| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
* Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California; and Chemistry Department, Wellesley College, Wellesley, Massachusetts
Correspondence: Address reprint requests to Dennis A. Dougherty, E-mail: dad{at}igor.caltech.edu
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMETHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
|---|
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
|---|
). On a very simplistic level, these channels exist in two states, an impermeable closed state and a permeable open state. A stimulus, such as ligand binding or a change in the electrical or osmotic environment of the cell, can induce a transition from a closed resting state to an open state that allows passage of a particular set of ions or molecules. An essential part of this gating process is the formation of a pore through the membrane, such that the barrier to ion passage is greatly reduced compared to that of the impermeable lipid bilayer.
The requirement for a low barrier demands the presence of water or similar coordinating groups in an ion channel pore. The selectivity filter of potassium channels, for example, is lined by backbone carbonyls that mimic the coordination of an aqueous potassium ion (2). In contrast, less selective channels such as the nicotinic acetylcholine receptor (1), the mechanosensitive channels of large (3) and small (MscS) (4) conductance, and 
-hemolysin (5) are thought to have open states with wider pores that support hydrated ions.
The properties of water in these small pores are very important to understanding ion channel function. The microscopic properties of water are not fully understood, and it is well established that water in narrow spaces such as might be seen in the pore of an ion channel (on the order of a few molecules across) does not necessarily have the same properties as bulk water (6). For example, molecular dynamics (MD) studies by Beckstein and Sansom have established the surprising result that a hydrophobic pore is not necessarily filled with water, even if it is large enough to fit several water molecules (7–9). Below a threshold radius, dependent on the hydrophobicity of the pore, water is essentially absent from a model pore even if there is space for it, producing a kind of "hydrophobic gate". For a purely hydrophobic model pore, the threshold radius is 
4.5 Å, large enough to accommodate three water molecules (7), and the threshold for ion occupancy of the pore is even larger (6.5 Å) (9). MD simulations of the hydrophobic pores of more realistic systems showed a similar threshold behavior, although the threshold radius varied from that in the simple model. For example, the threshold radii for the pores of the nicotinic acetylcholine receptor and a carbon nanotube were found to be 4.0 and 2.5 Å (10,11), respectively, and were quite sensitive to the parameterization of the interaction between the water and the pore wall, at least in the nanotube system (12).
As part of a general program investigating bacterial ion channels, we have been studying the bacterial MscS. This channel is gated by membrane tension, and it is thought that MscS functions as a "release valve" for the rapid efflux of osmolytes under conditions of osmotic stress (13,14). In addition, MscS is modulated by voltage and displays a slight anion preference for conduction (4). Despite its name, the channel shows a relatively large conductance of 1.0 nS, consistent with the proposed function.
The crystal structure of Escherichia coli MscS has been reported by Rees and co-workers (15). The protein is a homoheptamer of multidomain subunits of 286 amino acids in length (Fig. 1 A). From N- to C-terminus, the domain organization is as follows: a transmembrane (TM) domain comprised of three TM helices, a middle-ß domain that consists primarily of ß-sheet, and a C-terminal /ß-domain (Fig. 1 B). There are vestibules on either side of the pore: the periplasmic vestibule lined by the N-terminal halves of TM3, and the cytoplasmic vestibule surrounded by the middle-ß and C-terminal domains. The narrowest constriction, which shall hereafter be called the pore, is the region around two hydrophobic residues, L105 and L109 of TM3, near the cytoplasmic side of the bilayer. At its narrowest point MscS displays a pore radius of 3.5 Å, suggesting that the crystal structure may be a model of the open state of the channel (15). However, as noted above, 3.5 Å is slightly lower than the threshold radius for a hydrophobic gate determined by Beckstein and Sansom (7).
|
,17), we turned to full-scale MD simulations of MscS to illuminate this problem. While our efforts were in progress, two other MD simulations of MscS appeared. Anishkin and Sukharev reported a somewhat simplified model, involving only the channel-lining regions of the protein, harmonically restrained, and an octane slab to model the lipid (18). They found that the pore was generally empty of water, and even when the pore was occupied, there was rarely more than a single file of water molecules. Furthermore, when a chloride ion was forced through the mostly dehydrated pore, it experienced a large barrier to conduction. Anishkin and Sukharev concluded that, because the relatively large conductance of MscS demands a much lower barrier than that observed in their simulations, the crystal structure is a nonconducting state with a hydrophobic gate.
Sotomayor and Schulten reported much larger-scale simulations of MscS involving full-length protein with an explicit lipid bilayer (19). Like Anishkin and Sukharev, they found that simulations with a substantially restrained protein backbone produced a dehydrated pore region. Relaxing the restraints caused the protein to collapse, producing an occluded pore that is certainly nonconducting. However, when a large tension was applied to the system, the collapse was avoided, and a system with a substantially hydrated pore emerged.
