in channel diameter, which moves the gate closer to the closed configuration. The WT has 6 hydrating waters for the K⁺ ion, if a molecule 3.04 Å distant is counted in the hydration shell. The mutant has just five hydrating molecules, split into two separate sections. It is apparent that the proline is required to maintain the structure of the water in the gate. Both WT and mutant are somewhat asymmetric.

Electrostatics

The optimized WT structures, with and without ion, were used in a Gaussian cube calculation to obtain the electrostatic contours for the potential in the critical region. Fig. 2 shows the results. The potential with the ion is calculated for the contribution of everything except the ion; the contribution of the ion to the electrostatic potential is omitted as the potential acting on the ion is what is needed. Fig. 2 A shows the electrostatic contributions of all atoms, in the presence of an ion, whereas Fig. 2 B shows the contributions of the same atoms with no ion present. The difference between Fig. 2 A and Fig. 2 B is the contribution of the induced change in all other atoms due to the ion in the gate.

Figure 2.

The electrostatic contours from the NBO calculations for the two WT cases, with and without an ion, showing only the central region (as can be seen from comparing Fig. 1, some of the intracellular and extracellular part of the calculation has been omitted here). In Fig. 2A the K⁺ is labeled (K), and three of the waters (3, 4, and 6, the numbering corresponding to the lines in Table 2) that hydrate the ion are easily seen in high contours surrounding the ion, which is slightly left of the origin of the coordinates in this projection. Water molecules 1, 2, and 5 do not show clearly in this plane. Fig. S1 is complementary to this; it shows an orthogonal plane, including water molecules 1, 2, and 5. The geometric orientation for both (A) and (B) has the x and y axes tilted at 45° to the plane of the paper, with the vertical axis oriented such that it points to the intracellular (down) direction. The first four contours counting from the outside are at 1, 2, 4, and 8 mV. The two-dimensional projection has been rotated slightly to allow views of two sides of the ion instead of using a completely symmetric projection; the waters on the left are in the ion’s hydration shell, those on the right belong to the second shell (the ion to water distance on the line orthogonal to the pore axis, to the first water oxygen on the right is 4.7 Å). For case (B), no ion, the origin is placed in the same position. To see this figure in color, go online.

Bond order

In the protein case we have calculated there are three water molecules in the hydrating sphere that are rather strongly hydrogen bonded to water molecules in the second hydration shell. The calculation results are shown in Table 2. The primary shell acts as donor in each case, with bond order 0.133, 0.238, and 0.303, comparable or stronger than the bond order of water to ion. The other first shell water molecules have weaker hydrogen bonds outside the shell, or border the protein. The asymmetry in Fig. 1 D is reflected in the bond order. The mutant differs in bond order, as in other properties. The two top waters in Table 2 are above the ion, the three below are below, and as we have seen, are separated completely from the water molecules above (the xxx in Table 2 shows where the water is missing). This is very different from the WT, which, as can be seen from Fig. 1 C, has a complete water path from top to bottom, with bonding to the protein.

Table 2.

The K⁺ ion in the gate: two positions, plus the PVVV mutant: bond length and bond order^a

WT, ion at centerb	WT, ion 0.83 Å displacedc			PVVV mutante		PVPV
Bond lengthd	Bond order	Bond lengthd	Bond order	Bond lengthd	Bond ordere	2nd shell Bond orderf
3.04	0.0184	3.31	0.056	2.98	0.121	–
2.75	0.024	2.81	−0.036	3.03	0.187	–
2.89g	0.157	2.84	0.135	xxxe	xxx	0.133
2.82h	0.117	2.91	0.112	2.71	0.106	0.238
2.81	0.079	2.74	0.077	2.96	0.109	0.303
2.99	0.1349	2.86	0.165	2.77	−0.046	–

Water molecules here are ordered by position, from most extracellular to most intracellular.

^aNBO calculation from optimized structure with 48 waters, B3LYP/6-311G^∗∗; total 693 atoms.

^bCenter is defined as the position at the center of the near planar-square arrangement of the four nitrogens of the proline.

^cThe ion is started at a position 1 Å to the side of the previous position; optimization returns it to 0.83 Å off center.

^dBond length: K⁺ - O distance for the respective water molecules.

^eWater structure split into two separate domains, one above the ion, the other below; the last two water molecules in the table are not in the first shell of solvation.

^fThese three first shell water molecules of the WT structure have a hydrogen with a competing strength hydrogen bond to a second shell water oxygen; those bond orders are shown in this column; bond lengths are in the 2.7 to 2.9 Å range.

^gStrongest bond order of this water with a nonhydrating water: 0.133.

^hStrongest bond order, this water to nonhydrating water, 0.238.

