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Gating of the Large Mechanosensitive Channel In Situ: Estimation of the Spatial Scale of the Transition from Channel Population Responses

Department of Biology, University of Maryland College Park, Maryland

Correspondence: Address reprint requests to Sergei Sukharev, University of Maryland, Dept. of Biology, Bldg. 144, College Park, MD 20742. Tel.: 301-405-6923; Fax: 301-314-9358; E-mail: ss311{at}umail.umd.edu.

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX 1 APPENDIX 2 ACKNOWLEDGEMENTS REFERENCES

 
Physical expansion associated with the opening of a tension-sensitive channel has the same meaning as gating charge for a voltage-gated channel. Despite increasing evidence for the open-state conformation of MscL, the energetic description of its complex gating remains incomplete. The previously estimated in-plane expansion of MscL is considerably smaller than predicted by molecular models. To resolve this discrepancy, we conducted a systematic study of currents and dose-response curves for wild-type MscL in Escherichia coli giant spheroplasts. Using the all-point histogram method and calibrating tension against the threshold for the small mechanosensitive channel (MscS) in each patch, we found that the distribution of channels among the subconducting states is significantly less dependent on tension than the distribution between the closed and conducting states. At –20 mV, all substates together occupy 30% of the open time and reduce the mean integral current by 6%, essentially independent of tension or P_o. This is consistent with the gating scheme in which the major rate-limiting step is the transition between the closed state and a low-conducting substate, and validates both the use of the integral current as a measure of P_o, and treatment of dose-response curves in the two-state approximation. The apparent energy and area differences between the states E and A, extracted from 29 independent dose-response curves, varied in a linearly correlated manner whereas the midpoint tension stayed at 10.4 mN/m. Statistical modeling suggests slight variability of gating parameters among channels in each patch, causing a strong reduction and correlated spread of apparent E and A. The slope of initial parts of activation curves, with a few channels being active, gave estimates of E = 51 ± 13 kT and A = 20.4 ± 4.8 nm², the latter being consistent with structural models of MscL, which predict A = 23 nm².

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX 1 APPENDIX 2 ACKNOWLEDGEMENTS REFERENCES

 
MscL, a large-conductance mechanosensitive channel, first isolated from Escherichia coli (Sukharev et al., 1994), is a fast-acting pressure-release valve that prevents osmotic rupture of a bacterial cell when tension in the cytoplasmic membrane approaches the lytic limit (Levina et al., 1999; Booth and Louis, 1999). MscL is especially attractive from the biophysical point of view as an example of a transmembrane protein that dramatically changes its conformation in a tension-dependent manner. The solution of the crystal structure of MscL homolog from Mycobacterium tuberculosis (TbMscL) (Chang et al., 1998) had opened numerous possibilities for detailed studies of its gating mechanism.

The TbMscL structure, solved to a 3.5 Å resolution, revealed a tightly packed assembly of five identical subunits, each bearing two transmembrane helices, and was interpreted as a closed state. An atomic-scale homology model of closed E. coli MscL (EcoMscL) has been built and several hypothetical open conformations proposed (Sukharev et al., 2001b). Based on the previous kinetic analysis (Sukharev et al., 1999), the opening of MscL was modeled as a two-step process, with the first transition from the closed to a pre-expanded intermediate low-conducting state followed by a transition to the fully open state (Sukharev et al., 2001a,b). To model a pre-expanded nonconducting or low-conducting state, the N-terminal segments (unresolved in the crystal structure) were invoked and presented as a short helical bundle that can occlude the pore while the barrel is expanded. Further expansion of the barrel was proposed to separate the N-terminal bundle (cytoplasmic gate), resulting in full opening. Structural modeling (Sukharev et al., 2001b) and molecular dynamic simulations (Gullingsrud and Schulten, 2003; Colombo et al., 2003; Kong et al., 2002) suggested that the expansion of the barrel must be achieved through an outward movement of transmembrane helices associated with substantial tilting. The models of the EcoMscL in the closed and open (expanded) states were supported by cysteine cross-linking experiments in situ, as well as with patch-clamp experiments on cysteine mutants (Sukharev et al., 2001a; Betanzos et al., 2002). A similar character of the conformational transition was independently concluded from electron paramagnetic resonance studies of EcoMscL reconstituted in liposomes (Perozo et al., 2002). The open conformation depicts a pore of 9–10 nm² in cross section to satisfy the 3.2-nS conductance, and predicts a large-scale conformational rearrangement of the transmembrane part of the protein accompanied with a 40° tilting of helices and large in-plane expansion (Betanzos et al., 2002).

