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Copyright © 2007 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 92, Issue 3, 886-902, 1 February 2007

doi:10.1529/biophysj.106.095232

Channels, Receptors, and Electrical Signaling

Ion Conduction through MscS as Determined by Electrophysiology and Simulation

Marcos Sotomayor^*, 1, Valeria Vásquez^{†, ‡, 1}, Eduardo Perozo^† and Klaus Schulten^*, ,  

^* Department of Physics, University of Illinois at Urbana-Champaign, and Beckman Institute for Advanced Science and Technology, Urbana, Illinois
^† Institute for Molecular Pediatrics Science and Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, Illinois
^‡ Department of Molecular Physiology and Biological Physics, University of Virginia, Charlottesville, Virginia

Address reprint requests to K. Schulten.

¹ M. Sotomayor and V. Vasquez contributed equally to this work.

Mechanical forces are essential stimuli for living organisms: from cell volume regulation to perception of sound, life relies on mechanosensation. The ultimate and perhaps the most important molecules behind mechanosensation are mechanosensitive channels that widen significantly upon force activation and generate a signal by facilitating transport of solutes across the cell membrane 1,2,3,4,5,6.

The mechanosensitive channel of small conductance, MscS, is one of such membrane proteins and is thought to act as a safety valve in bacteria, preventing cell lysis upon osmotic shock by opening and closing in response to membrane tension 7,8,9,10,11. MscS-related proteins have been found in bacteria, archea, and plants 12,13,14. Accordingly, MscS is considered an archetypal mechanosensor. It is one of two mechanosensitive channels structurally known, yet details of its gating mechanism remain unknown. Interestingly, MscS is also voltage-modulated.

The conductance of the fully open channel has been measured in patch-clamp experiments to be ∼1nS; the channel is slightly anion-selective 7,10 and possesses at least one subconductance state 15. Activation of the channel has been found to be strongly dependent on the rate of pressure applied 11, while inactivation, rather than activation 7, has been found to be voltage-dependent 11,16.

The x-ray crystal structure of Escherichia coli MscS 17, solved at 3.9Å resolution, revealed a heptameric arrangement of subunits made of three transmembrane helices each (TM1, TM2, and TM3A-TM3B), with the transmembrane pore captured in a putative open state of radius ∼3.3Å (Fig. 1). The structure features a large, balloon-shaped, cytoplasmic domain with seven side openings and a distal entrance. This large cytoplasmic domain has been suggested to act as a molecular filter 17, to be involved in gating 18,19,20, and to stabilize the channel 21,22, but actually its function remains unknown.

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Figure 1

Architecture of the mechanosensitive channel of small conductance MscS. The crystal structure is shown as a transparent surface with two (out of seven) subunits depicted in cartoon representation (colored for better visualization). The putative location of the membrane is indicated along with the symmetry axis of MscS, and an exit/entrance pathway through one of the cytoplasmic side openings. Charged residues (R88 and K169) located at the entrance of the transmembrane channel and residues forming its narrowest section (L105) are shown in space-filling representation along with residues defining the transmembrane pore (V96 and G113).

Each MscS monomer has 286 amino acids. In the crystal structure the first 26 residues and the last six residues of each subunit were not resolved. Nevertheless, the crystal structure provides an excellent frame of reference to interpret experimental results as well as an essential starting point for simulations that seek to establish MscS's function/structure relationship 23,24,25. The structure poses a challenge for computational studies, since MscS is a relatively large protein that undergoes considerable, reversible structural rearrangement 11,18,26. Therefore, whether the crystal conformation represents an open, intermediate, inactive, or closed state 27, and how it goes from one state to another, are difficult questions, yet there exists an excellent chance to establish answers by combining experimental and computational approaches.

On the experimental side, replacement of conserved glycine residues by alanine along the pore-lining helices (TM3A) has been shown to increase activation pressure of MscS. A similar effect is observed when conserved alanines are replaced by larger amino acids. Conversely, introduction of glycine residues has been shown to lower the pressure required for gating 28. These results highlight the role in MscS function of hydrophobicity and complementarity of the surfaces of helices forming the pore, suggesting that the glycine-rich region of TM3 plays a “pivotal role” in gating 28. Whether these mutations affect the flexibility of TM3 helices (which present a pronounced kink at Gly¹¹³, see Fig. 1) and how concerted movements of TM3 are coupled to peripheral helices (TM1 and TM2) remains to be elucidated. The coupling of the latter helices (TM1-TM2) to lipids has been addressed in an elegant recent study in which hydrophobic residues along them are mutated to asparagine 29. Modification of the hydrophobic lipid-protein interface at both ends of the helices increased the gating threshold of MscS and decreased the viability of cells when subject to osmotic shock 29, pointing out the relevance of membrane-protein interactions for MscS gating. Based on electrophysiological measurements and a reinterpretation of the MscS crystal structure, a gating model of MscS has been put forward by Sukharev and co-workers 11. In this model, the crystal conformation represents an inactive state in which lipids impair coupling between TM1-TM2 and TM3 helices. In the open and closed states, however, these helices are tightly packed, forming either a wide pore or a very compact structure. The latter model of MscS gating, the actual size of the open pore, and the voltage dependence of gating and inactivation remain to be clearly elucidated by experimental means.

