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. 2021 Mar 22;1(4):467–474. doi: 10.1021/jacsau.0c00098

Hysteresis of a Tension-Sensitive K+ Channel Revealed by Time-Lapse Tension Measurements

Masayuki Iwamoto †,*, Shigetoshi Oiki ‡,*
PMCID: PMC8395652  PMID: 34467309

Abstract

graphic file with name au0c00098_0006.jpg

Various types of channels vary their function by membrane tension changes upon cellular activities, and lipid bilayer methods allow elucidation of direct interaction between channels and the lipid bilayer. However, the dynamic responsiveness of the channel to the membrane tension remains elusive. Here, we established a time-lapse tension measurement system. A bilayer is formed by docking two monolayer-lined water bubbles, and tension is evaluated via measuring intrabubble pressure as low as <100 Pa (Young–Laplace principle). The prototypical KcsA potassium channel is tension-sensitive, and single-channel current recordings showed that the activation gate exhibited distinct tension sensitivity upon stretching and relaxing. The mechanism underlying the hysteresis is discussed in the mode shift regime, in which the channel protein bears short “memory” in their conformational changes.

Keywords: bilayer tension, conformational change, lipid bilayer, intrabubble pressure, ion channel, single-channel current

Introduction

Cell membranes undergo dynamic membrane tension changes during cellular activities, such as cell migration, swelling, and division.1,2 Mechanosensitive channels vary their activity by tension changes,3−6 and various channels also exhibit tension sensitivity.7 The patch-clamp method has been a primary method to examine the tension sensitivity of channels, but composite configurations of the native membrane, involving cytoskeletal structure8 and condensed membrane proteins of various types,9 impede quantitative analysis.

Alternatively, lipid bilayer techniques have offered an experimental venue for channel–membrane interplay.6,10,11 With their simplicity and transparency, arbitrary chemical compositions of a bilayer and its changes12,13 and physical perturbations6 are enabled. Recently, the bilayer tension has been quantitatively evaluated in lipid bilayer methods,14,15 such as the droplet interface bilayer (DIB)16,17 and contact bubble bilayer (CBB)18,19 methods. These straightforward lipid bilayer systems have helped establish a mechanism of mechanosensitivity of channels obeying “the force-from-lipids” principle,4,20 which dictates that the bare lipid bilayer mediates forces on the membrane-embedded channels. However, the current lipid bilayer techniques, as well as the patch-clamp method, remain at the near-equilibrium characterization stage.14,15

To evaluate the dynamic responses of ion channels under quickly changing bilayer tension, we present a novel time-lapse evaluation method for the membrane tension. In prevalent bilayer formation methods, lipid-lined water-in-oil droplets (DIB) or bubbles (CBB) are docked to form a bilayer. The CBB method has advantages such that each monolayer-lined bubble is maintained by steadily applying an intrabubble holding pressure by manipulating a pneumatic injector18,21 (Figure 1). Thus, the membrane tension is readily controlled by dynamic handling of the intrabubble pressure via the Young–Laplace principle:

graphic file with name au0c00098_m001.jpg 1

where γmo is the monolayer tension and R1 and R2 are the principal radii of the bubble curvature) (pressure manipulation → tension change).22,23 In turn, measurements of the intrabubble pressure enable quantitative evaluation of the tension also via the Young–Laplace principle (pressure measurement → tension evaluation). Practically, however, pressure measurements have not been performed because the intrabubble pressure is expected to be very low, on the order of 100 Pa (0.75 mmHg). In this study, fine-tuning of intrabubble pressure measurements allows the establishment of a time-lapse quantitative bilayer tension evaluation system (Figure 1).

Figure 1.

Figure 1

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Principle of the time-lapse measurements of the bilayer tension (bubble pressure method). (A) Microscopic image of the CBB and the parameters relevant to the bilayer tension. The two bubbles are maintained at similar sizes. An intrabubble pressure as low as ∼100 Pa is measured using a fine pressure gauge, and with image-analyzed radii of the bubbles, the monolayer tension is evaluated via the Young–Laplace equation. (B) Contact angle. The bilayer tension is obtained by measuring the contact angle as well as the monolayer tension via the Young equation. (C) Experimental setup on an inverted microscope (left) and pressure measurements with factors affecting the intrabubble pressure.