Here we present the results of our MD simulations of MscS that were intended to shed light on whether or not the crystal structure is conducting or nonconducting, as well as provide further insights on the nature of hydrophobic pores. Our approach more nearly parallels that of Sotomayor and Schulten (19), in that we simulate nearly the entire protein in an explicit bilayer. An informative addition in the present simulations is an evaluation of the effect of an applied voltage on the MscS system. We find that an applied voltage can profoundly influence the hydration of the channel, whether in a restrained or unrestrained simulation. In addition, we find that an applied voltage can favor a hydrated state of the channel that, even during these relatively short simulation times, conducts a significant number of chloride ions. These results suggest that the image of MscS obtained from crystallography is likely more similar to an open, conducting state than to a nonconducting state.
|
METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
|---|
) were transformed so that the sevenfold axis was parallel to the z axis. Because MD simulations on full-length MscS would require huge amounts of CPU time due to the large number of atoms, the protein chains were truncated at the ends of the middle-ß domains, so that the model of each subunit extended from F27 (the N-terminus of the crystal structure) to S179. It is assumed that the truncated protein is a reasonable system for study because the cleaved portion, the C-terminal domain, is unlikely to strongly influence the region of interest, the pore. For all ionizable side chains, the protonation state was chosen to simulate a system at neutral pH. However, the N- and C-termini were kept neutral (NH2 and CO2H), reflecting the fact that the simulated peptide chains do not actually extend to the terminal residues of the protein.
The protein was embedded in a preequilibrated phosphatidylethanolamine (POPE) bilayer model in the manner described previously (20). SPC water was added to fill the remainder of the simulation box. Sodium and chloride ions were also added for two reasons. First, a salt solution is more physiologically relevant than a pure water solvent. Second, the large +42 charge on the protein must be neutralized to avoid artifacts in the long-range electrostatics algorithm (21). Therefore, for a low-salt system that approximates a NaCl concentration of 100 mM, 62 of the water molecules were replaced with 10 Na+ and 52 Cl– ions. Medium (200 mM) and high (300 mM) salt solutions contained 61 Na+ and 103 Cl– ions and 113 Na+ and 155 Cl– ions, respectively. The wild-type MscS, low-salt system contained seven protein chains of 153 residues each, 455 POPE molecules, 28,423 water molecules, 10 Na+ ions, and 52 Cl– ions, for a total of 118,665 atoms (Fig. 1 C). The simulation system was minimized using the steepest descents method.
Molecular dynamics
All minimizations and MD were performed with GROMACS 3.1.3 and 3.1.4 software (22,23) with the GROMACS force field supplemented by parameters for the lipid (24). van der Waals and short-range electrostatics were cut off at 1.0 nm, and the long-range electrostatics were treated with the particle mesh Ewald method of order 4 and grid spacing of 0.1 nm (21).
The minimized structures were heated to 310 K over 20 ps with heavy harmonic position restraints (force constant: 1000 kJ mol–1nm–2) on all C atoms. Once at 310 K, the heavy restraints were maintained for 180 ps and then gradually lifted over 330 ps. The frame at 350 ps (of the 530 ps total), which followed equilibration with a restraining force constant of 500 kJ mol–1nm–2, was used as the starting structure for the restrained simulations. The final frame (at 530 ps) was used as the starting frame for the unrestrained simulations.
In all simulations, the temperature was maintained at 310 K by coupling to Berendsen thermostats with a time constant of 0.1 ps (25). Separate baths were used for the protein, the lipid, the solvent, the Na+ ions, and the Cl– ions. Likewise, pressure was maintained with anisotropic pressure coupling in each direction to a Berendsen barostat at 1 bar with a time constant of 1.0 ps (25).
Fig. 2 indicates the salt system, restraints, electric field, initial pore hydration state, and start and end times of each wild-type MscS simulation. In all restrained simulations, all the atoms of the protein backbone were harmonically restrained with a force constant of 418.4 kJ mol–1nm–2 (1 kcal mol–1Å–2). The pore at time 0 of the restrained simulation was hydrated (Rh), and simulations with electric fields of 0 and +100 mV/nm were run for 2.5 ns. The frame at 1.47 ns of the 0 mV/nm simulation, which contains a pore empty of water, was used as the initial frame for other simulations (R), with applied electric fields of +100, +50, +20, –50, and –100 mV/nm.
|
Simulations with mutant MscS
Unrestrained simulations were also performed with mutant MscS proteins under low-salt conditions. Five charged residues in the TM domains of MscS—R46, R54, D67, R74, and R88—were explored by mutation in eight single mutants and one double mutant: R46Rn, R46A, R46E, R54Rn, D67N, R74Rn, R74A, R46Rn/R74Rn, and R88Rn. Rn is a neutralized arginine model in which one of the terminal protons has been removed, eliminating the charge on the side chain. Even though this residue is almost certainly never found in vivo, its parameters are available in the GROMACS force field. All of the mutations gave structures in which a charged residue was neutralized, except for R46E, in which the +1 charge was mutated to a –1 charge.