On the computational side, two independent all-atom molecular dynamics (MD) studies have shown that the MscS transmembrane pore closes asymmetrically on a nanosecond timescale 30,31. A symmetric closed state has been suggested based on site-directed mutagenesis and computational modeling of only a reduced section of the MscS pore 28. Three computational studies have reported dewetting transitions in the narrowest section of the MscS transmembrane pore as depicted by the crystal 30,31,32. The computational studies have suggested that the crystal represents an already closed or inactive state 11,32, a “close to conducting” state 31, or a not-fully-open and highly anion selective state 33. The latter study combined all-atom MD with a coarse-grained, particle-based methodology, BioMOCA 34, which simplifies the description of protein, lipids, and solvent, while reaching simulation timescales of microseconds. The BioMOCA methodology and similar widely used simplified approaches 35,36,37,38,39 may introduce systematic errors and all-atom MD simulations of the entire MscS structure are much needed to complement the coarse-grained, i.e., BioMOCA, simulations.

Needless to say, a thorough comparison of computational modeling to conduction and gating properties of MscS unambiguously determined by experiments are invaluable in the quest to relate function and structure of MscS. We present below such comparison suggesting that the available crystal conformation of MscS represents a not-fully-open or inactive conformation, while a modeled conformation may correspond to MscS's open state.

MscS was cloned in a vector containing an RGS-His6 epitope at the N-terminus (pQE32) and expressed by IPTG induction in an E. coli strain that lacks MscL, MscS, and MscK (MJF465), i.e., provides a genetically clean background. The E. coli strain MJF453 containing genomic MscS was used as well; no significant differences were found while using MscS expressed from the genome or from the plasmid. These strains were kindly donated by I. R. Booth (University of Aberdeen).

Channel activity was recorded by patch-clamping giant spheroplasts following the method described in Martinac et al. 7. Patch-clamp measurements were done in the inside-out configuration under symmetrical conditions (200mM KCl, 90mM MgCl₂, 10mM CaCl₂, and 5mM HEPES) or asymmetrical conditions (100mM KCl in the pipette/300mM KCl in the bath, all other salts as above), at pH 6 and room temperature. For both conditions, the bath solution contained 300mM sucrose to keep spheroplasts intact.

Pipettes were made out of glass capillaries (Sigma, St. Louis, MO: catalog No. P1174), and were fire-polished before use until a resistance between 2 and 2.5 MΩ was reached. Negative pressure on the patch was obtained by applying suction through a syringe and monitored with a homemade piezoelectric pressure transducer. Single-channel and macroscopic currents were sampled at 10KHz with an analog filter set to 2KHz. Single channel analyses were done using pCLAMP9 (Axon Instruments, Foster City, CA).

Macroscopic currents were measured using a two-pulse voltage protocol (an initial hyperpolarizing pulse to −65mV was followed by a set of depolarization pulses up to 60mV) and at constant negative pressure. The two-pulse voltage protocol reduced the variability in current amplitude due to changes between pressure and voltage pulses and was performed on the same patch with a 3-min interval between sets of pulses 16.

Selectivity of MscS was determined using the experimentally measured reversal potential and the Goldman-Hodgkin-Katz (GHK) equation 40

(1)

The experimental nominal open probability (NP_o) was determined using

(2)

Molecular dynamics simulations were performed on a system containing the entire crystal structure of MscS (Protein Data Bank code 1MXM 17) embedded in a membrane bilayer formed by 299 POPC lipids solvated in >50,000 explicit water molecules and 200mM of KCl (altogether a ∼224,000-atom system). Two different starting conformations were assumed. The first conformation (S0) was obtained after ∼4.5ns of dynamics with backbone atoms restrained to their positions in the crystal (k=1Kcal/mol/Ų). The second conformation (S1) was obtained after ∼5ns of molecular dynamics simulation in which opening was induced by forces applied radially in the x,y-plane to C_α atoms of residues 96–113. In both cases, S0 and S1, all Asp, Glu, Lys, and Arg residues were assumed to be charged, as expected from pK_a calculations (see Supplementary Material's Table 3). The sizes of the simulation cell were 108.3×111.4×178.6ų and 107.9×115.3×172.1ų for conformations S0 and S1, respectively. Details of the corresponding molecular dynamics simulations leading to S0 and S1 conformations can be found in Sotomayor and Schulten 30 and Sotomayor et al. 33.

Four different modifications of the simulated system were performed as listed in Table 1:

Molecular dynamics simulations were performed using NAMD 2.5 42, the CHARMM27 force field for proteins and lipids 43, and the TIP3P model for water 44. The simulations are listed in Table 1.