The KcsA potassium channel is a prototypical channel for understanding the structure–function relationship of ion channels, and a large amount of experimental data have been accumulated.12,24−26 The KcsA channel has been recognized as a nonstretch-activated channel,27 but recently, we found a unique tension sensitivity of the KcsA channel.15 The resting channel never responds to membrane stretch (hidden mechanosensitivity), whereas the channel in a ready-to-activate state under cytosolic acidic pH responds to the membrane stretch with the activation gate open. Here, we apply the time-lapse tension measurement system to examine the dynamic responsiveness of the KcsA channel to membrane tension through single-channel current recordings. We reveal unprecedented hysteretic responses of the KcsA channel to bilayer tension, which is attributed exclusively to channel conformational changes.

Results and Discussion

Measurements of the Bilayer Tension

The core of the present method lies in precise measurement of the low intrabubble pressure in the range of 100 Pa (Figure 1). The fine pressure gauge continuously monitors the intrabubble pressure, p, for each bubble. The pressure in the bubble relative to the atmosphere must be defined appropriately, and the capillary action and gravity are taken into account (described in detail in the Materials and Methods section). Water bubbles with azolectin as lipids are blown into an oil phase (hexadecane) by manipulating the pneumatic injectors until the desired size, such as 100 μm in diameter, is reached, followed by fine-tuning the injectors to maintain the size (see methods in the Supporting Information for details). The sizes of the two bubbles remain similar, and the bilayer shape is flat without discernible curvature (Figure 1A).28 Parallel to the pressure measurements, geometric features, such as the radius of each bubble and the contact angle between bubbles, are evaluated via off-line image analysis (Figure 1A,B; see Materials and Methods for details). The monolayer tension (γmo) of the bubbles is evaluated straightforwardly from the intrabubble pressure and the bubble radii using the Young–Laplace principle (eq 1). Then, the bilayer tension (γbi) is evaluated from the measured contact angle (θ) using the Young equation:

graphic file with name au0c00098_m002.jpg 2

This time-lapse evaluation is hereafter referred to as the bubble shape–pressure method.

Figure 2A shows cumulative data of the steady-state monolayer tension γmo as a function of the intrabubble pressure p and the harmonic mean of the radii (=2R1R2/(R1 + R2)). The two principal radii are similar (<15% difference), indicating a nearly spherical bubble shape. The p value is varied from several Pa to greater than 150 Pa by manipulating the pneumatic microinjector, whereas the mean radius is limited within the range of 20–50 μm. The monolayer tension γmo is mostly determined by the bubble pressure p in this range of the bubble size (Figure 2A; see SI Figure S1 for a precise relationship (see further discussion in Supporting Information).

Figure 2.

Figure 2

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Relations among the parameters for the CBB tension analysis. (A) γmo as a function of P and 2R1R2/(R1 + R2). A bubble is nearly spherical, giving similar values for R1 and R2; thus, these radii are averaged. (B) Contact angle θ as a function of P and γmo. (C) γbi as a function of each γmo. The size and pressure of each bubble are not identical, and γmo in each bubble shows variability.

Next, the contact angle θ is examined as a function of p and γmo (Figure 2B). As p and γmo increase, θ substantially decreases. From the values of γmo and θ, the bilayer tension γbi is calculated, and γbi as a function of each γmo is plotted (Figure 2C). γbi varies from <1 to ∼10 mN/m. In the present method, the real-time monitoring of p values reflects the pneumatic injector manipulation and reveals the trend of γbi because of the nearly linear relationship between p and γbi (SI Figure S1).