The mutant models were created from the initial low-salt structure, and with one exception (D67N) no additional minimization was required. For the D67N mutant, only the lipid molecules and side chains that were within 0.5 nm of the N67 side chains were allowed to move. In this way, the close contacts induced by the mutations were removed while minimizing the perturbation to the initial structure. Because of the changes in the protein charge, ions were added to the systems to restore neutrality. Simulations for all mutants were performed with an electric field of +100 mV/nm for 4.47 ns.
Data analysis
Standard GROMACS analysis tools allowed for the determination of water alignment and water binding energies.
The pore as defined for water and ion occupancy determinations consists of a cylinder with radius 1.5 nm between the centers of mass of the L105 and L109 C atoms. Water and ion occupancies of the pore were monitored as a function of time.
A conduction event is defined as the full transit of an ion through the pore. The total charge flow through the pore was monitored by keeping a running total of the conduction events in each simulation. A steady-state regime of the simulation was usually easily discernable as a linear region in the plot of total charge flow as a function of time. The slope of the function in each steady-state regime represents the average current, which was determined by dividing the cumulative charge flow by the time between the first and last conduction events. Currents in MD simulations have been calculated previously using a qualitatively similar technique (26).
Diffusion currents were calculated similarly. A diffusion event was defined as the movement of an ion into a vestibule. The periplasmic vestibule was defined as a cylinder of radius 1.5 nm between the centers of mass of the C of L105 and V91, and the cytoplasmic vestibule as a cylinder of radius 1.5 nm between the centers of mass of the C of L109 and G140 (Fig. 1 B). The cumulative number of diffusion events was plotted as a function of time, and the steady-state diffusion current was calculated by dividing the number of diffusion events by the time between the first and last events.
Electric potential profiles for negative ions for each of the six applied electric fields were determined for the restrained simulation system by calculating the average electrostatic energy of a chloride ion as a function of its position in the box. Chloride ions that sampled different regions of the simulation system were selected for analysis, but only for the times that they remained within 2 nm of the protein's sevenfold axis. For the selected chloride ions, both the z-position and the electrostatic energy between the ion and the rest of the system, including the electric field, were computed at each time in the simulation. The energy values were placed in bins of width 0.25 nm according to their corresponding z-positions, and the average energy was calculated for each bin. For some electric fields, no chloride ions were ever found in the pore region, so the potential profiles were incomplete.
Pore radii were calculated by HOLE (27), which moves a flexible balloon along the length of the channel, and at each point calculates the largest radius that can be accommodated.
TM1 and TM2 movements of wild-type and mutant MscS were analyzed in the following manner. For each simulation, the z-positions of the centers of mass of all the atoms in TM1, TM2, and lipid as a function of time were determined. For each time, the position of the lipid was subtracted from the positions of the TMs. The average of these differences over the last 500 ps of the simulation was calculated as the TM position relative to the lipid. Finally, these relative positions were compared to the relative position determined for U0.
Images of the simulation system were prepared with VMD (28) and Rasmol.
|
RESULTS AND DISCUSSION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
|---|
,19). Even though the pore of the restrained system was initially hydrated, it emptied of water rapidly (in 0.5 ns). The pore occasionally filled with water for periods of 200 or 300 ps, but for most of the simulation, it was completely empty (Fig. 3 A, gray trace). These results are consistent with previous simulations of hydrophobic nanopores, because the size of the MscS pore is smaller than the threshold for hydration (7,8).
|
). Given that this work employs a different force field and simulation package from that of Sotomayor and Schulten, the similarities are gratifying and enhance the confidence in the overall behavior of the system.
|
). Given the intense interest in the molecular mechanism of voltage sensing in ion channels in general and Kv channels in particular (29–34), we found this to be one of the most attractive features of the MscS channel. We, and others, were especially intrigued by the presence of a number of arginine residues in the TM domain of MscS (15). Arginine residues play a critical role in voltage sensing in the Kv channels, and we have sought, both experimentally and computationally, to probe their role in MscS. Of course, in its natural environment MscS is always exposed to a significant TM voltage. In fact, bacterial TM potentials are unusually high, perhaps in the range from –120 to –160 mV, or more (35). Also, all experimental studies of MscS using the patch clamp methodology require a TM potential to see conduction.
We began by subjecting the system with harmonic restraints to an applied electric field of +100 mV/nm. The sign convention is such that a negative electric field produces a bias that is in the same direction as a natural TM potential; the inside of the cell is negative relative to the outside. Therefore, with this field, our simulation represents a depolarized membrane. Under these conditions with an initially hydrated pore (Rh+100), the pore remained hydrated for the entirety of the simulation (Fig. 3 A, black trace). In addition, the initially empty pore of R+100 became hydrated very rapidly (0.1 ns) (Fig. 3 B, black trace). Again, the observation of the same steady-state behavior with different initial conditions indicates the robustness of the result. Thus, the application of a voltage to the system has qualitatively altered the behavior of the channel.
