2362
J . Phys. Chem. 1988, 92, 2362-2366
Theoretical Study of Double Ion Occupancy in a Gramicldln-llke Channel Shen-Shu Sung and Peter C. Jordan* Department of Chemistry, Brandeis University, Waltham, Massachusetts 02254 (Received: August I O , 1987)
The potential energy profiles for Cs+-Cs+,Na+-Na+, and Cs+-Cl- double occupancy in a gramicidin-likechannel are calculated by using the polarizable electropole model. The major part of the interaction energy is the summation of two single occupancy energies plus the Coulombic interaction energy between the two ions. The cooperative effect is small. The local solvation structure near each ion in the doubly occupied channel is very similar to that for single occupancy. Structural comparisons suggest that double occupancy is less probable with Na+ than with Cs+.A favorable cation-cation separation may lower the energy barrier for cation transport. Cation-anion double occupancy may account for possible anion contributions to conductance.
Gramicidin, a model system for biological channels, has been intensively investigated both experimentally and theoretically. Extending our previous work on valence selectivity,' we consider doubly occupied channels in order to investigate the effect that a second ion, in the opposite side of the channel, may have on selectivity and conductance. Experimental evidence is quite persuasive that a t least two K+,Rb+, Cs+, NH4+, or T1+ can occupy a gramicidin channel simultane~usly.~-~ The evidence for Na+ is ambiguous. This paper describes a theoretical study of double cation occupancy and simultaneous cation-anion occupancy in a gramicidin-like channel.
The Model and Method The predominant membrane bound electrically active gramicidin channel is the head-to-head dimer originally proposed by U r r ~ .In~ our calculations the coordinates of the atoms of the helical gramicidin backbone (the polyglycine analogue) are obtained from Koeppe and Kimura's conformational analysis6 A detailed description of both model and method has been provided in previous publication^.'^^ Here we only mention its main features. Each polar group (CO and N H ) of the peptide linkage is modeled by a polarizable dipole oscillating about its equilibrium position and tilting about its original orientation. The force constant and the torsional constant are chosen to be 0.5 mdyn/A and 0.5 X lo-'* J, respectively, corresponding to vibrational frequencies in the range of 200-500 cm-l. The permanent dipole moments of the C O and NH groups determined from their uncompensated partial charges are 2.262 and 0.864 D, respective1 the polarizabilities of C O and NH groups are 1.82 and 1.44 re~pectively.~ The polarizable electropole model of waterlo is used; water is described as a polarizable sphere with a dipole and a quadrupole located at its center of mass. The permanent dipole moment is 1.855 D, the experimental value in gaseous water." The quadrupole moments are Qxx = -4.844 D and Qyy = 5.060 D
TABLE I: Lennard-Jones Parameters interaction u. A water-water water-NH water-CO Na+-water Na+-NH Na+-CO
Cs+-water Cs+-NH
cs+-co
CI--water CI--NH
cr-co
3.149 3.149 3.149 3.3 3.3 3.3 3.8 3.8 3.8 3.8 3.8 4.0
e,
kcalimol 0.425 0.425 0.425 0.06 0.06 0.06 0.1 0.1 0.1 0.1 0.1 0.2
A,
obtained from quantum mechanical calculation,I2 and the p~larizability'~ is 1.444 A3. The ions are charged, olarizable for Na', spheres with polarizabilities 0.312, 2.855, and 2.156 Cs+, and C1-, respe~tive1y.l~The total dipole moment of the various polarizable moieties is the sum of the permanent dipole moment and an induced dipole moment, assumed to be the product of the electrical field and the isotropic polarizability. The resultant dipole moments are computed by an iterative method until selfconsistency is achieved. Thus, electronic reorganization is taken into account in this approach. Then the energy, the forces, and the torques are evaluated. The total energy is the sum of five terms: the electrostatic energy, the polarization energy, the Lennard-Jones energy, the vibrational energy, and the torsional energy. The parameters for the 6-1 2 Lennard-Jones potential describing water-water interaction are 3.149 