As a reference for the bilayer tension evaluation, the steady-state bilayer tension measured by the bubble shape–pressure method is compared with that measured by the previous method, in which independent principles without inspecting the intrabubble pressure (the Young–Lippmann principle) are applied (see Supporting Information for details, SI Figure S3).14,15 The steady-state γbi values are comparable between the two evaluation methods (SI Figure S3), rationalizing the procedures in the bubble shape–pressure method. In the non-equilibrium tension measurements, the previous method is inappropriate as several seconds are needed to complete a single measurement, whereas the bubble shape–pressure method allows time-lapse tension measurements.

Time-Lapse Measurements of the Bilayer Tension and Dynamic Responses of the Membrane

Time-lapse measurements of γbi are performed by increasing the image sampling frequency. Figure 3A,B shows representative data (see SI Video) of continuously measured intrabubble pressures for both bubbles (A) and geometric parameters obtained by off-line image analysis at 1 Hz (B). The relationships between these parameters disclose the systems’ dynamic responses.

Figure 3.

Figure 3

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Time course of bilayer parameters and KcsA (E71A mutant) single-channel currents. (A) Continuous recordings of the intrabubble pressures. Blue for the right bubble and red for the left bubble. (B) Time-lapse evaluation of geometric features, the principal radii, and the contact angle. From p and the geometry, the monolayer and bilayer tension are calculated. (C) Representative single-channel current of the noninactivating E71A mutant KcsA channel at +100 mV under varying bilayer tension. Inset: single-channel activity with an expanded time scale. (D) Time-lapse measurements of the bilayer tension and single-channel open probability Popen. Popen values were calculated with the time interval of 1000 ms every 100 ms and were picked up at the synchronized time for the geometric data (see Materials and Methods and SI Figure S5). Trends of the Popen values for the time interval of 500 ms were indistinguishable. The light blue and pink strips represent the decreasing and increasing phases of the bilayer tension, respectively.

Two bubbles are free-standing, retaining the contact bilayer under physical equilibrium between the monolayer and the bilayer (Figure 1B). The bilayer tension changes as bubbles rapidly undergo transitions to another equilibrium shape. In the visual inspection under microscopy, changes in the contact angle, which is a sign of bilayer tension, are immediate without apparent delay when manipulating the pneumatic injector. The underlying processes are the following: changes in the intrabubble pressure are nearly synchronized to those of the manipulated pressure, which is measured, thus, yielding monolayer tension changes followed by changes in the bilayer tension and the contact angle. Experimentally, the response time of the system can be traced by following the time course of observable parameters: the pressure and the contact angle. The dynamic response was analyzed quantitatively by increasing the image sampling frequency up to 10 Hz (Figure 4 and SI Figure S4).

Figure 4.

Figure 4

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Dynamic responses of the contact angle and bubble volume upon a step changes in the pressure. (A) Representative data for the right and left pressures, which differ substantially at the steady state. A step change was applied to the right bubble. The pressure was controlled manually, and the time course of the pressure change was not rectangular stepwise. The contact angle of both sides started to change with the time constant of 190 ms followed by a gradual increase because of the slow bubble inflation. (B) Representative data for the bubble volume changes upon the step application of pressure. The bubble volume started to change upon the pressure step and gradually increased with the time constant of 640 ms. From the volume change, the volume flow rate was calculated as differentiating the volume change (dV/dt).

First, we examined the contact angle changes upon voltage steps (electrostriction)29 as the voltage changes are completed within a millisecond under the voltage clamp. As shown in SI Figure S4A,B,D, changes in the contact angle were not immediate but gradual in the time range of 100 ms. The time courses were fitted with an exponential function, and the time constant was 173.1 ± 12.7 ms (n = 8) for step changes to +200 mV and 115.4 ± 9.2 ms for return voltage (SI Figure S4D). Upon voltage changes, bubble pressure did not change, and the time course of the bilayer tension followed that of the contact angle (SI Figure S4C–E). Accordingly, the response time of bilayer tension changes upon rapid perturbation of the system by voltage steps is in ∼150 ms, which is rapid enough for examining dynamic features of bilayer and channels therein.

Next, responses of the contact angle to step pressure changes were examined (Figure 4A). Stepwise pressure was applied manually, in which care must be taken not to blow out the bubbles; the time course of the pressure change was not right rectangular. The contact angle started to change after 150 ms from the midpoint of the pressure change, constituting an overall delay of this system.