The amount of in-plane expansion for a mechanosensitive tension-gated channel has the same fundamental meaning as the gating charge for a voltage-gated channel and defines the sensitivity to the stimulus. The cloning of V-gated channels, sequencing, and determination of the number of charged residues in voltage-sensor domains went in parallel with extensive experimental measurements of gating charges, as reviewed in Bezanilla (2000). Relating the amount of expansion for mechanogated channels with discrete conformations predicted by modeling and other methods appears to be a problem of the same significance. As the stereochemical aspect of MscL opening is becoming better understood, the thermodynamic description remains not only incomplete, but also inconsistent with the atomic model predictions. A previous thermodynamic treatment of multichannel recordings made in liposomes in the framework of the two-state model (Sukharev et al., 1999) estimated the intrinsic energy of MscL transition as 19 kT and the in-plane expansion as 6.5 nm², the latter being too small to accommodate the highly conductive pore. The dose-response curves recorded in situ from giant spheroplasts in preliminary trials have estimated A as 10–15 nm², which is larger than in liposomes, but still half of what the structural models predict. It seemed important to find what caused this apparent systematic discrepancy and to estimate the true values for A and E. It should be noted that experimentation with mechanosensitive channels is less straightforward than with V-gated channels, because membrane tension, which is the main thermodynamic parameter driving the transition, is not easily determined from the pipette pressure.

In this article we conduct a systematic study of single-channel traces and dose-response curves for MscL in patches excised from giant spheroplasts. We utilize the activation pressure of MscS as a reference point to assess the tension acting on MscL. By analyzing occupancies of major subconducting states as a function of tension we validate the use of the integral current recorded from multichannel patches as a measure of P_o and the two-state model for gross thermodynamic description of MscL gating. We also modify the kinetic scheme of MscL in accordance with the dependencies of subconducting states on tension and voltage. We estimate A and E from large data sets and show that when the channel population in the patch is nonuniform, the observed values may be substantially lower than true parameters. By measuring the limiting slope of dose-response curves we find a more realistic value for A that better corresponds to the model predictions.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX 1 APPENDIX 2 ACKNOWLEDGEMENTS REFERENCES

 
Spheroplast preparation
Giant spheroplasts were prepared essentially as described previously (Martinac et al., 1987). Escherichia coli pB104 mscL-, recA- cells harboring the p5-2-2b vector with mscL under the control of a lac-inducible promoter (Blount et al., 1996a) were used for all preparations. Overnight cultures grown in Luria-Bertani medium in the presence of 100 µM ampicillin (255 rpm, 37°C) were diluted 1:100 into the same medium and incubated for 3 h to an OD₆₀₀ of 0.4–0.8. This culture was then diluted 1:10 into (modified) Luria-Bertani medium containing 100 µM ampicillin and additional 60 µg/ml cephalexin (Sigma Chemical, St. Louis, MO), an antibiotic that blocks cell septation. The culture was incubated with shaking for 1.5 h at 37°C, until filamentous cells reached 50–150 µm in length. The mscL gene was induced by 1 mM isopropyl-b-d-thiogalactopyranoside (IPTG) (Research Products International, Mt. Prospect, IL) 30 min before harvesting. The filaments were gently spun down and converted into giant spheroplasts by 0.2 mg/ml lysozyme and 5 mM EDTA, at room temperature. After full induction by IPTG, 40–70 channels were observed in each patch. To decrease the number of expressed channels, the induction by IPTG was omitted, while bacteria were grown in (modified) Luria-Bertani medium or in the glucose-containing SOB medium. Noninduced cells typically exhibited 3–7 channels per patch.

Electrical recording
The standard patch-clamp technique (Hamill et al., 1981) was used to record MscL single-channel current in inside-out patches excised from giant spheroplasts. Patch electrodes were pulled from borosilicate capillaries (100 µL disposable pipettes; Fisher Scientific, Pittsburg, PA) on a Sutter P-97 micropipette puller (Sutter Instruments, Novato, CA) and were used without fire-polishing. All pipettes had bubble numbers near 4.5 in 95% ethanol, corresponding to a resistance 5 M in the symmetrical recording solution containing (in mM): 200 KCl, 90 MgCl₂, 10 CaCl₂, and 5 HEPES-KOH, pH 6. The bath solution was the same plus 0.3 M sucrose added to increase the osmotic stability of the spheroplasts. The currents were recorded using an Axopatch 200B amplifier (Axon Instruments, Foster City, CA) under the holding potential between –20 and –60mV, at room temperature. Currents filtered at 10 kHz by the built-in lowpass Bessel filter of the amplifier and an external 8-pole Bessel filter (Model 3381 filter, Krohn-Hite, Avon, MA) were digitized at 25 kHz with a Digidata 1322A data acquisition system and pCLAMP8 software (Axon Instruments).To better resolve short subconducting states, in some experiments patch electrodes were coated with dental wax (Kerr, Romulus, MI). Currents in such instances were filtered at 30 kHz and sampled at 100 kHz. Suction was applied to the patch-clamp pipette by a screw-driven syringe and measured with a digital pressure gauge (PM015D, World Precision Instruments, Sarasota, FL).

Data analysis
To identify the substates, continuous traces (typically 5-min long) were recorded at constant pipette pressures in the range of open probabilities (P_o) between 0.01 and 0.08. After baseline correction that removed drift and some obvious MscS fluctuations, probability density histograms were calculated and fitted by the sum of Gaussian functions, representing the closed and open states and a variety of subconductance levels using HISTAN, a software custom-written in Matlab. Five "long" recordings from two independent spheroplast preparations were subjected to current amplitude analysis. In patches where nonadapted MscS was present, the baseline itself was subjected to amplitude analysis to estimate the amount of interference that MscS activities potentially bring to MscL histograms (see Results).