The +100 mV/nm field is relatively large. We therefore considered smaller potentials and the consequence of reversing the field. As we saw in R+100, the presence of other moderate or high electric fields (±50 or –100 mV/nm) allowed rapid filling to create a hydrated pore, and the pore remained hydrated for essentially the entire length of the simulations. For a more modest field of +20 mV/nm, the pore displayed more frequent dewetting events, but we still observed increased hydration compared to simulations with no field (Fig. 3 B). Thus, an extraordinarily high field is not required to see qualitatively different wetting behaviors from the restrained simulations of Anishkin and Sukharev (18) or Sotomayor and Schulten (19). The hydrophobic gate of MscS seen in previous simulations is absent in the presence of a potential.
The probability distribution for water in the pore for each of the six electric fields clearly indicates a field dependence on the amount of water hydrating the pore in these restrained simulations (Fig. 3 C). Without a field, there is very little water in the pore, but as the magnitude of the field increases the pore is more likely to be hydrated. Electric field effects on the threshold radii for model hydrophobic gates have not yet been studied, but the data here strongly suggest that increasing the electric field reduces the threshold radius.
We next considered the effects of an applied voltage on the unrestrained system. Simulations with electric fields of ±100 mV/nm (U±100) displayed qualitatively similar water behavior to R±100, with one important difference. When beginning from a dehydrated pore, the unrestrained simulations revealed a competition between water and the pore-lining leucines to fill the vacuum in the pore. The inherently chaotic behavior of MD was especially evident here, in that subtle differences in the simulations led to two distinct pore states. The U+100 and U–100 simulations were each performed several times on different computer environments. In some simulations, inward collapse of the leucines resulted in an occluded pore (like that seen in U0, Fig. 4 D) that contained no water. However, in other simulations, water entered the pore first and formed a stably hydrated state. Clearly, the pore state is very sensitive to the initial conditions of the simulations. However, it is notable that once a certain threshold of hydration was attained by the pore (5 water molecules), the channel remained fully hydrated throughout the simulation (the red and purple traces in Fig. 4, A and B, are representative examples of the simulations that contained stably hydrated pores).
In the simulations with a stably hydrated pore (U+100, U–100, Uh–100), the water prevented the collapse of the pore-lining leucines and maintained a pore approximately the same size as that of the crystal structure (Fig. 4 E). Because there were no restraints on the protein conformation, the pore was free to widen slightly and accommodate more water molecules than were present in the restrained simulations. As in the restrained simulations, a large potential stabilized a hydrated pore, further suggesting that MscS does not have a hydrophobic gate in a high electric field. Again, the results here are analogous to the work of Sotomayor and Schulten, who demonstrated that membrane tension, like the TM potential in our simulation, is sufficient to maintain a wide, hydrated MscS pore (19). It should be mentioned that voltage and tension affect MscS in different ways. Tension is the primary stimulus for activation, but recent electrophysiological results indicated that voltage modulates its deactivation (36). However, it is interesting that both tension and voltage are separately sufficient to maintain the pore state of the crystal structure.
However, a notable difference between the restrained and unrestrained simulations was observed with applied fields of lower magnitudes (from +50 to –50 mV/nm). Field-dependent hydration of the pore was not observed in these unrestrained simulations. Instead, with lower fields, the system quickly evolved into the dehydrated, collapsed state, regardless of whether the pore was initially empty or hydrated (Fig. 4, A and B).
The fact that the hydration state of the pore is dependent on its flexibility, as observed in our simulations with +20 or ±50 mV/nm fields, is in agreement with recent work by Beckstein and Sansom that showed a general inverse relationship between the flexibility of a hydrophobic pore and the probability of water occupancy (9). They attributed this phenomenon to a decrease in the depth of the attractive well of the van der Waals potential of a water molecule interacting with the fluctuating walls. The results here suggest that in moderate electric fields, the shallower wells destabilize the water to the point that the field energy is no longer sufficient to maintain a hydrated pore. However, large fields of ±100 mV/nm maintain a hydrated MscS pore even with no restraints at all.
We hypothesized that the mechanism by which a large field contributes to pore hydration involves the field-induced alignment of water dipoles in the pore. As such, we plotted the alignment of the water (
cos 
, where is the angle between the water dipole and the z axis) as a function of position in the periodic box for the R simulations (Fig. 5 A). In the regions near the edge of the box, in which the environment is most similar to bulk water, the water shows only a slight orientational preference, which is independent of the applied field. The fact that there is no field dependence to the alignment is not surprising, because the dipole orientation energy of an individual water molecule in even the largest electric field is only one-sixth of kT. The small nonzero net dipole in these regions is likely an artifact of the periodic boundary conditions, as recently reported (37). The large dipoles of MscS and its infinite images lead to ordering of the water structure even in the bulk regions. In other regions of the simulation system, local interactions between polar groups in the protein and bilayer tend to orient the water in a field-independent manner.
|
cos approach 0.8, a very high degree of alignment. The observation of water alignment in stronger fields provides an explanation for the influence of an external field on pore hydration. In a hydrophobic pore, a water molecule oriented with its dipole parallel to the pore interacts through hydrogen bonds with the water molecules above and below it. Rotation of this dipole toward the wall of the pore is unfavorable, because the weak interaction between the water and the hydrophobic wall does not compensate for the energy lost from the weakened hydrogen bonds with the waters above and below.