Water flows in and out of the bubble across the pipet tip, generating a potential error in evaluating the intrabubble pressure from the measured one. Upon pressure change, the intrabubble pressure changes immediately before bulk flow starts, which was shown as rapid changes in the contact angle (Figure 4A). Subsequently, bubbles change their volume, and the flow generates a pressure gradient (Figure 4B). The Bernoulli principle indicates that flow velocity determines the pressure gradient (see details in the Supporting Information). The flow velocity is evaluated from the changes in the bubble size given the pipet tip size (upper limit of 0.8 mm/s), and the pressure difference in the bubble is estimated as 0.733 mPa at the maximal flow rate. Accordingly, the experimental error in evaluating the intrabubble pressure is negligible.

The operation and principle underlying the bubble shape–pressure method are straightforward, that is, the Young–Laplace principle (eq 1) for the monolayer tension and the Young principle (eq 2) for the bilayer tension. Upon pressure increases, the time course of bubble surface expansion is much faster than partitioning additional lipids to the expanded surface from the reservoir (SI Figure S2), and the monolayer tension is rapidly increased. Rapid responses of the contact angle to the pressure change indicates that pressure manipulation is readily transferred to the bubble geometry. Overall, the bilayer tension changes rapidly (∼150 ms) upon the pressure manipulation.

Hysteretic Responses of the Tension-Sensitive KcsA Channel

Now, the dynamic responsiveness of the tension-sensitive KcsA channel is examined using the time-lapse bubble shape–pressure method. The KcsA channel reconstituted into the azolectin membrane is in a ready-to-activate state by setting the intracellular pH acidic (pH 4.0), while the extracellular pH is set neutral (pH 7.5; see Materials and Methods for details). A noninactivating E71A mutant KcsA channel is used to examine the effects of bilayer tension on the activation gate.15 Single-channel currents are recorded under a steadily changing bilayer tension. Representative real-time data of the single-channel current and the time-lapse bilayer tension are shown in Figure 3C,D. Five active KcsA channels are discernible, undergoing stochastic gating (inset). The bilayer tension is varied from 1 to 6 mN/m (Figure 3D, purple). The single-channel open probability Popen is readily evaluated by fitting with the binomial distribution (see Materials and Methods and SI Figure S5), and the time course of Popen is shown (Figure 3D, orange). As the tension increases (pink strip regions), Popen increases in parallel with γbi. In contrast, in the tension-decreasing phase (light blue strip regions), the response of Popen is substantially delayed from that of γbi.

The time course of the channel response is plotted as a three-dimensional plot (Figure 5A). A spiral trajectory is observed; the response follows distinct routes in the increasing and decreasing phases of the bilayer tension, and the up and down trajectories are reproducible. This behavior is a typical hysteresis of tension sensitivity. In the γbi–Popen plot (Figure 5B), the experimental data points are colored differently for those obtained in the tension-increasing (stretching, pink) and -decreasing (relaxation, blue) phases. The two classes of data are fitted with the Boltzmann function (see Materials and Methods for details), demonstrating the different sensitivities to the membrane tension (Figure 5B legends).

Figure 5.

Figure 5

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Hysteretic responses of the KcsA channel to the bilayer tension. (A) Time course of the Popen change as a function of γbi. The bilayer tension was increased and decreased, and Popen as a function of γbi is plotted based on the moving average of the data (see Materials and Methods). Overall, the trajectory is a spiral. In the tension-increasing (stretching) phase, Popen responds in a linear manner, whereas in the tension-decreasing (relaxation) phase, Popen decreases in a nonlinear manner. (B) Popen as a function of γbi. The response is discriminated for the stretching phase and the relaxation phase. These two phases are fitted with the Boltzmann function, Inline graphic, with a ΔG0 of 8.95 ± 0.71kBT, a ΔA of 2.60 ± 0.20 nm2, and a half-activation tension of 3.44 ± 0.11 mN/m for the stretching phase and a ΔG0 of 9.67 ± 0.83kBT, a ΔA of 4.04 ± 0.37 nm2, and a half-activation tension of 2.40 ± 0.09 mN/m for the relaxation phase. (C) Side view of the closed (1k4c) and stable open (3f5w) channel. The transmembrane helices are shown as rods with different colors for each subunit. (D) Mode shift model with four open and closed states for the tension-dependent gating of the KcsA channel. The KcsA crystal structures (transmembrane domain) viewed from the cytoplasmic side are schematically shown with their M1 and M2 helices (see also SI Figure S6). CSym: symmetric closed conformation (stable; pdb code: 1K4C). OAsym: asymmetric open conformation (metastable; 3EFF). OSym: symmetric open conformation (stable; 3F5W). CAsym: asymmetric closed conformation (metastable; 3PJS).