8,and 0.425 kcal/mol, determined by Gellatly et al.I5 by fitting the water dimer properties. For ion-water interaction the parametersI6 were obtained by fitting the experimental hydration enthalpiesL7and ion-water distances.18 These parameters are listed in Table I. The potential energies and the structures were calculated by a molecular dynamics program. At each position along the channel axis (defined as the z axis) the ions were allowed to move in the plane perpendicular to the axis to minimize the energy at the given z value. The energies and the equilibrium geometries were obK. Because more than tained by cooling down the system to one minimum is possible for each value of z, several initial configurations were tested and the lowest energy obtained was taken as the potential energy at that z. The algorithm proposed by
l3
i;,
(1) Sung, S S . ;Jordan, P. . Biophys. J . 1987, 51, 661. (2) Andersen, 0. S. Annu. Rev. Physiol. 1984, 46, 531. (3) Eisenman, G.; Sandblom, J.; Neher, E. Biophys. J . 1978, 22, 307. (4) Myers, V. B.; Haydon, D. A. Biochim. Biophys. Acta 1972, 274, 313. Procopio, J.; Andersen, 0. S. Biophys. J . 1979, 25, 8a (Abstract). Schagina, L. V.; Grinfeldt, A. E.; Lev, A. A. Nature (London)1978,273,243. Schagina, L. V.; Grinfeldt, A. E.; Lev, A. A. J. Membr. Biol. 1983, 73, 203. Urban, B. W.; Hladky, S. B.; Haydon, D. A. Biochim. Biophys. Acta 1980,602, 331. (5) Urry, D. W. Proc. Natl. Acad. Sei. 1971, 68, 672. Urry, D. W.; Trapane, T. L.; Prasad, K. U. Science (Washington, D.C.)1983, 221, 1064. Wallace, B. A. Biophys. J . 1986, 49, 295. (6) Koeppe, R. E., 11; Kimura, M. Biopolymer 1984, 23, 23. (7) Lee, W. K.; Jordan, P. C. Biophys. J. 1984, 46, 805. (8) Schulz, G. E.; Schirmer, R, H. The Principles of Protein Structure; Springer: New York, 1979. (9) Pething, R. Dielectric and Electronic Properties of Biological Materials; Wiley: Chichester. England, 1979. (10) Barnes, P.; Finney, J. L.; Nicholas, J. D.; Quinn, J. E. Nature (London) 1979. 282. 459. (1 1) Shepard, A. C ; Beer, Y.; Klein, G. P.; Rothman, L. S . J . Chem. Phys 1973, 59, 2254 \-
0022-3654/88/2092-2362$01.50/0
(12) Neumann, D.; Moskowitz, J. W. J. Chem. Phys. 1968, 49, 2056. (1 3) Eisenberg, D.; Kauzman, W. The Structure and Properties of Water; Clarendon: Oxford, 1969. (14) Gowda, B. T.; Benson, S. W. J. Phys. Chem. 1982, 86, 847. (15) Gellatly, B. J.; Quinn, J. E.; Barnes, P.; Finney, J. L. Mol. Phys. 1983, 50, 949. (16) Sung, S.-S.; Jordan, P. C. J . Chem. Phys. 1986,85, 4045. (17) Ashadi, M.; Yamdagni, R.; Kebarle, P. J . Phys. Chem. 1970, 74, 1475. Dzidic, I.; Kebarle, P. J. Phys. Chem. 1970, 7 4 , 1466. (18) Desnoyers, J. E.; Jolicoeur, C. In Modern Aspects of Electrochemistry; Bockris, J. O M . , Conway, B. E., Eds.;Plenum: New York, 1969; Vol. 5, Chapter 1.
0 1988 American Chemical Society
The Journal of Physical Chemistry, Vol. 92, No. 8. 1988 2363
Double Ion Occupancy in a Gramicidin-like Channel
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Gearlg and the Cayley-Klein parameter method of Evans and MuradZ0were used in solving the equations of motion.
Two Cations in an Empty Channel In this section we discuss the interaction between the cations and a gramicidin-like channel with no water present. Figure l a illustrates the interaction energy between the channel and Cs+. The single ion energy is the difference between the energy of an ion-channel system and that of an empty channel. As mentioned in our previous publication,' the potential energy curve for a single Cs+ has its major minima near the channel mouths, about 12.8 8,from the dimer midpoint. Between these two binding sites the curve is relatively flat. This is consistent with the two binding site modeLZ1 The average energy per ion in the doubly occupied channel is half the difference between the energy of two symmetrically located cations in a channel and the energy of an empty channel. (19) Gear, C . W. Numerical Initial Value Problems in Ordinary Differential Equations; Prentice-Hall: Englewood Cliffs, NJ, 1971. (20) Evans, D. J.; Murad, S . Mol. Phys. 1977, 34, 327. (21) Urry, D. W.; Prasad, K. U.; Trapane, T. L. Proc. Narl. Acad. Sci. U . S . A . 1982, 79, 390.