To record dose-response curves, the suction applied to the pipette interior was first increased relatively quickly with the rate of 60 mm Hg/s, passing the MscS activation point, until we observed first MscL openings. Then the pressure was changed in smaller increments of 10 mm Hg and kept constant for 5 s between the steps. The open probability (P_o) was calculated for each pressure step as the mean integral current divided by the maximum current which could be attained at saturating pressures. For multichannel patches, the maximal conductance (and the total number of channels) was estimated by extrapolating partial activation curves. This could be done with a >5% accuracy after reaching 80% of saturation. Most of the traces used for analysis displayed >95% current saturation as assessed by the sigmoidal fitting procedure (see Appendix 2 for analysis of fitting errors). The integral conductance G normalized to the inferred maximal G_max conductance produces effective open probability P_o^eff that includes contributions from all subconducting states. In addition to measurements of P_o^eff, the recordings were analyzed using the amplitude threshold detection technique. In this method, traces containing <6 channels were idealized and transitions were scored when the current crossed the threshold line (set at 0.1 of full conductance) between the levels representing the closed and fully open states. From idealized traces, the closed and open state durations for the channels were measured, P_o was calculated, and the gating parameters were extracted as described below. Both methods gave similar results and the potential discrepancies are estimated in the Discussion.

Because MscL is activated by tension but not directly by pressure, the pressure gradients (p) across the patch were converted to tensions () by the Laplace's law, = pr/2, where r is the radius of patch curvature. Without imaging, the patch curvature is not generally known. Therefore we used the activation threshold of the ever-present small conductance mechanosensitive channel (MscS) as a reference point. Previous studies (Cui and Adler, 1996; Sukharev, 2002) have suggested that the midpoint for MscS activation by membrane tension (_1/2^MscS) is 5.5 ± 0.1 dyn/cm. By scoring the pressure at which half of MscS channels become active (p_1/2^MscS) in each record, we converted the pressure gradient scale into the tension scale using the formula: = (p/p_1/2^MscS) x 5.5 dyn/cm, where is the tension at a given p pressure across the patch. Such a conversion implies that the radius of curvature of the patch is independent of pressure in the given range. Based on observations of liposome patches (Sukharev et al., 1999), the membrane is essentially flat at a zero pressure, and becomes spherical under a gradient. As the pressure increases, the curvature of liposome patches saturates and remains stable at tensions >4–5 dyn/cm, which is likely to be true for spheroplast patches as well.

The dose-response curves for MscL were fitted with the two-state Boltzmann-type model,

(1)

where P_o and P_c are the open and closed state probabilities, E is the energy difference between the states in an unstressed membrane, A is the in-plane protein area change upon the gating transition, is the membrane tension, and kT has the conventional meaning (Howard and Hudspeth, 1988; Sachs, 1992; Sukharev et al., 1999).

Protein area calculations
The molecular models of the closed and the open states that satisfy the 3.2-nS unitary conductance—conformations 2 and conformation 11, respectively—were taken from Sukharev et al. (2001b). PDBAN, the program for analysis of cross-sectional areas was custom-written in Matlab. Solvent-accessible surfaces were created from PDB coordinates using the surface of a rolling spherical probe. For the outer protein surface, which is in contact with lipid, the probe radius was chosen as 4 Å; for the inner water-accessible surface it was 1.4 Å. The cross sections of the solvent-accessible surfaces normal to the pore axis were generated and the areas were calculated. The areas of two protein slices located at the positions ±12 Å from the midplane of the membrane, i.e., near the hydrophobic core boundaries, were averaged, and the numbers taken as in-plane cross-sectional areas for a particular conformation.

Statistical modeling of the tension response of a mixed channel population
The amount of channel expansion A_o = 23.3 nm² was estimated from molecular models, and the corresponding energy of the transition, E_o = 58.9 kT was calculated using Eq. 1 and the condition of _1/2 = 10.4 dyn/cm determined in experiments (see Results). These values were taken as the initial single-channel parameters for simulations. Sets of normally distributed random numbers E_i and A_i with different standard deviations were generated using the randn function of Matlab. The standard deviations were varied, between 1 and 20 kT for E (58.9 kT), and between 0.5 and 3.5 nm² for A (23.3 nm²). Pairs with a fixed E and random A, random E, and fixed A, or both random parameters, modeled individual channels in a population. P_o/P () curves for each channel were generated using Eq. 1 and then superimposed to simulate the dose-response curves of the entire channel population in the patch. Fitting of the population dose-response curves in the range of P_o/P_c from 0.01 to 100 (measurable in a typical experiment) to the two-state model yielded apparent parameters, E_app, A_app, which were then plotted as a function of standard deviation of the corresponding parameter. Based on the average numbers of channels per patch typically observed in uninduced or IPTG-induced spheroplasts, we repeated such simulations for 5- and 50-channel populations to determine at what standard deviations of true E and A the distributions of E_app and A_app would resemble the experimentally observed scatter (see also Appendix 1).