Changes in the cross-sectional area (ΔA) of the channel are deduced from the fitting, and the ΔA values differ substantially for the stretching and relaxation phases (Welch’s t test P value: P < 0.01); in the relaxation phase, ΔA is larger than that in the stretching phase, suggesting that the footprint area of the channel conformation expands upon the transition from the stretching phase to the relaxation phase. In this measurement system, the contact angle, as a measure of the bilayer tension, changes with the time constant of ∼150 ms (SI Figure S4 and Figure 4). In the frequency of 1 Hz for channel activity measurements, the transient changes of the fluidic membrane are completed more than 99.9%. Thus, the hysteresis is attributed exclusively to the channel protein undergoing conformational changes of the activation gate under varying bilayer tension.

Generally, hysteresis of gating for various types of channels to various types of stimuli has been reported.30−35 The voltage-gated channel exhibits a hysteretic response to the membrane voltage relevant to the operation of the voltage sensor domain.35 The KcsA channel, even without the voltage sensor domain, exhibits hysteretic responses to the membrane potential, which is related to coupling with the inactivation gate.30 In this study, the noninactivating mutant of the KcsA channel exhibits a hysteretic response to the membrane tension, indicating that hysteresis is relevant to activation gating, involving a large conformational change36 (Figure 5C).

To understand the hysteresis, a simple two-state open–closed model cannot afford the mechanism. The concept of mode shift is frequently applied as an underlying mechanism of hysteresis;35 the channel sensitivity changes as a function of activity via a shift to another active state, to which the closed state cannot reach immediately upon stretching (Figure 5B,D).

In the activation gating of potassium channels, global twisting of the helical bundle of the transmembrane domain occurs,25 and the cross-sectional area of the transmembrane domain expands upon opening15 (Figure 5C,D). Thus, under the open activation gate, the helical bundle is loosely packed. From a structural point of view, the crystal structure of the homotetrameric KcsA channel in the closed and open conformations is solved under symmetric conditions36,37 and considered to be symmetric in physiological conditions (pdb: 1K4C, 3F5W, Figure 5D and SI Figure S6). In contrast, the crystal structure of the full-length channel is asymmetric for open and closed conformations (Figure 5D asymmetric structure, pdb: 3EFF, 3PJS),38,39 indicating that an asymmetric structure is feasible even for the homotetrameric KcsA channel.

We hypothesize a putative mechanism of the hysteresis based on the mode shift paradigm, in which structural asymmetry is implemented. Upon stretching, the closed channel is driven to an open conformation, and the channel may not maintain a symmetric structure during opening conformational changes. Loosening of the helical bundle in asymmetric open conformations is metastable.40,41 Meanwhile, by maintaining high tension and thus longer residency in the open conformation, the channel structure shifts to a more stable symmetric open state,42 with a larger cross-sectional area than that of the metastable open conformation. This constitutes a mode shift (OAsym → OSym; Figure 5D). In the relaxation phase, this stable open state undergoes closure, and the closed state also adopts an asymmetric metastable conformation. Subsequently, the asymmetric closed state is stabilized by shifting to a symmetric closed conformation (CAsym → CSym). Thus, the different conformational changes in the stretching and relaxation phases offer different tension sensitivities.