A uniform integration time step of 1 fs was assumed for most of the simulations. However, when stated, a multiple time-stepping (MTS) algorithm 45 was employed in which interactions involving covalent bonds were computed every 1 fs, short-range nonbonded interactions every 2 fs, and long-range electrostatic forces every 4 fs. In all cases a cutoff of 12Å (switching function starting at 10Å) for van der Waals interactions was assumed, and the particle-mesh-Ewald (PME) method was used to compute long-range electrostatic forces without cutoff. The density of grid points for PME was at least 1/ų. All simulated systems were properly neutralized by adjusting the number of ions in the system; periodic boundary conditions were assumed in all cases.

Langevin dynamics was utilized to maintain a constant temperature of T=300K, with the damping coefficient set to 1ps⁻¹ for all heavy atoms in all simulations except those labeled NpTM or NVTM (see Ensemble column of Table 1). In the latter cases, the damping coefficient was set to 1ps⁻¹ for lipid heavy atoms only and zero for all other atoms, thereby avoiding artificial heating caused by electric fields and artificial viscosity for bulk electrolyte introduced by the Langevin dynamics. Constant pressure simulations at 1atm were conducted using the hybrid Nosé-Hoover Langevin piston method with a decay period of 200 fs and a damping timescale of 50 fs.

Biasing voltages were applied through a uniform electrostatic field to all atoms of the system along the z axis (perpendicular to the membrane plane) 46,47. The voltage difference V across the simulated cell is

(3)

Coordinates of all atoms of the system were saved every picosecond of simulation for later analysis. Structural deformation of the protein was monitored by computing root mean-square deviations (RMSD) over entire trajectories using VMD 41. The crystallographic structure served as the reference point, and only positions of protein backbone atoms were compared.

Computation of the electrostatic potential ϕ(r) for different trajectories was carried out using the PME method 42,48,49 through a modified version of the VMD plugin PMEpot. The underlying algorithm solves the Poisson equation

(4)

(5)

The radius profile of the MscS transmembrane pore along the axis perpendicular to the membrane plane was computed using HOLE 50 for snapshots of the simulated system taken every 100ps. The default all-atom set of van der Waals radii from AMBER was used and sample planes were spaced uniformly at 0.5Å in the z direction. Once the radius profile was determined, the minimum value around the constriction zone (Leu¹⁰⁵) was employed to construct radius versus time plots.

All densities of ions and water were computed and averaged over stored trajectories using the VMD plugin volmap and a grid spacing of 1.5Å. Computed densities are stored in a three-dimensional array of voxels used to generate two-dimensional slices of one grid-cell thickness as well as one-dimensional profiles along the channel axis. The number of ions crossing the MscS transmembrane pore was computed for different trajectories with VMD. A crossing event was defined by the passage of an ion from the cytoplasmic to the periplasmic bath or vice versa, with boundaries determined every picosecond by the single-frame average position of C_α atoms of residues Val⁹⁶ (periplasmic boundary) and Gly¹¹³ (cytoplasmic boundary) of all subunits (see Fig. 1). Since the potential drop occurs mainly at the transmembrane pore (see below) and no major electrostatic forces arise in the cytoplasmic openings of MscS, it seems reasonable not to include them in the definition of the crossing region. Ionic currents through the MscS transmembrane pore were then computed by performing a linear fit to the number of crossing events plotted versus time (when applicable). When the number of crossings was too small to perform a reliable fit, the current was estimated using

(6)

Ten control simulations of a system containing 200mM of KCl in water (11,703-atom system, 50ų) were performed to determine bulk conductivity of KCl as reported in Aksimentiev and Schulten 48. After 1ns of dynamics in the NpT ensemble (Langevin temperature control was applied to all heavy atoms with a damping coefficient of 1ps⁻¹, the PME method was employed, and a uniform time step of 1 fs was chosen), three sets of simulations were performed in the NVT ensemble, each set consisting of three simulations (4ns each) where electrostatic biases of 0, +1.2, and −1.2 Volts were applied. The first set was performed using a Langevin damping coefficient of 1ps⁻¹, the second set utilized a damping coefficient of 0.1ps⁻¹, and in the last set the PME method for computation of long-range electrostatic properties was turned off, while the Langevin damping coefficient was set to 0.1ps⁻¹.

Induced currents and bulk resistivity of the electrolyte were estimated by counting the number of ions that crossed a virtual box (with l=l_x=l_y=48.3Å and l_z=25Å or l_z=12.5Å) along the z axis. The number of crossing events, found to be roughly independent of l_z, was plotted against time (see Supplementary Material's Fig. 15 B) and currents I_i were determined by corresponding linear fits to the data, yielding I₁=17.2 nA for the first set, I₂=20.1 nA for the second set, and I₃=13.3 nA for the third set. The associated resistivities ρ₁=0.34 Ωm, ρ₂=0.29 Ωm, and ρ₃=0.44 Ωm were computed using the magnitude of the uniform applied electric field E and the measured current density J_i employing the expression

(7)

The experimental conductivity of KCl at 0.1M and 25°C is κ=1.28217 S/m, and the estimated experimental resistivity at 0.2M is ∼0.4 Ωm. Thus, currents computed with the CHARMM force field at 0.2M are slightly overestimated when using PME and small values for the Langevin damping coefficient, as already reported in Aksimentiev and Schulten 48. Therefore, scaling was applied to ionic currents as specified below.