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX 1 APPENDIX 2 ACKNOWLEDGEMENTS REFERENCES

 
Pressure-current responses of spheroplast patches and the tension scale
Current traces from two representative patches with 52 and five MscL channels are shown in Fig. 1, A and B, respectively. Both recordings were made in spheroplasts in inside-out configuration at –20 mV (pipette positive). The total number of channels per patch was 50 ± 5 (n = 11) in induced cells and 5 ± 2 (n = 20) in noninduced spheroplasts. The later number of channels illustrates the leakage of the vector promoter. This minimal level of expression, combined with possible clustering of channels, did not permit reproducible recordings from true single-channel patches.

View larger version (27K): [in this window] [in a new window]   FIGURE 1  Activation of MscL by transbilayer pressure gradients. (A) Patch-clamp recordings of channels at –20 mV (pipette positive) from spheroplasts expressing the wild-type MscL after induction with IPTG (1 mM, 30 min). A total of 52 channels were observed at the pressure close to saturating. (B) MscL activities recorded without IPTG induction. Five channels are observed in this particular experiment. The pressure traces measured in mm Hg are shown below each current trace. The points of half-maximal activation of MscS and first openings of MscL are indicated by arrows and asterisks, respectively. Using pressure that elicits half-maximal activation of MscS, p1/2MscS (which corresponds to tension of 5.5 dyn/cm), the pressure scale was converted into the scale of tensions. Inset represents the distribution of radii of curvature (r) calculated from the law of Laplace in 21 patches sampled with standard 5 MOhm pipettes.

Having p_1/2^MscS one can also estimate r for a given size of pipettes, which provides information about patch geometry. In 21 independent trials, p_1/2^MscS was determined as 148 ± 29 mm Hg. Based on this data, the law of Laplace produces r = 0.58 ± 0.12 µm, with the actual distribution illustrated in Fig. 1 A (inset). Assuming that patches are hemispherical caps delineated by 60° angle relative to the axis of the pipette (Sukharev et al., 1999), their areas can be estimated as 1.1 ± 0.46 µm² (n = 21).

The structure of subconducting states
To address the question of whether the mean current would be an adequate measure of open probability of MscL at each pressure step, we analyzed the occupancies of subconducting states under different conditions. Fig. 2 A shows the fragment of a typical MscL trace recorded at –20 mV. The openings activated by moderate suction display short-lived substates seen as downward flickers from the fully open state (<0.5-ms long) and distinct long-lived subconductance levels (>2 ms). The short-lived substates are visited predominantly from the open state. Transitions to similar short substates are also observed from the long-lived substates. A typical all-point amplitude histogram constructed from a 5-min long continuous recording is presented in Fig. 2 B. A reasonably good fit of the experimental histogram by a sum of nine Gaussian curves indicates several discernable peaks with amplitudes of 0.22, 0.54, and 0.78 relative to the amplitude of the fully open state. The fit also suggests the presence of less prominent and more scattered intermediate levels centered near 0.7 and 0.93. The accuracy of fitting also required two low-populated peaks positioned near 0.33 and 0.45, and two more peaks with amplitudes of 0.07 and 0.13; however, their closeness to the highly populated closed state reduces the confidence of their exact position and occupancy. The prominent peak at 0.78 represents the long-lived subconducting state (L_0.78) visited predominantly from the fully open state. L_0.78 is kinetically different from short-lived substates S_0.22, S_0.45, S_0.70, and S_0.93. Its occupancy relative to the fully open state varied from patch to patch and had a tendency to increase with tension (see below). The occupancies of all other subconducting states varied in different trials with average standard deviation of ±26% relative to the mean (n = 8), whereas positions of the peaks were reproducible with the accuracy of 2%.

View larger version (36K): [in this window] [in a new window]   FIGURE 2  Representative single channel currents of MscL recorded in a 30-kHz bandwidth from an inside-out patch at –20 mV (A). A 0.15-s fragment of a 5-min trace is shown with openings as upward deflections. The all-point amplitude histogram (B) compiled of 120 bins (solid envelope curve) includes the entire 5-min data set. It was fitted by a sum of 11 Gaussian distributions (dashed line). The peak positions shown by numbers represent amplitudes of subconducting states relative to the amplitude of the fully open state.

The total occupancies were remarkably reproducible (for a set of eight traces recorded at low P_o), being 0.26 ± 0.09 for all substates and 0.74 ± 0.09 for the fully open state, together making 0.93 ± 0.02 of the current expected for an ideal open channel without substates. The long-lived substate of 0.54 relative amplitude (L_0.54) appeared in approximately one-third of patches and its occupancy positively correlated with the occupancy of L_0.78. The short substates S_0.22, S_0.45, S_0.70, and S_0.93 are visited not only from the fully open state, but also show up as brief (10–40 µs) intermediate stair-like levels observed during opening or closing transitions (not shown). These levels correspond to the amplitudes of short substates (0.28, 0.71, and 0.90) previously reported in liposome-reconstituted patches (Sukharev et al., 1999). Because the fragments of liposome recordings were much shorter than those used in the present work, the substate with the relative amplitude near 0.45 was unaccounted for in the previous analysis. The substate L_0.78 was not considered previously either (Sukharev et al., 1999), as it seemed to represent not an intermediate, but an alternative open state (see Discussion).