Conclusion

This study establishes the straightforward bubble shape–pressure method for the time-lapse measurement of the bilayer tension under arbitrarily controlled pressure. Free-standing bubbles readily change their shape through rapidly equilibrating forces. Intrabubble pressure, under freely manipulatable, is a primary factor to govern the tension. Using this method, we reveal that the tension-sensitive KcsA channel exhibits unprecedented hysteretic responses to the bilayer tension. No hysteresis is found for the lipid bilayer in the time range of seconds (SI Figure S4). Accordingly, the hysteresis is unequivocally attributed, for the first time, to the channel molecule per se.

Hysteresis of channel responses has been reported for various stimuli but not for the bilayer tension because of the experimental limitations in the quantitative evaluation of rapidly varying tension. The native membrane patch itself may exhibit hysteretic behavior under the influence of various factors accompanying the patch membrane, such as cortical actin networks.8,43 Dynamic responses to mechanosensitive channels have recently been reported, such as the rebound phenomenon of channel activities to decreased bilayer tension44 and channel inactivation under sustained bilayer tension.43 In these studies, liposome-patch or bleb-patch was used. Still, a lipid bilayer tethered to the pipet glass surface demonstrates unexpected mechanical behavior because the tether is not tight but undergoes annealing (seal annealing43). Thus, observed phenomena are difficult to assign whether they are originated from either the membrane or the channel molecule therein.

The CBB equipped with the bubble shape–pressure method is promising for investigating these intriguing issues. In the absence of interaction with the glass surface, free-standing lipid bilayers equalize the tension immediately throughout the membrane due to the in-plane fluidity of the bilayer.45 The bubble shape–pressure method of the CBB allows variation of the physical and dynamic nature in lipid bilayers, through which channel dynamics are characterized.

The KcsA channel is a prototypical channel, and the protein architecture of the pore domain and its conformational changes upon gating are shared with a variety of channels belonging to a very large superfamily of voltage-gated cation channels.46 In these channels, global conformational changes undergo upon the opening of the gate, involving loosening of bundle helices of the pore domain, which are under the influence of the force from lipids.25 Accordingly, hysteresis of the tension sensitivity plausibly occurs for these and other types of channels. Our time-lapse tension measurement system would permit quantitative characterization of the tension sensitivity of various types of channels, finding hidden hysteresis of tension sensitivity as a more general feature of channel proteins. The physiological roles of the hysteretic responses of channel molecules remain elusive, but channel molecules acquire “memory” through hysteresis in mechano-electrical transduction. Therefore, the tension sensitivity and its hysteresis are operative in dynamic mechanical changes of the membrane under physiological functions.

Materials and Methods

Reagents

Azolectin (l-α-phosphatidylcholine type IV-S) was purchased from Sigma-Aldrich (St. Louis, MO, USA). Other chemicals were purchased from Nacalai Tesque (Kyoto, Japan).

Sample Preparation

Expression and purification of the E71A mutant of the KcsA channel are described elsewhere.12,47 Liposomes and channel-incorporated liposomes (proteoliposomes) were prepared following a previous report15 with modification (see Supporting Information). Azolectin (10 mg/mL) in chloroform solution was dried and dispersed in 200 mM KCl solution (pH 7.5 or 4.0), producing a liposome suspension (2 mg/mL). The purified channel proteins were incorporated into the liposomes by the dilution method15 with a lipid–protein weight ratio of 2000.

Experiments for Measuring the Bilayer Tension Using the CBB

The experimental setups for the CBB were the same as those previously reported15,18,19 except for the pressure measurement system. The pressure gauge (DP103; Validyne Engineering, Los Angeles, CA, USA) was connected to a glass pipet holder, and the pressure was continuously monitored via a signal amplifier (PA701; Krone, Tokyo, Japan).

A glass pipet (i.d./o.d., 1.05/1.5 mm; tip diameter, 50 μm) was set in a micropipet holder with a pressure port, which was connected to the motor-driven micromanipulator (EMM; Narishige, Tokyo, Japan) on the stage of an inverted microscope (IX73; Olympus, Tokyo, Japan). The glass pipet tip was immersed into the liposome (or proteoliposome) suspension solution with the pressure port open for minutes. After equilibration of the capillary action (see methods in the Supporting Information for details). The pressure line was closed, and the intrabubble pressure was defined as zero.