Discussion

Ion-water energy minimum at the gate

The first result is that there is an energy minimum for the hydrated ion at the gate. The water molecules are at reasonable distances from the ion, oriented appropriately. These molecules transfer charge to the ion, and fit it into the gate, creating the energy minimum. There is a second shell of water, at least at part of the gate, with hydrogen bonds to the first shell water, and attachment to the protein. This should allow the ion, with at least some first shell water, to slide upward toward the cavity. When P407 is replaced with valine, the water structure is destroyed, and the energy minimum seems to bond the ion to the protein, which would prevent it from moving forward to the channel cavity, leading to much lower conductivity. The WT protein largely maintains its coordinates during optimization. The conformation of the water changes, which helps to produce the required energy minimum. The difference in channel diameter and protein backbone distances does not appear sufficient to close the channel by itself; even the 12.47 Å and 11.35 Å diameters of the narrowest section in the PVVV case are large enough to allow an ion to pass. The V399-V399 corresponding distance in the pore cavity is 12.46 Å, and in the gate, V406-V406 in PVPV is 12.14 Å. The proline distance is slightly larger, appropriate for the hydrated ion, which optimizes to the space between prolines. A study of a mutant in a related channel, K_v1.4, showed a much smaller alanine residue, in the K_v1.4 equivalent of the P407A mutant (that is, P558A in the K_v1.4 channel), produces a significantly right-shifted channel (32). The P558G mutant in that channel, which changes to a still smaller residue, produces a right-shifted channel even though it should leave a larger opening. Simply opening the gate wider makes it harder for the channel to conduct. Both a smaller and a larger diameter appear to reduce the current, suggesting that an optimal structure, not just optimal diameter, is needed for proper conduction. It appears that the ion in the WT channel could slide through the gate region, essentially lubricated by the water, although the mutant, lacking the wrapping of water molecules around the ion, could prevent the ion from sliding past. A recent paper, albeit on a different type of channel, and using MD instead of quantum calculations, reaches conclusions that are somewhat similar to ours (33).

Cavity-gate interaction

The ion in the gate must push the ion above it further up (that is, push an ion in the cavity of the channel, which is to the extracellular side of the gate, to the selectivity filter above it). For the cavity ion (which can be seen in the x-ray structure) to be pushed up (knocked on (34)), the ion in the gate must be held tightly enough for the repulsion to drive the cavity ion up, rather than the gate ion down (9). The minimum energy position is not necessarily in the geometric center of the gate, but may be slightly above or below this point, and it is not on the axis (see Figs. 1 and 2). However, to have a current, the ion in the gate must replace the ion in the center when that location is vacated. This requires a minimum in the free energy at the cavity center that is low enough for the gate ion to move there. The gate position then becomes vacant, and the energy minimum at the gate accepts the next ion from the solution (9). The minima adjust to make the transition from the gate to the cavity possible. The magnitude of this shift remains to be calculated. With both occupied, the potential curve allows the cavity ion to move up to the selectivity filter, as one would expect from simple electrostatics. The shifts in energy minima are postulated to result from interaction of the ion with water and protein in the different configurations; shifts of the protein side chains may also contribute. The limited number of physical states that we can calculate gives the fundamental picture. Further work will be needed to find the water structure below the gate, as well as the detailed path followed by the ion through the cavity to the selectivity filter. In addition, multiple groups have calculated the barrier at the selectivity filter and considered it as another gate; we do not discuss it in those terms here, but we do agree that the barrier must exist, and that an electrostatic push is needed to get the ion from the cavity into the selectivity filter, which thus interacts indirectly with the gate in this calculation.

Electrostatics

Fig. 2 A shows that the ion is in a broad electrostatic minimum in the x-y plane. Because the minimum that is 0.83 Å off center is at ≈2.5 kcal higher energy, there is more than electrostatic force involved. The potential along the pore axis is also small in the region of the minimum, but it rises, so that there is an electrostatic barrier of almost 2 k_BT already visible in this calculation, (the figure does not extend far enough up toward the cavity to show this: cf. Fig. 1); it is likely that a higher barrier actually exists, but it may include the effect of several hydrogen bonds. Any contribution from an ion in the center of the cavity above the gate is omitted in this calculation; therefore, the forward barrier shown is smaller than that actually present in the channel when the ion is approaching the gate from the intracellular side. We noted previously that a particular sequence of states must exist for the ion to progress up the pore axis. It is clear that there is an electrostatic component to this, but that electrostatics is not the entire story; at least hydrogen-bonded water molecules, and charge transfer between water and ions, must contribute. This charge transfer does affect the electrostatics in that there is charge on the water molecules due to the electron transfer to the ion, nearly 0.04 charges per hydrating water on average; these charges are part of the source of the electrostatic field.