MscS activity was characterized using an E. coli strain lacking MscS, MscL, and MscK channels 9, which ensures that the recorded response corresponds only to that of the recombinant MscS. Patch-clamp experiments were performed on giant-spheroplasts under the inside-out configuration and revealed MscS activity when a gentle pressure (such as −40mmHg) was applied. The current-voltage relation obtained under these conditions is shown in Figure 2A and exhibits a slight rectification for positive membrane potentials, which becomes more evident when using asymmetric conditions. The estimated conductance at 200mM of KCl is ∼1.16 nS, in agreement with previous electrophysiological measurements of MscS 11,28. Under asymmetric conditions, the reversal potential is estimated to be +2.2mV, which is small compared to the theoretical reversal potential for a completely selective anion channel (+28.4mV according to the Nernst equation). Using the GHK equation (see Materials and Methods), the selectivity of the channel is estimated to be P_Cl+/P_K−=1.19, slightly smaller than the previously reported ratio of ∼1.48 10. Thus, MscS seems to be only very slightly selective for anions.

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Figure 2

Current-voltage relation in symmetric and asymmetric conditions of wild-type MscS under constant pressure as determined by patch-clamp experiments. (A) The current-voltage relation, recorded at a constant pressure of −40mmHg, shows a slope conductance of ∼1.16nS in symmetric solutions (200mM KCl, pH 6.0) and a slope conductance of ∼1.19nS in asymmetric solutions (100mM KCl pipette/300mM KCl bath, pH 6.0). Under these conditions the reversal potential of MscS is ∼2mV. MscS shows a slight rectification at positive potentials. Mean±SD are shown. (B) Representative single-channel traces of MscS (in pQE32, see Materials and Methods) expressed in MJF465 (an E. coli strain lacking MscL, MscS, and MscK) were recorded by patch-clamping giants spheroplasts under inside-out configuration. Traces were obtained at the voltage indicated and at a constant pressure of −40mmHg.

Single-channel traces of MscS activity shown in Figure 2B exhibit a behavior that depends on the sign of the applied bias. While MscS remains steadily in an open state at negative membrane potentials, the single channel transitions measured for positive biases are less well defined and more flickery, likely indicating that under these conditions MscS adopts multiple and unstable open conformations.

Macroscopic currents and the corresponding nominal open probability of MscS (NP_o, Figure 3A) seem to indicate that the number of open channels depends on the applied voltage. The higher the magnitude of the voltage applied, the lower the open probability 51. However, this behavior might be caused by differences in the rate of pressure application (see 11) and/or differences in the total number of channels available in the corresponding patches. Another reason might be associated with the very slow recovery of MscS from inactivation 11,16, coupled with the intrinsic variability of mechanical stimulation of membrane patches 52,53. The midpoint activation value determined from NP_o is voltage-independent, as shown in Figure 3B, i.e., the pressure required to open MscS does not depend on the applied voltage. In contrast, a two-pulse voltage protocol used to measure macroscopic currents revealed that MscS inactivation depends strongly on the applied bias. Indeed, the decay time-constant for the macroscopic current depends dramatically on the sign of the second voltage pulse (Figure 3CD). The voltage dependence of inactivation appears to be the determinant of channel activity at positive potentials, although the channels also inactivate at negative potentials. The latter result, first reported in Vasquez and Perozo 16, agrees well with data presented in Akitake et al. 11, but differs from previous studies suggesting voltage-independent adaptation 51. The disagreement may be due to differences in the range and/or duration of applied voltages. While voltages utilized in Koprowski and Kubalski 51 did not exceed ±30mV, the voltage dependence of inactivation observed here arises at voltages larger than ±40mV (Figure 3D).

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Figure 3

MscS gating is dependent on tension and modulated by voltage. (A) Macroscopic MscS currents adjusted to a Boltzmann-function fit to the NP_o (nominal open probability) versus pressure at different transmembrane potentials. The inset shows macroscopic currents (at least 30 channels in the patch) corresponding to ±20mV, elicited by an increase in negative pressure up to −80mmHg. (B) Midpoints of activation (P_1/2) plotted against transmembrane voltage (derived from the Boltzmann-function fit shown in panel A) suggest that opening of MscS at different potentials has approximately the same P_1/2 value. Mean±SD are shown. (C) Macroscopic currents obtained from two-pulse protocol experiments under constant pressure reveal the presence of a voltage-dependent inactivation; the rate and extent of inactivation speeds-up significantly with membrane depolarization. (D) Decay time constant τ obtained from fitting a single exponential to the macroscopic records obtained from the two-pulse protocol showing the voltage dependence of the inactivation.