The enthalpic gain from hydrogen bonding in forming a water column in a hydrophobic pore comes with an entropic penalty for forming such an ordered structure. In the system here, the enthalpy of the hydrogen bonding alone is insufficient to overcome this cost, as evidenced by the fact that in the absence of an electric field a hydrated pore occurs only rarely. However, an electric field provides further stability for the water column, in that the orientation energy of the several aligned water dipoles contributes favorably to the enthalpy and the overall energy is lowered in a field-dependent manner. This can be clearly seen by comparing the interaction energy distributions for water in the pore in the various electric fields (Fig. 5 B). The energy distributions from the different fields form approximately Gaussian curves, all with about the same width. However, with an increasing field (and increasing alignment), the midpoints of these distributions are shifted toward lower energies, and the energies approach those for bulk water. For an individual molecule, the dipole orientation energy is small, as mentioned earlier, but for several molecules, the energy becomes more significant. In this way, a hydrated pore is preferentially stabilized by larger electric fields.
The degree of alignment of the water with no applied electric field gives a sense of the strength of the electric field inherent to the protein itself. The pore is lined by seven -helices, all with their helical dipoles pointing generally in the +z direction. Dipole-dipole interactions favor an arrangement of water oriented with its dipole in the –z-direction, exactly as observed in our simulations. This may be why, in the R simulations, the –50 and –100 mV/nm fields had slightly greater hydration than the +50 and +100 mV/nm fields, respectively (Fig. 3 C).
Spontaneous conduction of ions through the hydrated channel
A stably hydrated pore is necessary but not sufficient for ion conduction through the MscS crystal structure. Sotomayor and Schulten's work showed that membrane tension could oppose collapse and produce a hydrated channel, but no ionic conduction was seen in their simulations (19). However, in the present simulations, the application of a TM potential provides a natural driving force for ions to pass through the channel. Indeed, we observe a significant number of spontaneous ion transits through the channel when a voltage is applied.
We define a conduction event as the movement of an ion through the full length of the pore. For each simulation, a running total of the number of conduction events can be plotted as a function of time; on such a plot, a constant current is characterized by a more or less linear function. An approximation of the current can be calculated by dividing the number of events by the time between the first and last event. The most compelling case is U+100. Fig. 6 A (upper light gray trace) shows that many conduction events are observed during this simulation, and from 3.3 ns onward the charge movement data show a linear appearance. The current for this steady-state regime is calculated to be 4.9e ns–1, equivalent to 790 pA.
|
|
,38). This phenomenon arises because the bath solution is a highly conductive environment compared to the membrane, so there is no potential difference throughout the aqueous region. Therefore, the entirety of the potential drop across the box is concentrated across the bilayer and protein, as discussed in more detail below. Therefore, the TM potential 
Vz can be determined as follows:
 | (1) |
Vz is 1100, 550, 220, 0, –550, and –1100 mV, respectively.
Single channel conductances calculated from the currents and TM potentials for each simulation are shown in Table 1. U+100 and H+100 (H indicating high salt; Fig. 2) have calculated conductance values of 0.75 nS, close to experiment (1 nS). R+100 and M+100 (M indicating medium salt; Fig. 2) have slightly lower conductances, although they are still within a factor of 2.5. Thus, in the field of +100 mV/nm, the conductance agrees quite well with experiment. Since the protein in these simulations shows only minor structural deviation from the crystal structure (Fig. 4, C and E), it is clear that the MscS crystal structure conformation can sustain a conductance that is consistent with the experimentally observed value.
The steady-state conductance measurements from –100 mV/nm fields are much lower than those from +100 mV/nm fields, indicating a deviation from Ohm's law. However, this is not because of changes in the inherent conductance of the channel. Instead, it is due to the fact that the current in the negative but not the positive fields is limited by diffusion, as discussed in the following section.
Diffusion properties of chloride ions
The discrepancy in steady-state conduction currents between +100 and –100 mV/nm fields can be attributed to the differing abilities of the protein to resupply charge carriers to the periplasmic vestibule (the chloride source for conduction in the positive field) versus the cytoplasmic vestibule (the chloride source for conduction in the negative field). In any channel, a current can be sustained only if the arrival of new charge carriers at the channel's mouth is fast enough to replenish the ions that are conducted. The rate of diffusion to the mouth, therefore, is an upper limit on the current that a channel can sustain. Applying larger electric fields cannot increase the current beyond this limit, so when currents are near the diffusion rate, the channel no longer follows Ohm's law (1).
Diffusion currents (the flow of ions into the vestibules before their conduction) can be calculated in a manner similar to conduction current. Fig. 6 B and Table 1 summarize the data. The differences in diffusion into the periplasmic and cytoplasmic vestibules are immediately obvious. For R+100, Rh+100, and U+100, we observe relatively large diffusion currents into the periplasmic vestibule. However, in the steady-state regimes of R–100, U–100, and Uh–100, there are no diffusion events into the cytoplasmic vestibule. These observations lead to the conclusion that diffusion can adequately resupply chloride ions to the periplasmic vestibule under positive potentials, but chloride ion flow into the cytoplasmic vestibule at negative potentials is limited by the rate of diffusion.