The upper curve in Figure l a is half the electrostatic repulsion energy between the two ions. Dominated by the electrostatic repulsion, the energy in the doubly occupied channel goes up as both cations move close to the dimer midpoint. As in the singly occupied channel, the fine structure in the two cation energy profile is due to the interaction of cations with the peptide's polar groups. The major binding site for Cs' double occupancy is, as was the case for single occupancy, in the mouth, about 12.8 8,from channel center. The radial positions of the two cations at the same axial distance from the dimer midpoint are symmetrically located, governed by the dimer symmetry; they are almost identical with those in a singly occupied channel with a cation at the same axial position. The energy per ion in the doubly occupied channel is nearly equal to the energy per ion in the singly occupied channel plus the electrostatic repulsion. The small difference between these two terms, the cooperative effect, arises from channel group reorientation and polarization in the doubly occupied channel. It decreases from 0.8 kcal for ions at 12.5 and -12.5 8, to -3.3 kcal for ions at 3.6 and -3.6 8,. The axial components of the electrical fields due to each of the cations oppose each other in the region between the two ions and reinforce each other outside. Consequently, the reorientation and polarization effects interfere destructively for those channel groups between the two ions and interfere constructively for the groups exterior to both ions. When both ions are in mouth regions, most of the groups are between them and, therefore, cooperative interactions are destabilizing; the net effect is to increase the energy. When both ions are close to the dimer midpoint, there are more groups outside than between the two ions and the cooperative interactions are stabilizing; the energy is decreased. This effect is large only when two cations are close to each other; however, such configurations are not likely because of electrostatic repulsion. There is an indication, experimentally, for cooperative effects in doubly occupied states, as described in terms of "conformational stabilization".26 The qualitative features of the energy profile of Naf (Figure lb) are very similar to that of Cs' (Figure la). Because it is smaller, Na+ tends to stay closer to the channel wall and interacts more strongly with the nearby peptide groups; consequently, there is more detailed structure in the potential energy profile for both singly and doubly occupied channels. In order to mimic the energetics of transport, we have calculated the energy for a pair of cations translocating in the same direction with constant axial separation in the channel. Our motivation for this procedure is the fact that transport is single file, with a fixed number of water molecules separating the ions. Because of the pseudoperiodicity of the channel structure, if both cations are initially placed at energy minima, the total energy for two cations translocating with constant axial separation will have more pronounced saddle points and deeper minima than in the case for a single cation. If the separation corresponds to one cation initially at a saddle point and the other a t an energy minimum, the energy profile for the pair of ions is relatively flatter. The main reason is that at any point in the channel the total energy is essentially the sum of single ion energies and the repulsion term. Cooperative effects are small. As an example, consider a Na+ initially placed at the minimum located at 8.35 8, translocating to the minimum at 12.25 8,and a second Na+ at the -12.25-8, minimum translocating simultaneously to the minimum at -8.35 8,. The total energy profile exhibits a barrier of 12.8 kcal/mol. This is larger than the corresponding barrier in the singly occupied channel, 10.8 kcal/mol. If the first ion is initially placed at the saddle point at 7.45 A, the resulting barrier for translocation is about 8.6 kcal/mol, noticeably smaller. In other words, the energy required for the second ion to pass over the barrier located near -10 8, is less than that needed for the first ion. This is analogous to an observation of Pullman et al.; however, in their model the barrier is at the dimer midpoint.22 (22) Pullman, A,; Etchebest, C. FEBS Lett. 1983, 163, 199.
2364 The Journal of Physical Chemistry, Vol. 92, No. 8, 1988
Sung and Jordan
-10
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Figure 2. Average cation-channel interaction energies (0)for two Cs' separated by the axial distance of 23.6 A and translocating in a channel without water. ( 0 ) ' s are the single occupancy energies.