Using the pneumatic manipulator (IM-11-2; Narishige, Tokyo, Japan), the liposome (or proteoliposome) suspension was swollen into the oil phase from the tip of the pipet, forming a water-in-oil bubble lined with a lipid monolayer. A lipid bilayer (CBB) was formed by contacting two bubbles. Electrical recordings were performed using an amplifier (EPC800; HEKA, Lambrecht/Pfalz, Germany), and microscope images were recorded with a digital camera (ORCA-Flash2.8; HAMAMATSU, Hamamatsu, Japan).

Evaluation of the Bilayer Tension

From the time-lapse bubble images, the radius and contact angle were evaluated using the image analysis method (Figure 1), in which the bubble images were fitted to ellipses using data analysis software (Origin Pro; OriginLab, Northampton, MA, USA), and the intersections of two ellipses were solved using a free computer algebra system (wxMaxima, Maxima.sourceforge.net). The geometric parameters R1 and R2 represent the principal radii of curvature of the bubble. Accordingly, with the continuously measured intrabubble pressures, the monolayer tension γmo was obtained from the Young–Laplace equation, γmo = (R1R2)/(R1 + R2)Δp. Then, from the contact angle θ, the bilayer tension γbi was calculated from the Young equation, γbi = γmo–L cos θL + γmo–R cos θR, where L and R indicate the left and right bubbles, respectively.

Electrophysiological Recordings

Membrane electrical features, such as the membrane capacitance and resistance, were recorded by applying ramp potentials of ±10 mV and analyzed using software (pCLAMP; Molecular Devices, San Jose, CA, USA). From the image-analyzed membrane area, the specific membrane capacitance was evaluated. For the channel activity measurements, the channel-containing proteoliposome suspension was swelled to form the bubble. Some of the channel molecules were spontaneously incorporated into the CBB and exhibit single-channel current. The single-channel current resolvable traces of the noninactivating E71A mutant KcsA channel were recorded under a constant Vm of +100 mV, whereas Δp was arbitrarily manipulated during the recording.

Tension–Popen Relationship

To obtain the tension–Popen relationship, experimental data of three different categories must be integrated. Single-channel currents and the bubble pressures were recorded with the sampling frequency of 5 kHz, whereas the bubble images were mostly collected with 1 Hz. For evaluating Popen values, current data were event-detected and integrated for the probability of each current level for an interval of tInt every 100 ms throughout the trace (see Supporting Information for details). Then, Popen values and the pressure values at the instances of the image captured time were collected. The bilayer tension was evaluated from the pressure and the geometrical parameters (the principal radii for both bubbles and the contact angle), and the γbi–Popen relationships were obtained (see further details in Supporting Information).

Statistical Analysis

Average values are expressed as means ± SEM. For comparison of means between categories, Welch’s t test (two-tailed, no assumption of variance) was carried out, and P values were obtained from a t-value lookup table.

Acknowledgments

We thank Drs. Masahiro Sokabe (Nagoya University), Toshiyuki Yoshida (University of Fukui), and Hidehiko Okazawa (University of Fukui) for discussions, and Springer Nature Author Services for providing English language editing. This work was supported, in part, by KAKENHI Grant Nos. 17K07360 and 20H03219 to M.I. and 19K22382 and 20H00497 to S.O.

Glossary

Abbreviations

CBB

contact bubble bilayer

DIB

droplet interface bilayer

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.0c00098.

  • Materials and methods, text, references, and figures (PDF)

  • Video showing continuously measured intrabubble pressures (AVI)

Author Contributions

M.I. contributed to data collection, and M.I. and S.O. contributed to the analysis and interpretation of data and writing of the manuscript.

The authors declare no competing financial interest.

Supplementary Material

au0c00098_si_001.pdf (798.8KB, pdf)
au0c00098_si_002.avi (14.5MB, avi)

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