Relevance to physiology

The calculations find the energy minimum that the system would occupy at 0 K. There is therefore a question of the relevance to the room temperature behavior of the channel. We make the following two observations: First, our result is quite close to the x-ray structure, for the case in which they can be compared. The x-ray structure, however, is determined at roughly 100 K. At that temperature, water is well below any phase change; even amorphous water is not important below ∼220 K (35), so the x-ray structure is also a low temperature form. Nevertheless, the x-ray structure is generally considered to be relevant to understanding the properties of channels. Because the quantum structure comes close to matching the x-ray structure for the case calculated in this study (Fig. 1 A), it applies equally at physiologically relevant temperatures. The slight loss of symmetry predicted by the calculation is reasonable too; symmetry in the x-ray structure is imposed. If this case is realistic, it makes it likely that the other computed structures are also relevant at room temperature. Second, when the structure changes, as in the mutation or the addition of the ion, the largest part of the change is the change in electronic energy. There may in principle be some exchanges of hydrogen bonding partners, as bond arrangements within k_BT of the lowest state also contribute, but these must be effectively equivalent, if the energies are essentially equal. For smaller systems it is possible to calculate the frequency distribution and from this the thermodynamic functions (see the Supporting Material, Table S1). The protein system is far too large for a frequency calculation. If energy differences from one structure to another are large compared to k_BT (e.g., the 0.83 Å K⁺ position shift in the alternate calculation is already ∼4 k_BT above the central minimum), the lowest energy structure will be preserved at physiologically relevant temperatures. One would need energy minima such that significantly different structures are available within <4 k_BT, as exp(−4) <0.02; structures higher in energy than this would contribute too little to matter. With the ion 0.83 Å off center, the structure difference is too slight to alter any of the conclusions of this work: water to ion bond orders differ by an average of 0.026, and the distances by 0.11 Å (maximum 0.27 Å, for the most distant water), so that a displacement to the side of the center of the pore returns to a very similar configuration of hydrating waters. Larger deviations of the ion from this position in the plane orthogonal to the pore axis would distort even the protein structure, so that they would necessarily be at still higher energy. The physiologically relevant structure must therefore be very close to the calculated structure. Hydrogen bonding, although dynamic at room temperature, will have an average very similar to that of the optimized structure.

Implications for gating

Although the primary emphasis of this work concerns the relation of water structure to conduction, it also brings implications for gating. In earlier work (9) we showed that a residue below the gate, H418, when protonated, rotated toward the gate, with the histidine side-chain moving up almost 3 Å; we summarized arguments for the importance of protonation, which changes both the potential at the gate and (not yet calculated, but very probably) the arrangement of water all the way from that residue to the gate (a Δ418 mutant does not function as a channel (36), so it appears that H418 must be important in structuring the channel to allow conduction). From the previous calculation, protonation of H418, and possibly two neighboring glutamates, should close the channel. The present calculation reinforces this, showing it to be very surprising if the protonation did not cause a major change in the probability of the ion being able to enter the gate. We also note that about a third of a century ago it was shown that D₂O slowed gating (37,38), and about a decade later it was shown that it was the last stage of gating that was most affected (39); standard gating models have not always attempted to account for this, but a model in which deprotonation effects gating would do so. Deprotonation would affect the gate through effects on charge transfer, hydration, and water structure, all of which would change with D₂O, as well as potential. Further work will be required to fill in details that would test this model.

Other related phenomena

Two more questions related to electric field, electroosmosis, and electrorheology, require future investigation. The fields here exceed a drop of 1 mV Å⁻¹, or 10⁷ V m⁻¹ in sections of the gate near the minimum, enough to make these real questions; in fact, it is almost certain that electroosmosis must occur, with water pulled through with the ion. This would also be consistent with the alternating water/ion occupation of the sites in the selectivity filter, which seems to require that one water molecule pass through with each ion. If the ion passing through the gate pulls a water molecule with it, this requirement would be satisfied. Furthermore, the fields are large enough that there should be an electrorheological effect, in which the water viscosity depends on the field, however, given the level of evidence now available, it is too early to discuss this here.

Summary

• 1)We have calculated the optimized structure of the gate region of the K_v1.2 (pdb: 2A79) channel, showing the water structure with and without an ion in the gate.
• 2)The ion is well hydrated, although the bond orders are not as strong as for an ion in a water cluster in the gas phase; the water molecules form a continuous hydrogen-bonded structure from the bottom to the top of the gate with the ion present or absent. The hydrated ion structure provides a sort of sleeve that allows the ion to slide through the gate region.
• 3)The ion must have a finely tuned energy minimum at the gate to allow conductance to exist at all.
• 4)A mutant, P407V, would be expected to conduct poorly, if at all, based on the break in the water column. The PVPV sequence at the gate is well conserved, and it appears that this can be attributed to the effect on the water structure, as the major difference with the mutant is in this water structure. Gating the mutant should be appreciably right shifted. The state of local protonation must affect water structure, which suggests that it must affect gating.
• 5)Bond order calculations are consistent with this picture.
• 6)The shorter pore diameter distances for the V407 in the mutant, compared to the shortest WT distance (V406) also suggest a reason for the lower, more difficult conduction in the mutant, and probably are at least part of the reason that the water structure shifts so drastically. Because larger diameters also lower current, it is apparent that the optimum diameter is needed for the fully functioning channel; the Goldilocks (optimum) dimensions just accommodate a hydrated ion, at ∼12 to 12.5 Å.
• 7)The electrostatic contours in the gate region help in understanding much of the barrier that an ion must cross to enter the gate, and then to enter the cavity. There is a large area (on an atomic scale) with relatively flat potential, so that the ion is held more by hydrating water than by an electrostatic minimum at the center of the gate. However, the electrostatic potential is also significant.

Computational details

These are found in the Supporting Material, with references to techniques (40–43).