Cs+ is larger and, consequently, has a less structured energy profile. Figure 2 illustrates the potential energy profile for a pair of Cs+ ions translocating in the channel. The single occupancy curve, the same as that of Figure l a (with a different scale), is shown for comparison. A major feature of the energy profile in the singly occupied channel is the deep minimum near the mouth at -12.85 A and the adjacent barrier at -10.75 A. The shar energy increase for a cation leaving the channel from the -12.85binding site is partly due to the absence of the bulk water outside the channel mouth in our calculations. If bulk water is included, its interaction with the cation will compensate for the loss of binding energy; as a cation leaves from the -12.85-A binding site, the energy increase will be smaller. A similar artifact is noticeable in the double occupancy energy profile. In Figure 2 the upper curve is the average energy for a pair of Cs' translocating in the same direction with constant axial separation. The first cation translocates from 10.15 to 13.45 A going out of the channel, while the second cation translocates simultaneously from -13.45 to -10.15 A entering the channel. The axial separation is kept constant, 23.30 A. The average energies in Figure 2 are plotted vs the axial location of the second cation. The average energies for the first cation are, of course, the same and would be in the positive z coordinate region. Because they are symmetric, only the part with negative z coordinates is shown in Figure 2. However, it should be kept in mind that the energy at -12.85 A, for example, is actually the average value for two cations, one at -12.85 8 and another at 10.75 A, with axial distance 23.60 A from the first one. The plot is truncated at -10.15 A. At this point, the first ion is at 13.45 8. As the second ion moves further into the channel, the first ion moves out and double occupancy becomes single occupancy. The higher average energies at the right end of the plot are partly due to the absence of the interaction of the first ion with the bulk water and those at the left end due to the absence of the interaction of the second ion with the bulk water. During this translocation the energy barrier between -1 2.85 and -10.75 8, is only 0.7 kcal/mol, substantially reduced from the value of 6.7 kcal/mol for a single ion moving from -12.85 to -10.75 A. The presence of a cation at one side of the channel lowered the energy barrier for a second cation entering from the other side. The single file property assures coupling during the two ion transport. The physical basis for the constant axial separation constraint in the calculation is not justified if one ion moves out of the single file region, for example, at 13.45 8, from the dimer midpoint (the end points in Figure 2). Because of electrostatic repulsion, the total energy per ion for double occupancy is always higher than that for single occupancy. At low concentrations single occupancy is still preferred.
K
Two Cations in a Water-Filled Channel With some water molecules in a gramicidin channel the ionchannel interaction becomes much more complicated. With the cations at the same axial positions many stable configurations are
found because of the different water structures. Figure 3 shows a low-energy configuration of 16 water molecules and 2 Cs' cations near each mouth of a channel. Unlike the symmetrical structure found when water is not included, with water present it is almost invariable that the water molecules are not symmetrically oriented because they bind to each other and to the polar groups of the channel wall. Water orientation is usually determined by the nearest ion. Because of the presence of ions of the same charge in both mouths, the water dipoles in the single file region change their axial directions at the middle part of the single file chain. A central water molecule (the one at z = -1.05 A in Figure 3) orients differently. It binds to the polar groups of the channel wall (not shown in Figure 3) via its hydrogen atoms and to the neighboring water molecules via its oxygen atom. The axial locations of the two cations are -12.68 and 12.71 A. However, the local solvation structures for each ion (the ion and its first neighbors) are very similar. If we rotate the ion-water structure in the left mouth region in a manner accounting for the dimer symmetry, we get a structure almost identical with that in the right mouth region. Therefore, only one detailed local structure is shown in Figure 4a. This is a view down the channel axis from the outside. In addition to Cs' and its neighboring water molecules, the channel groups no. 11 CO, no. 13 CO, no. 15 CO, and no. 16 CO are shown. The groups are numbered from 0 for the formyl CO to 16 for the ethanolamine C O H group. The hydrogen atom of the C O H group is not shown. The numbers in parentheses are the axial distances from the dimer midpoint to the center of mass of these moieties. Cs+ binds to the no. 11 CO group at a distance of 3.14 A. Within 4 8,of the ion, there are four neighboring water molecules (first-neighbor water molecules) at distances of 3.19-3.27 8,. The water molecule at z = 15.50 is 4.91 A from Cs'. Instead of binding to Cs', it binds to two first-neighbor water molecules with its oxygen atom at distances (center of mass) of 2.97 and 3.03 8, and to no. 15 CO with one of its hydrogen atoms at a distance of 2.91 8. In Figure 4 Cs' has five nearest neighbors (no. 11 C O and four water molecules). But there is room, e.g., the space directly above the Cs', for a sixth water molecule in the bulk domain (which is absent from the calculation). Therefore, the coordination number for Cs' a t this site could be six (or larger). The ethanolamine COH group is 3.76 8, from Cs', but its contribution to cation binding is not energetically favorable because, for computational simplicity, the ethanolamine end is not allowed to rotate freely in this study. Its rotation lowers the binding energy, as discussed previously' and as found in other model calculation^.^^ This local structure is also the stable configuration in a singly occupied channel. Significant differences in the local configurations between doubly and singly occupied channels are not observed unless the two cations are close to each other. This structural feature is consistent with the fact that the cooperative effects have little influence on energy unless two cations are close together. For Na', the configuration is similar, as shown in Figure 4b. This is the local structure surrounding a Na' ion in a doubly occupied channel with 16 water molecules, analogous to Figure 4a for Cs'. The Naf binding site is 11.9 8, from the dimer (23) Etchebest, C.; Ranaganathan, S . ; Pullman, A. FEBS Lett. 1984, 173, 301.