The overall behavior of MscS as determined by patch-clamp experiments reported here agrees well with previous experiments performed using the same E. coli strain 11. This experimental characterization of MscS activity suggests that MscS adopts an open state, a closed state, and an inactive state. Therefore, we asked whether the crystal structure of MscS represents either of such states.

To determine the conduction properties of the MscS crystal structure one needs to invoke simulation. For this purpose two sets of simulations with MscS's backbone atoms restrained to the crystal conformation were performed. A first set of simulations was performed in the NVT ensemble and consisted of four different simulations in which the system was subject to biasing voltages of 0, +1.2, −1.2, and −0.6V (sim1a, sim5a, sim7a, and sim9a in Table 1, respectively). A second set of simulations of MscS with its backbone restrained consisted of three simulations in which temperature control was applied to heavy atoms of lipids only, to avoid both artificial heating caused by fields and artificial viscosity for bulk electrolyte introduced by Langevin dynamics (sim2a, sim6a, and sim8a, with biasing electrostatic potentials of 0, +1.2, and −1.2V, respectively). In all cases the transmembrane pore remained in an “open” conformation as observed in the crystal, although side chains, but not backbone atoms, were free to move (see Figure 4A with the pore featuring a radius of ∼3Å in the constriction zone, as quantified in Figure 8A).

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Figure 4

Top views of MscS's transmembrane pore (residues 96–128) shown in cartoon and transparent surface representations (residues 96–128) at the end of simulations (A) sim5a (+1.2V, backbone restrained), (B) sim5b (+1.2V, backbone released), (C) sim6b (+1.2V, backbone released), and (D) sim5d (0V, backbone released).

Application of external electrostatic potentials resulted, as expected, in transport of ions through the transmembrane pore. Figure 5A shows Cl⁻ permeation events throughout simulations in which a +1.2V bias was applied while the protein was restrained to its crystallographic conformation (sim5a and sim6a, see Table 1,Table 2). From the data it is evident that the crystal conformation exhibits low conductance and high selectivity for Cl⁻. Indeed, meaningful conduction was observed only for simulations at +1.2V and was driven entirely by Cl⁻ ions. The maximum estimated current for the restrained structure is ∼237±61 pA (sim5a), which corresponds to a conductance of ∼198 pS at +1.2V. If one takes into account the overestimate of bulk KCl conductivity using identical simulation conditions (as described in Materials and Methods), the conductance scales down to ∼169 pS, a value that is small compared to the expected 1 nS conductance of the fully-open channel. Furthermore, reversal of the applied potential to −1.2 and −0.6V in simulations sim7a, sim8a, and sim9a resulted in negligible ion transport.

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Figure 5

Ionic currents through MscS as determined by all-atom MD simulations. (A) Ion crossing events (Cl⁻) through MscS's transmembrane pore versus time for simulations sim5a (solid black), sim5b (solid gray), sim6a (dashed black), and sim6b (dashed gray). A clear steady-state ionic current driven by chloride ions (enhanced upon release of restraints) is observed for simulations sim5a, sim5b, and sim6b (+1.2V). The inset shows crossing events during sim5a, sim5b, and sim5c-sim5d (black, gray, and light gray for Cl⁻ and K⁺ ions). High anionic selectivity is evident, and ions stop crossing the channel when the biasing potential is turned off in sim5c-sim5d (as expected). (B) Ion crossing events in simulations where only the transmembrane domain of a wider conformation of MscS (residues 27–128) was included in the system (sim15c at +1.2V and sim15d at −1.2V). Black and gray curves show crossings for Cl⁻ and K⁺ ions, respectively.

Table 2 Summary of conduction events through MscS

	Label	tsim (ns)	Voltage (V)	K+ +z	K+−z	Cl− +z	Cl−−z	–	I pA	I/ pA	Iscaled pA
	sim1c	5	+1.2	0	0	6	0	large	192	78	139
	sim2b	5	0.0	0	0	1	0	–	32	32	23
	sim5a	12	+1.2	0	1	14	0	14	237	61	203
	sim5b	10	+1.2	0	4	58	0	14.5	1051	133	893
	sim5c-sim5d	10.9	0.0	1	0	2	5	–	59	20	50
	sim6a	10	+1.2	0	1	3	0	3	64	32	46
	sim6b	5	+1.2	0	4	45	0	11.3	1586	226	1150
	sim6c	3.5	0.0	0	0	0	2	–	92	65	67
	sim7a	12	−1.2	1	0	0	1	1	27	19	23
	sim7b*	4.5	−1.2	4	0	0	15	3.75	676	155	575
	sim10a	9.5	0.0	1	1	2	4	–	34	12	25
	sim10b	9.6	+0.1	2	2	8	0	large	134	38	97
	sim10c	9.5	−0.1	0	0	0	4	large	68	34	49
	sim15a	1	0.0	0	0	0	1	–	160	160	136
	sim15b	4.8	0.0	0	0	2	1	–	33	33	24
	sim15c	4.7	+1.2	0	11	38	0	3.45	1656	236	1200
	sim15d	5.4	−1.2	7	0	0	32	4.5	1086	192	787