To verify this idea, unrestrained simulations with higher salt concentrations (200 and 300 mM instead of 100 mM; designated as M and H, for medium and high salt) were performed to increase the diffusion rate. If the conduction current is determined by the inherent conductance of the channel (Ohm's law), increasing the concentration of the charge carriers should have no effect. However, if it is dictated by diffusion, increasing the concentration of the charge carriers should lead to increased conduction currents.
The former case is observed for fields of +100 mV/nm. For both M+100 and H+100, the conduction and diffusion currents are reasonably close to those in R+100 and U+100 (both of which use low salt). The independence of the current on the salt concentration indicates that with a +100 mV/nm field we have not reached the diffusion-limited current. In contrast, whereas the steady-state diffusion rates for R–100, U–100, and M–100 are essentially zero, increasing the salt concentration (H–100) increases the diffusion and conduction currents to measurable values (–260 pA and –220 pA). The fact that increasing the concentration of the charge carriers leads to higher currents in the –100 mV/nm field indicates that diffusion is indeed the rate-limiting factor.
Furthermore, the absolute value of the diffusion current (260 pA) is in reasonable agreement with the theoretical rate of diffusion to the cytoplasmic side of the MscS pore. The rate of diffusion of ions to a channel can be approximated as the rate of diffusion 
into a hemisphere of radius r spanning a channel's mouth (1). In the absence of any gradients, this rate is determined as follows:
 | (2) |
). Therefore,
 |
As such, if there were no gradients, the maximum sustainable current by a model pore of the dimensions of MscS is 1.2e ns–1, equivalent to 180 pA. The acceptable agreement between the H–100 currents and this theoretical diffusion rate provides further evidence that diffusion limits the negative current in –100 mV/nm fields.
Because diffusion issues are not a concern in the +100 mV/nm simulations, it is appropriate to use these for an accurate determination of the conductance of MscS in our simulations. As mentioned earlier, the calculated value from these simulations is in good agreement with experiment. It is also worth noting that in the initial phase of Uh–100, when there are ample charge carriers in the cytoplasmic vestibule, the conductance of the channel is 0.71 nS, very near to that for U+100 (Fig. 6 C). Only when the charge carriers are depleted (and not replenished by diffusion) does the current drop to its low steady-state value.
It should be noted that MscS in the simulation system is truncated after the middle-ß domain. The cytoplasmic vestibule is surrounded by the seven middle-ß domains on the sides but is open on the bottom. In contrast, the cytoplasmic vestibule in full-length MscS is surrounded by the middle-ß domains and the large C-terminal domains, with only small portals allowing ions to enter (15). Thus, the full-length protein provides an even larger physical barrier to ionic diffusion into the cytoplasmic vestibule than does the model, and it is likely that the simulations overestimate the rate of diffusion of ions into the cytoplasmic vestibules. In addition, there are 26 disordered residues at the N-terminus of the crystal structure, which are not included in the simulation (15). Because there is no known structure for this region, it is not clear how it influences diffusion rates into the periplasmic domain.
Potential profile of the simulation system
In the +100 mV/nm simulations, we observe diffusion currents that are significantly larger than the theoretical maximum of 180 pA. Therefore, in contrast to the cytoplasmic vestibule, the periplasmic vestibule must be an attractive sink for chloride ions. This is seen more clearly from analysis of the potential profile of the channel.
For each of the six applied electric fields, we determined the electric potential profile of the restrained simulation system (Fig. 7). As mentioned above, like previous descriptions of TM potentials, the entirety of the potential drop of the periodic box occurs in the actual TM region (26,38). However, the protein environment causes the potential to deviate from the linear drop that would be expected for a homogeneous aqueous channel (38). In our system, almost the entirety of the potential drop occurs in the very narrow region of the pore. In addition, the relatively higher potential in this region indicates a significant barrier for chloride movement in either direction. This is undoubtedly due to the partial desolvation of the ion as it passes through the pore, as discussed below.
|
Structural features of the conducting versus the occluded states
Our results provide the opportunity to compare the structures of a conducting form and an occluded form of the MscS channel. The contrasts are seen clearly in snapshots of MscS in the presence of a field of +100 mV/nm, in which the pore remains fully hydrated and conducts well, and in the absence of a field, in which the pore has collapsed (Fig. 4, D and E). We will emphasize this pair in the analysis.