Effect of voltage on subconducting states
Hyperpolarizations beyond –40 mV substantially increased the occupancy of the long-lived subconducting states of MscL, consistent with observations by other groups (B. Martinac, personal communication). In this type of experiment, the combined action of negative pressure of 200–300 mm Hg and voltage compromised the stability of patches, which precluded steady recordings at voltages more negative than 60 mV. Fragments of the continuous trace recorded at constant pressure of 207 mm Hg and three different voltages (–20, –40, and –60 mV) are presented in Fig. 3 A. The pressure was initially chosen such that at –20 mV the openings were infrequent. As the voltage increased, the frequency of openings did not change substantially, but the dwell time in conducting states increased due to switching to the long-lived substates. The expanded traces recorded at –40 mV showed that the preferential sequence of transitions is such that the two long-lived substates are visited sequentially and exclusively from the fully open state. To close, the channel has to make a brief return to the fully open state. At –60 mV, however, closing transitions from intermediate conducting states were scored, or the brief full openings before closures in these instances were too short to be resolved (not shown).

View larger version (40K): [in this window] [in a new window]   FIGURE 3  Long-lived subconducting states of MscL are voltage-dependent. (A) Representative fragments of a continuous MscL trace recorded under constant 207 mm Hg suction at –20 (bottom), –40 (middle), and –60 mV (top). (B) All-point amplitude histograms generated from 1-min fragments of the continuous trace recorded at a constant tension and three different voltages. The occupancies of the long-lived substates with the relative conductances of 0.78 and 0.64 increase at more negative membrane potentials. (C) Occupancies of the fully open state (open symbols) and the two long-lived substates L0.78 (solid symbols) and L0.64 (shaded symbols), normalized relative to the occupancy of the closed state. The solid lines represent the mean probability slopes for four independent data sets. The transferred net charges (qik) resulted from transitions between any two states i and k and were calculated from the ratios of probabilities by fitting with equation pk/pi = [pk(0)/pi(0)] x exp(–qik V/kT), where pi(0) and pk(0) are the probabilities of specified states at 0 voltage. An outward movement of 0.8 e and inward movement of 3.5 e across the entire field were associated with CO and OL0.78 transitions, respectively.

Effect of tension on subconducting states
To analyze how the occupancy of individual substates changes with tension, a number of traces containing 3–5 channels were recorded in the range of open probabilities between 0.02 and 0.85. Amplitude histograms for one-channel fragments recorded at constant tensions were generated and compiled as a smooth three-dimensional diagram (see Fig. 4 A and its legend for details). The surface represents the probability density for conducting states with amplitudes between 0.1 and 1.1, as a function of tension. The ridge on the far right edge represents the fully open state, whereas the lower ridge next to it corresponds to the prominent L_0.78. The elevated point in the corner closest to the viewer indicates the presence of low-conducting substates, which gradually disappear as tension increases. Because the patches contained different number of channels, the baseline was excluded from the statistics and the ridge corresponding to the closed state is not shown. The total probability of conducting states between 0.1 and 1.1 at each tension was normalized to be unity. The inset above shows the actual open probability (calculated from the integral current of the entire channel population) plotted against tension in the same scale. It is evident from the diagram that whereas P_o changes by more than two orders of magnitude in the given range of tensions, the shape of the landscape remains essentially the same and the relative occupancies of major subconducting states do not change substantially.

View larger version (44K): [in this window] [in a new window]   FIGURE 4  Relative occupancies of the MscL conductive substates as a function of applied tension. (A) The three-dimensional amplitude histogram representing the probability of a single MscL channel to be in a particular conductive state at different tensions is compiled from 10 independent traces. The x axis indicates the magnitude of applied tension, , relative to the midpoint tension for MscL activation, 1/2; the y axis shows the relative conductance of ion channel normalized to the conductance of the fully open state. The z axis displays the probability density in a logarithmic scale. The inset above is the plot of open probability (Po) versus /1/2, which represents a simultaneous fit of 10 dose-response curves with Eq. 1. (B) Occupancies of conductive states derived from amplitude histograms, as that in Fig. 2, recorded at different tensions (see Materials and Methods). Only the relative occupancies of S0.22 (), L0.78 (•), and S0.93 () versus tension are presented. The combined relative occupancy of all nine substates together () as well as occupancies of the fully open state () remained practically constant over the range of tensions relative to the total occupancy of all conducting states taken as unity. The represents the effective amplitude of the integral current AIC, which is the sum of all substate occupancies multiplied by the corresponding amplitudes over the total probability of being open (see Appendix 2).