Simulations are labeled as in Table 1. Ion-crossings (as defined in Materials and Methods) are indicated for all simulations in which at least one ion crossed MscS's transmembrane pore. Conduction events are labeled as +z for an ion going from the periplasmic to the cytoplasmic bath and −z for an ion going in the opposite direction. Selectivity can be estimated from the ratio of the number of permeation events for each ion, . Ionic currents were determined as indicated in Materials and Methods for simulations that showed Ohmic behavior (sim5a, sim5b, sim6b, sim15c, sim15d) or by simply dividing the total number of permeation events by the corresponding simulation time. An error for ionic currents can be estimated from I/. The values presented in the last column are scaled according to estimated KCl bulk conductivities as indicated in the main text.

* The integrity of the pore was compromised during this simulation and ions permeated through interstitial openings between TM3A helices.

The small currents and strong rectification observed for negative biasing potentials contrast with the experimental data showing only a weak rectification that becomes more apparent under asymmetrical conditions (Figure 2A). The discrepancy may be a consequence of the large voltages used in the simulations, since the maximum current flowing through the channel is limited by free diffusion of ions being supplied to the periplasmic and cytoplasmic ends of the pore 40, as discussed in Spronk et al. 31. However, the same behavior was observed in BioMOCA simulations of the MscS crystal conformation lasting 100ns each and using smaller biases of ±50mV and ±100mV 33 (see comparison below). Moreover, crude estimates of MscS's conductance presented in Sotomayor and Schulten 30 and Anishkin and Sukharev 32 agree well with the observed behavior. Overall, different computational results (obtained in some cases from independent groups) seem to converge to the same conclusion 30,32,33,39.

What determines then the strong selectivity seen in the prior 33 and present simulations given the fact that electrophysiological measurements do not show such selectivity? Averaged electrostatic potentials, shown for each of the restrained simulations in Fig. 6 and Supplementary Material's Fig. 9, along with distribution of ions and density of water molecules throughout the simulation cell, described below, partially answer this question.

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Figure 6

Averaged electrostatic potential of MscS as determined through all-atom MD simulations and the PME method. (A) Three-dimensional surface showing the electrostatic potential of MscS averaged over 10ns of simulation (sim9a) in which the protein backbone was restrained to its original crystallographic conformation and a biasing potential of −0.6V was applied to the simulated system. The surface corresponds to the electrostatic potential of a slice perpendicular to the membrane plane passing through the center of the channel. (B) Two-dimensional contour plot of the electrostatic potential shown in panel A. The crystal structure (shown in cartoon representation) is superimposed as a reference. Twenty contour lines are drawn over the range of voltages of the corresponding data set. All values above or below the scale limits (see color bar) are shown at the same level. (C) Electrostatic potential (as in panel B) averaged over 10ns of simulation in which the protein backbone was restrained and no biasing potential was applied (sim1a). (D) Electrostatic potential averaged over 10ns of simulation in which the protein backbone was restrained, no biasing potential was applied, and N- and C-termini were modeled as neutral entities (sim4a). (E) Electrostatic potential averaged over 10ns of simulation in which the protein backbone was restrained and a biasing potential of +1.2V was applied to the simulated system (sim5a). (F) Electrostatic potential averaged over 10ns of simulation in which the protein backbone was restrained and a biasing potential of-1.2V was applied to the simulated system (sim7a).

Electrostatic potential maps were computed for simulations in which the backbone of MscS was restrained to its crystal conformation (simulations sim1a, sim2a, sim5a, sim6a, sim7a, sim8a, and sim9a). The most interesting feature of the computed electrostatic potentials without bias is a positive barrier (+320mV) observed along the transmembrane pore (see Figure 6CC and Figure 8CC). The barrier arises in a hydrophobic region of low water concentration and explains the accumulation of Cl⁻ ions observed in the vicinity of this region (Figure 7A), as well as the ion selectivity described below. Several simulations were carried out to investigate the electrostatic barrier. Termini were neutralized (sim4a), different sets of charged residues were mutated (R88Q in sim12a, K169Q in sim13a, and R88Q/K169Q in sim14a), and arginine residues located in the transmembrane domain were neutralized (sim11a, R46/R74), the latter simulation motivated by recent experimental and theoretical results suggesting that arginine residues in a low dielectric environment may not be charged 54 (Danilo Gonzales-Nilo, Universidad de Talca, Chile, personal communication, 2005). As documented in the Supplementary Material , mutation K169Q showed a major effect on the barrier.