In the hydrated pore, the narrowest constriction—formed by L105 and L109—defines a pore radius of 3 Å, similar to the crystal structure. This is the case for both +100 and –100 mV/nm fields. When there is no water in the pore, in low or moderate fields (–50 to +50 mV/nm), the constriction shrinks to <1 Å (Fig. 8).
|
). In U+100 we observe a different type of motion. During the expansion, TM3 of subunit F moves relatively far from the center, and its kink moves from G113 to A108, with a less severe kink angle. A similar movement is observed for the adjacent TM3 from subunit G (Fig. 9, D and E). Because the timescale of the simulation is short, we cannot say that this is a relevant motion in a global conformational change, but it is notable that TM3 displays so much flexibility.
|
). The high degree of desolvation required to conduct an ion provided some of the evidence for their claim that the MscS crystal structure must be a nonconducting state. For our simulations, we analyzed the solvation of the chloride ions passing through the pore by calculating their radial distribution function (RDF) 
(r). Fig. 10 shows the calculated RDF of water oxygen atoms around chloride ions in bulk water, as well as the averaged RDF of 33 chloride ions in the steady-state phase of U+100 for only the times that they were in the pore. The "pore" chloride RDF is relatively noisy because there are fewer data points available for chloride ions in the pore than in the bulk.
|
0.32, 0.50, and 0.73 nm. The number of waters present in each shell can be determined by integration of the function r2(r). For chloride in the bulk, the shells are occupied by 7, 21, and 35 waters, respectively, although it is difficult to determine a precise endpoint for the third shell. These results—both the radii and occupancy of the solvation shells—agree well with those from previous experimental and computational work (39).
The RDF for the chloride ions in the pore shows different characteristics. A chloride in the pore does have a reduced solvation shell, but its first hydration shell is still essentially intact. Only the second shell and beyond has a lower occupancy. Integration of the peaks reveals that whereas the first shell has the full 7 waters, the second shell contains only 16 waters, and there is only a faintly discernable third shell. Although this amount of solvation is significantly less than that observed for the bulk chloride ions, it is much greater than that reported previously (18).
Studies of selected mutant channels
MscS contains a number of charged residues in its TM domains, including R46, R54, D67, R74, and R88 (Fig. 11 A). As noted above, TM arginine residues likely play an important role in voltage sensing in other ion channels, so we performed several simulations, all completely unrestrained, of MscS mutants in which these charges were altered. The following mutants were studied: R46Rn, R46A, R46E, R54Rn, D67N, R74Rn, R74A, R46Rn/R74Rn, and R88Rn. Rn refers to a "neutralized arginine" residue that is missing one proton from the guanidinium group.
|
A possible explanation for these effects is that the charges, although distant, still contribute significantly to the electrostatic character of the pore. In model pores, partial charges greatly reduce the hydrophobicity and lead to greater pore hydration (9,40). In our case, the charges do not lie directly on the pore wall, but apparently they create a more hydrophilic environment. Removing the charges may make the pore more hydrophobic, thus reducing the hydration.
As expected from the fact that R54, D67, and R88 mutants have similar water behavior to wild-type, conduction current data for these mutants are also reasonably close to wild-type (Table 2). R46 and R74 mutants, on the other hand, have lower currents, in line with the fact that they generally have less hydrated pores. R74Rn is an apparent exception to this trend, although the number of conduction events is small (only three in the steady-state regime) and probably does not accurately reflect the true conductance. These data indicate that mutations at R46 and R74 may result in loss of function channels.
|
), so it is unlikely that the exaggeration is severe.
Investigation of the mechanism for voltage modulation
Electrophysiological studies have demonstrated that voltage modulates MscS function. Early work suggested that depolarization of the membrane leads to increased open probabilities and a decreased threshold for activation by tension (14), but more recent work has indicated that voltage modulates deactivation but not activation (36). In either case, MscS is sensitive to voltage changes. The crystal structure provided insight into a possible mechanism for this: a hinging motion of the TM1-TM2 arm that correlates lateral expansion (tension sensitivity) with upward movement of positive charges on the TM domains (voltage sensitivity) (15). Our MD simulations shed some light on this mechanism, in that we can observe TM domain motion under the influence of different electric fields. The U simulations show that the positions of the TM1 and TM2 helices are indeed correlated with the field. Relative to the unperturbed channel (in the absence of a field), the TM helices are nearer to the periplasm in the +100 mV/nm field, nearer to the cytoplasm in the –100 mV/nm field, but relatively unchanged in the low and moderate fields (Fig. 12 A).
|
It should be noted, however, that in our simulations the positions of the helices do not correlate with the hydration and conduction of the channel. In +100 and –100 mV/nm fields, MscS contains a stably hydrated pore but has TM domains in quite different positions within the membrane. Taken together with the fact that MD simulations of only a few nanoseconds are too short to show protein conformational changes, it is not clear if the TM domain motions observed here are relevant to the activation or deactivation processes.
|
SUMMARY AND CONCLUSIONS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
|---|
) provided many insights but also raised intriguing questions about the relationships between structure and function in this channel. The simulations presented here confirm and expand upon previous work and also provide valuable new insights into the workings of MscS.
Both the minimalist system of Anishkin and Sukharev (18) and the much more complete model of Sotomayor and Schulten (19) concluded that, in the absence of a TM potential, the crystal structure contains a "hydrophobic gate" that excludes water from the narrowest region of the channel and cannot be conducting. Our studies support that conclusion. However, this is only part of the story.