As a result of opposite tendencies for the short- and long-lived substates, the combined occupancy of all subconducting states remains practically constant () relative to that of the fully open state (), as well as relative to the total occupancy of all conducting states (). The numbers show that all subconducting states occupy 26% of the time the channel conducts above the threshold of 0.1 and reduce the mean current by 6% relative to the level of the fully open state, essentially independent of tension and P_o (for estimations of the accuracy of such approximation, see Discussion). This is consistent with the model which includes one dominant tension-dependent transition (CS₀₂₂) and with previous observations (Sukharev et al., 1999) that once MscL makes a transition from the closed state to the low conducting substate, it quickly becomes distributed between the fully open state and a group of upper substates with shallow dependencies on tension.

Dose-response curves
We analyzed 29 dose-response curves from patches with a few or multiple MscL channels, obtained with or without induction, respectively. The combined data are presented as log (P_o/P_c) versus tension in Fig. 5 A. Scaling of tensions was done for each dose-response curve individually using MscS as an internal gauge. Before fitting and statistical treatment, we compared the open probabilities estimated from the same traces with two different methods. As illustrated by the inset to Fig. 5, the P_o/P_c values obtained from a five-channel patch are the same when measured from the integral current () or using the threshold method (•); the difference in parameters E and A estimated from the fits was <1%. Note that the amplitude threshold technique can be easily applied when the number of MscL channels in the patch is <5; smearing of levels in recordings containing more channels, however, makes the threshold assignment difficult. Assessment of P_o from integral current, in contrast, is insensitive to the number of channels in the patch. For uniformity, the entire data set presented in Fig. 5 was obtained using the integral current only.

View larger version (14K): [in this window] [in a new window]   FIGURE 5  Dose-response curves and apparent gating parameters of MscL. (A) Twenty-nine independent curves (10 from induced and 19 from uninduced patches) plotted as Po/Pc ratio versus membrane tension and fitted to the two-state model. Apparent parameters E, A, and 1/2 were extracted from each fit, averaged, and presented as the mean ± SD. The thick solid line represents the curve with the average parameters. Thin solid lines are examples of individual curves with varying slopes. (Inset) Po/Pc versus tension plots obtained from the same trace with five active channels. represent Po obtained from the integral current; • show Po determined using the amplitude threshold (0.1) detection technique. (B) Energies of MscL gating transition (E) plotted against apparent protein area changes (A) calculated from individual traces. Vertical, horizontal, and diagonal error bars represent standard deviations of E, A, and 1/2 = E/A, respectively, around their mean values. Dotted line is the linear fit passing through the origin. Pirson's correlation coefficient of E and A values is 0.98.

Intrinsic gating parameters and statistical modeling of population response
To explain the correlated variation of E and A we analyzed several potential sources of systematic and random errors and their effects on the combined population response. We were unable to reproduce this linear correlation by introducing a systematic deviation of gating parameters in Eq. 1 uniformly for all channels in a patch. Indeed, an error in pressure-to-tension conversion (due to the accuracy of p_1/2^MscS determination, for instance) changes only effective A and _1/2, whereas E should stay constant. Conversely, if, for instance, applied pressure had an uncontrolled offset from trial to trial, then we would observe a variation of the midpoint position (_1/2), which would convert into a variation of E, but not A. Simultaneous random variations of A and E from patch to patch are not expected to correlate.

We inferred that a large scatter in the slope of the activation curves, and a much smaller scatter of _1/2 may be specifically due to heterogeneity of channel population in each patch. Indeed, if the midpoint positions of activation curves for individual channels in the patch are scattered around the mean, the midpoint of the curve measured on the entire population should not deviate much from that mean. However, because some channels activate earlier, and some later on tension, the smearing of the resultant curve is expected to decrease the slope. Since we never observed any significant deviation of MscL unitary conductance from 3.2 nS, we presumed that the channel conformation in the open state is rather uniform and the protein expansion between the states, A, is most likely to be the same across the channel population. The local tension, however, may vary due to a local mechanical inhomogeneity of the membrane, and the term A is expected to vary. Because only the product contributes to the free energy (Eq. 1), the variation of would be equivalent to variation of A. The intrinsic energy of the gating transition (E) of the channel may also be sensitive to the lipid or protein microenvironment in the membrane in which a particular channel resides. The scatter of E and/or A among channels in the population is predicted to reduce the apparent slope of the combined activation curve, and this reduction would be more pronounced when standard deviations of E and/or A increase.

To choose realistic initial parameters, E_o and A_o, reflecting the intrinsic behavior of channels (unperturbed by the surroundings), we analyzed previously developed molecular models of MscL. The open conformation 11 (as in Sukharev et al., 2001b) with helical tilts of 72° (M1) and cross-sectional pore area of 10 nm² gave the closest prediction of the channel conductance (A. Anishkin, unpublished calculations). This conformation is compared with the closed MscL in Fig. 6, where both models are shown with their solvent-accessible surfaces and the in-plane cross sections. The mean cross-sectional areas of the open and closed conformations were computed as 40.8 and 17.5 nm², respectively. The difference of 23.3 nm² was taken as the initial parameter A_o. The energy of the transition, satisfying this area change, and the midpoint tension of 10.4 dyn/cm in Eq. 1 is 58.9 kT, which was taken as the initial E_o.