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Figure 7

Two-dimensional slices showing Cl⁻, K⁺, and water oxygen concentrations for different all-atom MD simulations. Concentrations are plotted in moles per liter (M) on a logarithmic scale. All values above or below the scale limits are shown at the same level. (A) Average concentrations for a 10-ns MD simulation in which the protein backbone was restrained and no biasing potential was applied to the system (sim1a). A clear separation in the distribution of Cl⁻ and K⁺ is observed, but conduction of ions through the transmembrane pore did not occur. The water oxygen concentration is reduced at the narrowest sections of the transmembrane (see inset) and cytoplasmic distal pore. (B) Average concentrations over 10ns from an MD simulation in which the protein backbone was restrained and a biasing potential of +1.2V was applied to the system (sim5a). While the Cl⁻ density shows a rather flat profile along the transmembrane pore, the K⁺ ion density is clearly reduced at the narrowest sections. For both Cl⁻ and K⁺ ions, transport occurs through the side openings of MscS's cytoplasmic domain. The water density at the narrowest section of the pore is larger than that observed when no biasing potential is applied (see panel A). (C) Average concentrations over 10ns of MD simulation in which the protein backbone was restrained and a biasing potential of −1.2V was applied to the system (sim7a). No conduction of K⁺ ions is observed through the transmembrane pore, since the only permeation event reported for K⁺ (see Table 2) occurred outside of the time-window used for averaging. An increased penetration of Cl⁻ ions through the cytoplasmic side of the membrane is discernible.

An even larger electrostatic barrier (+530mV) is observed across the distal “bottom” (oriented as in Fig. 1) entrance of the cytoplasmic domain. This entrance is hydrophobic and features few water molecules; it is far from the location of the potential drop observed when biasing potentials are applied and, therefore, should not play a direct role in ion transport. Side openings in the cytoplasmic domain exhibit smaller or almost nonexistent electrostatic barriers to ions.

In addition to the features described above, all the computed electrostatic potentials were found to be flat in bulk electrolyte, to exhibit a focused drop across the transmembrane pore of MscS when external biases were applied, and to be positive within proteinaceous and lipidic regions.

The flat potential in bulk electrolyte suggests that simulation times (5–12ns) were long enough for ions to reach a stationary state. Moreover, despite the large voltages applied during our simulations, the membrane did not break apart, but functioned as an effective barrier for ions and water molecules.

Positive values of the electrostatic potential (∼+800mV) in the lipid region, observed in all simulations, are consistent with the membrane dipole potential caused by lipid headgroups and surrounding water molecules. First postulated to explain experiments in which hydrophobic anions readily permeated across membrane bilayers (in contrast to structurally analogous hydrophobic cations) 55,56,57,58, positive membrane dipole potentials have been observed in multiple all-atom, explicit-solvent molecular dynamics studies 48,59,60,61,62,63,64 and mixed implicit/explicit solvent Poisson computations 65. Positive values of the electrostatic potential in protein domains have been reported earlier as well and attributed to the distribution of charges in the backbone dipoles 66.

The distribution of ions around MscS was not completely uniform and exhibited an accumulation of Cl⁻ ions at the periplasmic and cytoplasmic ends of the MscS transmembrane pore in the absence of biasing potentials (Figure 7A), consistent with the electrostatic potential maps described above. Potassium ions, on the other hand, accumulated in the distal zone of the cytoplasmic domain (Figure 7A).

From the distribution of ions it can be confirmed that permeation events did not occur across the transmembrane domain unless biases were applied (compare Figure 7AC). Indeed, upon application of electrostatic biases, Cl⁻ ions were observed to permeate the transmembrane pore, while K⁺ ions did so more rarely, as clearly seen in the corresponding density plots (Figure 7BC), which also show how ions permeate through the protein's cytoplasmic side openings. During these simulations, Cl⁻ ions were observed to temporarily bind to a pocket formed by residues 83–98 of adjacent subunits at the periplasmic entrance of the channel, directly involving Arg⁸⁸ and Thr⁹³, the latter residue causing a gain of function phenotype when mutated to Arg 21 (the simulations are shown in Supplementary Material's movies ). An unusual increase in the Cl⁻ concentration in the cytoplasmic boundary of the membrane (at the interface with the protein) is observed for simulations with a negative biasing potential; ions indeed penetrated hydrophobic crevices of the protein.

Only a single potassium ion was observed to permeate the restrained channel in simulations sim5a, sim6a, and sim7a. The positive ion used chloride ions as a ladder to climb across the transmembrane pore, a behavior reflected also in an unusual peak in the K⁺ ion density at the center of this region.

Is water distributed homogeneously throughout the simulation cell? This question is relevant since hydration may affect conduction through MscS. The average water density is uniform throughout bulk regions and in the interior of MscS's cytoplasmic domain (∼56M, see Fig. 7 and Figure 8F). However, a drastic reduction in water density can be observed along the transmembrane pore and at the distal “bottom” entrance of the cytoplasmic domain. The reduction in density is consistent with observed dewetting transitions in hydrophobic pores 30,31,32,67,68,69 and disappears when a large electrostatic bias is applied. The latter effect is very similar to that reported in Dzubiella et al. 70 for ion transport through generic hydrophobic nanopores. In addition, Spronk et al. 31 presented compelling evidence suggesting that hydration of the pore is indeed favored by application of an electrostatic potential and the energetics of water molecule orientation within the transmembrane pore. However, only simulations of hydrophobic pores with and without ions and subject to small electrostatic fields will demonstrate if dewetting transitions are totally eliminated, and whether this is caused by the action of the electrostatic potential itself 71, or is a consequence of movements of ions and their respective hydration shells.