We now find that an applied voltage can prevent collapse of the unrestrained channel. Sotomayor and Schulten showed that the collapse could also be prevented if a substantial tension is applied to the membrane (19). Importantly, in our simulations the open channel is extensively hydrated, and the degree of hydration depends on the magnitude of the voltage. This hydrated channel is able to conduct chloride ions, and the single channel conductances seen are comparable to experimentally observed values. Much lower sodium ion conductance is seen, consistent with the known anion selectivity of the channel. Also, the severe desolvation of pore chloride ions seen by Anishkin and Sukharev is not seen here (18). The hydrated channel under the influence of an electric field can readily accommodate a well-solvated chloride. As anticipated, preliminary simulations of mutant channels show that key TM arginine residues play a critical but as yet not fully understood role in controlling the voltage sensitivity, hydration, and conductance of the channel.
To our knowledge, this is the first MD investigation of the influence of a TM potential on the hydration of hydrophobic nanopores. Our results suggest that an increasing potential reduces the threshold radius for pore hydration. Although the TM potentials applied in these simulations (at least 220 mV) are substantially higher than the 120–160 mV reported for bacterial membranes (35), the tensions employed by Sotomayor and Schulten are also unphysiologically high (19). It has been noted before that, to observe effects on MD timescales, the magnitudes of external stimuli (both tension and voltage) generally must exceed the physiological range (42,43). Also, previous simulations of ion movement in membrane channels have used potentials as large or larger than the potentials used here (38,44).
Of course, the simulations presented here and elsewhere are still quite approximate. The timescales are relatively short, and the force fields are imperfect. Furthermore, with a resolution of 3.9 Å and sevenfold averaging, there is still some uncertainty on precise details of the MscS structure. Nevertheless, all the observations derived from these simulations are consistent with experimental facts, and it seems likely that the qualitative behaviors seen here do reflect the situation under physiological conditions. Based on these observations, we conclude that the image of MscS derived from the crystal structure is more nearly that of an open, conducting state of the channel than a nonconducting state.
|
ACKNOWLEDGEMENTS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
|---|
Submitted on December 26, 2005; accepted for publication February 1, 2006.
|
REFERENCES |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
|---|
2. Zhou, Y., J. H. Morais-Cabral, A. Kaufman, and R. MacKinnon. 2001. Chemistry of ion coordination and hydration revealed by a K+ channel-Fab complex at 2.0 Å resolution. Nature. 414:43–48.[CrossRef][Medline]
3. Betanzos, M., C. S. Chiang, H. R. Guy, and S. Sukharev. 2002. A large iris-like expansion of a mechanosensitive channel protein induced by membrane tension. Nat. Struct. Biol. 9:704–710.[CrossRef][Medline]
4. Sukharev, S. 2002. Purification of the small mechanosensitive channel of Escherichia coli (MscS): the subunit structure, conduction, and gating characteristics in liposomes. Biophys. J. 83:290–298.
5. Song, L., M. R. Hobaugh, C. Shustak, S. Cheley, H. Bayley, and J. E. Gouaux. 1996. Structure of staphylococcal alpha-hemolysin, a heptameric transmembrane pore. Science. 274:1859–1866.
6. Evans, R. 1990. Fluids adsorbed in narrow pores—phase-equilibria and structure. J. Phys. Condens. Matter. 2:8989–9007.[CrossRef]
7. Beckstein, O., P. C. Biggin, and M. S. P. Sansom. 2001. A hydrophobic gating mechanism for nanopores. J. Phys. Chem. B. 105:12902–12905.
8. Beckstein, O., and M. S. Sansom. 2003. Liquid-vapor oscillations of water in hydrophobic nanopores. Proc. Natl. Acad. Sci. USA. 100:7063–7068.
9. Beckstein, O., and M. S. Sansom. 2004. The influence of geometry, surface character, and flexibility on the permeation of ions and water through biological pores. Phys. Biol. 1:42–52.[CrossRef][Medline]
10. Corry, B. 2006. An energy-efficient gating mechanism in the acetylcholine receptor channel suggested by molecular and Brownian dynamics. Biophys. J. 90:799–810.
11. Wan, R., J. Li, H. Lu, and H. Fang. 2005. Controllable water channel gating of nanometer dimensions. J. Am. Chem. Soc. 127:7166–7170.[CrossRef][Medline]
12. Hummer, G., J. C. Rasaiah, and J. P. Noworyta. 2001. Water conduction through the hydrophobic channel of a carbon nanotube. Nature. 414:188–190.[CrossRef][Medline]
13. Levina, N., S. Totemeyer, N. R. Stokes, P. Louis, M. A. Jones, and I. R. Booth. 1999. Protection of Escherichia coli cells against extreme turgor by activation of MscS and MscL mechanosensitive channels: identification of genes required for MscS activity. EMBO J. 18:1730–1737.[CrossRef][Medline]
14. Martinac, B., M. Buechner, A. H. Delcour, J. Adler, and C. Kung. 1987. Pressure-sensitive ion channel in Escherichia coli. Proc. Natl. Acad. Sci. USA. 84:2297–2301
of L109 of each subunit. (C–E) Snapshots of TM3 of the E, F, and G subunits at the end of U+100. Red spheres represent the C