View larger version (67K): [in this window] [in a new window]   FIGURE 6  The models of the E. coli MscL in the open and closed conformations shown with solvent-accessible surfaces. The positions of the transmembrane helices forming the barrel correspond to conformations 2 (closed) and 11 (open) from Sukharev et al. (2001b), whereas the bundle-like arrangement of the C-terminal segments in the open state is taken from Anishkin et al. (2003). The cross-section planes are positioned approximately at the boundaries of the hydrophobic core of the membrane (±12.5 A along the z axis). The average cross-sectional areas of the modeled closed and open states are 17.5 and 40.8 nm2, respectively, predicting the transition-related area change of 23.3 nm2.

View larger version (29K): [in this window] [in a new window]   FIGURE 7  Simulated tension responses of nonuniform channel populations. Intrinsic gating parameters based on the atomic models Eo = 58.9 kT and Ao = 23.3 nm2 were randomized with variable standard deviations. The combined dose-response curves for 100 channel populations were then computed and fit with Eq. 1 to obtain apparent parameters Aapp and Eapp. (A) A three-dimensional representation of Aapp/Ao as a function of relative (A) and (E). The surface illustrates that a 5% scatter of either parameter reduces Aapp to approximately one-half. (B) Simulated results for 15 populations of 50 channels and 15 populations of five channels in which both E and A were simultaneously varied around their mean values (cloud of small dots). Pairs of E and A are shown with . The • in the center of the scatter shows mean values for Aapp and Eapp. The (overlapping with the circle) represents the mean parameters observed in the experiment (same as in Fig. 5). The values of standard deviations that closely reproduce the experimental scatter are denoted in B. See Appendix 1 for details of simulations.

View larger version (21K): [in this window] [in a new window]   FIGURE A1  Statistical simulations of tension responses of nonuniform channel populations. (A) Simulated population dose-response curves with fixed Eo = 58.9 kT and A scattered Ao = 23.3 nm2 with standard deviations (A) varying from 0 to 10 nm2 (100 channels). (B) Simulated results (pairs of Aapp and Eapp) for 15 populations of 50 channels and 15 populations of five channels obtained either with varied E and constant A (), or varied A and constant E (). The inset shows the dependence of the mean Aapp on standard deviation (A); the dashed line marks the experimental A. The parameters and standard deviations denoted in B produce the mean Eapp and Aapp shown by and • in the middle of each scatter. The represents the parameters observed in the experiment (same as in Fig. 5). The same populations as in B were simulated with both E and A parameters randomized around their mean values, which is illustrated in Fig. 7 B.

View larger version (20K): [in this window] [in a new window]   FIGURE 8  Examples of experimental activation curves of wild-type MscL exhibiting different degrees of slope variation. The curves display a noticeable S-like shape with a steeper slope at the ends, and more shallow dependence near 1/2. The inflection was more pronounced in patches with smaller number of channels (3–7). Linear fit of initial points (solid line) defines the limiting slope, which gives higher estimates for E and A than the fit of the middle region (denoted by line). The inset illustrates procedure of reconstruction of the mean single-channel activation curve for channel populations of A. The inflected spline line represents the population dose-response curve. The fit of the initial region is shown by solid line. A parallel translation of this line to the population midpoint (1/2) yields the mean for a population with varying E only (dashed line). Rotating the initial fitting line around the vertical axis intercept, such that it crosses the horizontal axis at 1/2, yields the mean curve for a population with varying A (dot-dashed line). The hatched area represents possible intermediate line positions for populations in which E and A may vary simultaneously.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX 1 APPENDIX 2 ACKNOWLEDGEMENTS REFERENCES

Liposome patches are large enough for imaging, but during continuous recordings are mechanically unstable, having a tendency to slide up the pipette under pressure (Sukharev et al., 1999). Here we presented an analysis of MscL activity recorded from smaller patches in spheroplasts. Instead of video imaging (which is inaccurate due to small patch size), we used MscS as an internal tension gauge (Fig. 1). A steep activation of MscS at 5.5 dyn/cm in both liposomes (Sukharev, 2002) and spheroplasts (Cui and Adler, 1996) made this channel a good standard for two reasons. First, MscS appears to exhibit a more consistent behavior in spheroplasts and liposomes, whereas MscL exhibits a time-dependent decrease in activity in liposomes (Hase et al., 1995). For this reason the midpoint of 11.8 dyn/cm determined in liposomes may be a slight overestimation compared to that in the native membrane. Second, if we were using _1/2 of MscL as a reference point, we would have to measure the entire activation curve for every patch, which is not feasible. To our advantage, MscS activates at lower tensions than MscL, thus it automatically gauges the entire range of stimuli, including those situations where MscL was activated to low P_o. The established procedure of recording and treatment allows us to present disparate P_o-pressure curves in unified tension scale without patch imaging, as well as compare different MscL mutants in other studies. The accuracy of pressure-to-tension conversion is estimated as ±8% (see Appendix 2). The midpoint of MscL activation determined from 29 independent traces as 10.4 ± 0.8 dyn/cm (Fig. 5 A), is a key parameter, which now permits thermodynamic analysis of MscL function in the native membrane. MscS, present in the majority of patches, also allowed us to assess the radius of curvature for each patch and its variability (Fig. 1, inset), which usually remains out of sight in most channel studies.