Double Ion Occupancy in a Gramicidin-like Channel 0. _
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The Journal of Physical Chemistry, Vol. 92, No. 8, 1988 2365
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midpoint. The Na+-no. 11 CO distance is 2.77 A; the N a t w a t e r distances are from 2.51 to 2.62 8, for the four first neighbors. At this site Na+ is five-coordinated and a sixth neighbor (water molecule) can hardly squeeze in. The structure is similar to Urry's observation based on N M R spectra2' that the Na+ binding site is between no. 11 and no. 13 CO. However, in our calculation binding to no. 13 CO is much weaker, at distance of 4.41 A. Instead, a first-neighbor water molecule for Na+ binds to no. 13 C O via its hydrogen atom at distance of 3.0 A. The large water polarization due to Na+, an indirect effect of Na+, together with the direct interaction of Na+ may contribute to the carbonyl chemical shift change in the N M R spectra. In addition, the thermal motion of Na+ cations certainly has some effects on the spectra. Compared with Cs+, the Na+ binding site is deeper in the channel and closer to the single file region. This makes it harder for a second Na+ to reach the empty binding site (it is actually occupied by water molecules) in an already singly occupied channel because it has to force its way in against the water molecules in the mouth region. Pushing the whole single file of water to reach this binding site may cause the dissociation of the first ion from its binding site on the other side of the channel. In contrast, with a binding site (12.7 A from the dimer midpoint) that is not as far into the mouth, the second Cs+ ion from the bulk water can bind more readily. Furthermore, at the deeper binding sites there is somewhat higher electrostatic repulsion energy between the two cations. Therefore, one might expect double occupancy to be less probable with Na+ than with Cs'. Some estimates of the binding
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constants show this qualitative trend for different alkali-metal cations.24 This preliminary observation needs to be verified by molecular dynamics simulations including more water molecules, as well as by calculations for other alkali-metal cations. With water between the two cations it is not meaningful to compute a continuous energy curve for symmetrically placed cations at arbitrary separation because the single file water chain between the two cations should not be compressed or elongated artificially. Instead, we focus on the translocation of two cations separated by fmed number of water molecules. Figure 5 compares translocation energy profiles for singly and doubly occupied channels with 13 water molecules present. First consider the single occupancy energies. These are the lowest energies among many stable configurations for each given axial position of the cation. They are usually found when the 13 water molecules are relatively evenly located in the channel. For example, when a cation is at -12.0 8, in a singly occupied channel, there are 3 water molecules at axial locations less than -12.0 8, and 10 water molecules at axial locations greater than -12.0 A. When the cation is in the midpoint of the dimer, there are six water molecules on one side of the cation and seven on the other side. As in Figure 2 where water was not included, the single occupancy curve with 13 water molecules has a deep minimum near the mouth and is relatively flat in the single file region. But, due to .water-channel interaction, energy variation in Figure 5 is more pronounced than that in Figure 2. (Both figures are drawn to the same scale.) The binding site near the mouth is at 12.68 A, 0.17 A closer to the dimer midpoint than when no water is present. This indicates that water has some effect on the exact location of the binding site. In these calculations bulk water and membrane lipids are not included. As mentioned, this may partly account for the sharp increase of energy when a cation leaves the channel. There is a similar, but smaller, energy increase in the doubly occupied channel when one cation leaves the channel. In Figure 5 , a Cs+ ion is initially put at an axial position ( z coordinate) of 9.9 A. Assuming 7 water molecules traveling through the channel with each cation,2 the second Cs' was put at z = -13.2 A, separated from the first ion by 7 water molecules. The first ion translocates to 13.2 A, going out of the channel. Keeping a constant axial separation, 23.1 A, the second ion translocates in the same direction to -9.9 A, entering the channel. The actual Cs'-Cs+ distance varies between 23.1 and 23.2 A, as the radial location changes. The average channel solvation energy per Cs+ in this doubly occupied channel shown in Figure 5, is defined as half the difference between the energy of the channel system with 2 Cs+ and 13 water molecules and that of the same channel and water without ions. It is plotted vs the z coordinate of the second cation in the negative z region. The symmetrical part for the first cation in the positive z region is not shown in the figure. The plot (24) Urry, D. W.; Trapane, T. L.; Venkatachalam, C. M. J . Membr. Biol. 1986, 89, 107.