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Figure 8

Dynamics and electrostatics of MscS. (A) Time evolution of the radius at the constriction of MscS's transmembrane domain (Leu¹⁰⁵) for simulations sim1a-sim1b (solid black), sim4a-sim4b (dashed black), sim5a-sim5b (blue), sim5c-sim5d (dashed blue), sim9a-sim9b (red), and sim1c (green). Harmonic restraints applied to backbone atoms maintained the pore in an open state with a radius of ∼3 Å in simulations sim1a, sim4a, sim5a, and sim9a. A clear decrease in the radius can be observed for simulations in which restraints were released and no biasing potential was applied. (B) Root mean-square deviations for the transmembrane domain of MscS (residues 27–128) during simulations sim1a-sim1b-sim1c (black), sim5a-sim5b-sim5c-sim5d (blue), and sim9a-sim9b (red), as well as for the cytoplasmic domain of MscS (brown, purple, and orange). RMSD values for simulations without bias seem to converge at a rather large value (∼5Å) after 10ns of dynamics. (C) Time-averaged electrostatic potential along the symmetry axis of MscS for sim1a (solid black), sim4a (dashed black), sim5a (blue), sim7a (solid red), and sim9a (dashed red). The approximate location of MscS is indicated in this and subsequent plots. (D) Time-averaged ion concentration profile in moles per liter (M) along the symmetry axis of MscS for Cl⁻ (red) and K⁺ (blue) during simulations sim1a (solid line), sim5a (dashed line), and sim7a (pointed line). (E) Ionic concentrations averaged over time and space (along y axis) shown as in panel D. (F) Time-averaged water oxygen concentration during simulations sim1a (black), sim5a (blue), and sim7a (red). Dashed lines correspond to the concentration profile along the symmetry axis of the channel. The concentration of water in the narrowest section of the channel increases when biasing potentials are applied to the system. Solid lines correspond to time and spatial averages along the y axis (slightly displaced for better visualization). The concentration in bulk is ∼56M.

Overall, the simulations of MscS restrained to its crystal conformation show consistent electrostatic potential maps as well as ionic and water distributions depicting a channel with small conductance and high selectivity for anions over cations.

Properties of MscS described above correspond to those of a structure restrained to its crystal conformation. Release of restraints lead to dramatic changes in the MscS transmembrane domain conformation. Indeed, when restraints were released under equilibrium (no bias) conditions, the channel closed asymmetrically (simulations sim1b, sim3a, and sim4b, discussed in the Supplementary Material ), while release of restraints in the presence of sufficiently strong electric fields resulted in a wider transmembrane pore (simulations sim5b and sim6b).

Surprisingly, release of restraints applied to backbone atoms while the protein was subject to large and positive electrostatic biases lead to channel conformations that feature a transmembrane pore wider than the one depicted by the crystal structure (sim5a, compare Figure 4AB). Widening proceeded by straightening of TM3A-TM3B helices (which partially established contact with peripheral helices TM2) and is likely caused by forces arising from ions and water rushing through the transmembrane domain. Salt-free simulations should clarify whether ions, water, or charges in the protein itself are responsible for opening.

The increase in pore size seems to be larger than that reported in Spronk et al. 31, and has a direct impact on the magnitude of the ionic currents through the channel, as discussed below. The radius of MscS's constriction zone during 22ns of simulation (sim5a and sim5b) is shown in Figure 8A (solid blue curve). The increase in magnitude upon release of restraints is evident, reaching a steady value of 5Å. A second set of control simulations (sim6a and sim6b), in which release of restraints was performed while an NpTM ensemble was adopted, resulted in the same qualitative behavior, i.e., an increase in size of the transmembrane pore (see Figure 4C and Supplementary Material's Fig. 16 A, red curve). Thus, widening of the MscS pore seems to be a rather robust event.

Widening was only observed when positive biases were applied to the system, resulting in Cl⁻ ions permeating from the periplasmic to the cytoplasmic bath. A large negative bias prevented closure (−1.2V, sim7b), but negative ions permeated hydrophobic crevices in the transmembrane zone of MscS and the integrity of the pore (residues 96–113) was compromised, with water and ions pouring through contact regions of adjacent TM3A helices. It is not clear if this kind of behavior will result in a disordered pore and whether poor packing of lipids around the protein or steric/electrostatic barriers in the transmembrane pore are its cause.

A second simulation with a smaller negative electrostatic bias was performed as well (−0.6V, sim9a-sim9b). MscS's transmembrane pore remained intact, and a less dramatic tendency to close upon release of restraints was observed in the time evolution of the computed constriction radius (see Figure 8<