Previous time-resolved recordings revealed complex channel behavior involving transitions between several subconducting states. How applicable, then, is a simple two-state model to MscL characterization? The multistate analysis, however, showed that only the first transition from the closed to the low-conducting substate is strongly tension-dependent (Sukharev et al., 1999). Thus, the presence of a single dominant tension-dependent step in the linear kinetic scheme suggested that a two-state model is still a reasonable approximation for overall thermodynamic description. Indeed, if beyond the single tension-dependent step the channel is distributed between several conducting states in a tension-independent manner, the kinetic description becomes simpler, and the total occupancy of conducting states may be reasonably characterized by the integral current. The analysis of substate occupancies of MscL and integral currents in native membranes presented above supports these notions. Ideally, the calculations of occupancies and areas related to each subtransition and the entire CO transition could be done from single-channel traces, in which there is no ambiguity as to which conducting state belongs to what channel. This was not feasible and the substate analysis as well as recordings of dose-response curves had to be done on multichannel populations.

Out of the nine subconducting states detected by Gaussian fits of amplitude histograms (Fig. 2), the three most prominent were characterized in more detail. The occupancies of short-lived substates S_0.22 and S_0.93 are near 10^–3 and 10^–1 relative to the occupancy of the fully open state (O), and decrease with tension (Fig. 4 B). This is consistent with the notion that S_0.22 and S_0.93 are intermediate states characterized by smaller area changes, constituting of 74 and 85% of A for the fully open state. In contrast, the occupancy of the long-lived substate L_0.78 increases with tension (Fig. 4). The dependencies of the L_0.78 occupancy on tension and voltage (Figs. 3 and 4) show that the OL_0.78 transition is associated with 14% additional protein expansion and an equivalent of an inward transfer of 3.5 positive charges across the transmembrane field. The occupancy of the second long-lived state L_0.64, which is visited from L_0.78, increases with voltage in proportion with the occupancy of L_0.78, suggesting no additional charge transfer during the latter transition (Fig. 3). The fact that the long-lived substates are visited exclusively from the fully open state places L_0.78 and L_0.64 beyond the open state in the kinetic scheme aligned with the coordinate representing the cross-sectional area of the protein (Fig. 9).

View larger version (8K): [in this window] [in a new window]   FIGURE 9  The kinetic scheme of MscL aligned with the reaction coordinate representing the protein in-plane area change. The main tension-dependent transition from C to S0.22 is associated with the largest area increase. The long-lived subconducting states (L0.78 and L0.64) are characterized with larger in-plane areas than the open state (O). Uncorrected estimates of area and energy differences between the major states are presented in Table 1. According to the data presented in Fig. 8, the corrected area and energy changes between the closed (C) and fully open (O) states are 20.1 nm2 and 52 kT. Correspondingly, the distances from the closed state to other substates can be rescaled as 14.8 nm2 (49 kT) for S0.22, 17.0 nm2 (47 kT) for S0.93, and 22.9 nm2 (61 kT) for L0.78.

We first define how the measured integral current depends on the probabilities and conductances of individual states. Suppose each of the i^th conducting states is characterized by its probability, p_i, and conductance, g_i, which can also be denoted through the fractional conductance f_i = g_i/g_O, where g_O is the conductance of the fully open state. The area differences, A_i, and intrinsic energies in the absence of tension, E_i, are measured for each conducting state relative to those of the closed state (C). The probability of being in any of the conductive states, i.e., nonweighted (by conductance) open probability, can be presented as the sum

where P_c() is the probability of any nonconducting state, on the assumption that MscL has only one closed state (C), P_c() = p_C(). The probabilities of individual states can be calculated according to Boltzmann, with the free energies written as E_i–A_i, which include the work of externally applied tension,

To account for contributions of substates in the total current, we use their probabilities and fractional conductances. The time-averaged fractional conductance of the channel can then be expressed as

The difference of the total fractional conductance from unity 1 – f() therefore represents the reduction of the time-averaged conductance of a multistate channel (observed as integral current) from that of an ideal channel that displays only a fully open state. The integral conductance at a given tension can be written as

In the following numerical simulation we approximated the system with a five-state model C S_0.22 S_0.93 O L_0.78 with the parameters for each state listed in Table 1. The calculated occupancies of each substate, p_i(),f(), and the effective channel conductance, G(), are shown in Fig. 10. The computed G() dependence was then treated as an experimental curve. It was fitted with a sigmoidal curve to find G_max and calculate the effective conductance-weighted open probability P_o^eff = G()/G_max, the same as values measured in the experiments. As seen from the plot, P_o, P_o^eff, and G()/g_O increase in proportion; however, G()/g_O does not saturate, but asymptotically approaches f(). The probabilities for intermediate states S_0.22 and S_0.93 behave non-monotonously and the probability for the fully open state (p_O) starts declining at high tensions