2366 The Journal of Physical Chemistry, Vol. 92, No. 8, 1988
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is truncated at -9.9 A. At this point, the first ion is at 13.2 A and is exiting the channel. Again, the higher average energy at the right end of the plot is partly due to the absence of the solvation of the first ion by the bulk water and that at the left end due to the absence of the solvation of the second ion by the bulk water. Analogous to the water free case (Figure 2), the double occupancy energy profile illustrated in Figure 5 exhibits a much lower intermediate energy barrier than the single occupancy one. As an alternative way to mimic the double cation transport, one cation could be constrained to translocate to a series of fixed axial positions while the second cation and water molecules are allowed to move freely. Because our simulation is near 0 K temperature and does not include the bulk water, the second cation and the water molecules do not always all move freely when the first cation translocates a small distance. The system is too easily trapped in spurious local minima. Furthermore, this alternative way is not clearly an improvement because the actual forces driving the cations and the water molecules during the transport are not known in detail. Also, due to the calculational limitations mentioned, exerting a moderate external electrical field did not result in reasonable transport in the near 0 K simulation.
Cation-Anion Double Occupancy First, consider the interaction of an anion with a channel with no cation present. The origin of gramicidin valence selectivity is the large energy barrier outside the channel mouth for an anion, arising from the dipolar orientation and polarization of the channel groups.25 The interaction energy for C1- with a channel, shown
Sung and Jordan in Figure 6a, is compared to that for Cs'. An energy barrier for C1- is clearly indicated at about -16.4 A. For computational simplicity the water molecules were not included. Because the barrier is outside the channel mouth, too many bulk water molecules have to be included in order to consider water interaction. Naturally, one expects that the presence of a cation in the channel lowers the energy barrier for anion entry. With a Cs+ cation at 12.5 A on the other side of the channel, the barrier is lowered by 12.4 kcal/mol, of which 11.2 kcal/mol is direct electrostatic attraction between the two ions and 1.2 kcal/mol (or 0.6 kcal/mol per ion) is the cooperative effect, as shown in Figure 6b. The anion and cation reorient and polarize most of the channel groups in the same direction, increasing the cooperative effect above that for cation double occupancy (Figure la,b) at the same interionic distance. The modulating influence of water will reduce the electrostatic attraction substantially, and less lowering of the energy barrier is expected. The dehydration energy will reduce the sharp drop in energy when an ion enters the mouth region. A more realistic calculation needs to include at least 200 water molecules as well as account for the influence of the membrane lipid molecules. This is an ongoing project in our group. What is presently clear is that there is a large energy barrier for anions outside the channel mouth and the presence of a cation in the other side of the channel reduces this barrier, mainly by direct cation-anion attraction but also by channel reorientation and polarization. This lowering of the barrier could account for possible anion contributions to channel conductance at high salt concentra tion.
Summary In a doubly occupied gramicidin-like channel, the major part of the interaction energy is the sum of the energies for independent single ion occupancy plus the direct Coulombic energy between the two ions. The cooperative effect is small for cation-cation double occupancy and slightly larger for cation-anion double occupancy. The local solvation structures for each ion are very similar to those for single occupancy. Structural comparison suggests that double occupancy is less probable with Na' than with Cs+. With a favorable cation-cation separation or a favorable number of water molecules between two cations the energy barrier for cation transport may be reduced. Cation-anion double occupancy may account for possible anion contributions to conductance. Acknowledgment. This work is supported by Grant GM-28643 from the National Institutes of Health and by instrumentation grants from the National Institutes of Health and the National Science Foundation. Registry No. Na, 7440-23-5;Cs, 7440-46-2;gramicidin, 1405-97-6. (25) Sung, S.-S.; Jordan, P. C . Biophys. Chem. 1987, 27, 1. (26) Eisenman, G.;Sandblom, J.. In Physical Chemistry of Transmembrane Zon Motions; Spach, G., Ed.; Elsevier: Amsterdam, Netherlands, 1983; p 329.
