Quantitative video microscopy of patch clamped membranes stress, strain, capacitance, and stretch channel activation.

Membrane patches from chick skeletal muscle were stretched by applying controlled suction or pressure to the pipette. From images of the patch, the patch dimensions (area and radius of curvature) were computed by nonlinear regression of the images to a geometric model. With no applied pressure, patch membranes are nearly planar and normal to the wall of the pipette. With increasing pressure gradients, the patch bulges, the radius of curvature decreases, and the area increases. The patch capacitance changes in exact proportion to the change in area at a rate of 0.7 microF/cm2. The increase in area is due to a flow of lipid (with perhaps small amounts of diffusible protein) along the walls of the pipette into the patch. The flow is reversible with a relaxation of the pressure gradient. The area elastic constant of the membrane is approximately 50 dyn/cm, insensitive to cytochalasin B and probably represents the elasticity of the underlying spectrin/dystrophin network. Simultaneous measurements of stretch activated (SA) ion channel activity in the patch showed that the sensitivity of channels from different patches, although different when calculated as a function of applied pressure, was the same when calculated as a function of tension. Because patch lipid is free to flow, and hence stress-free in the steady state, SA channels must be activated by tension in the cytoskeleton.     

Lipid bilayer mechanics in a pipette with glass-bilayer adhesion

Electrophysiology is a central tool for measuring how different driving forces (e.g., ligand concentration, transmembrane voltage, or lateral tension) cause a channel protein to gate. Upon formation of the high resistance seal between a lipid bilayer and a glass pipette, the so-called “giga-seal”, channel activity can be recorded electrically. In this article, we explore the implications of giga-seal formation on the mechanical state of a lipid bilayer patch. We use a mechanical model for the free energy of bilayer geometry in the presence of glass-bilayer adhesion to draw three potentially important conclusions. First, we use our adhesion model to derive an explicit relationship between applied pressure and patch shape that is consistent with the Laplace-Young Law, giving an alternative method of calculating patch tension under pressure. With knowledge of the adhesion constant, which we find to be in the range ∼0.4–4 mN/m, and the pipette size, one can precisely calculate the patch tension as a function of pressure, without the difficultly of obtaining an optical measurement of the bilayer radius of curvature. Second, we use data from previous electrophysiological experiments to show that over a wide range of lipids, the resting tension on a electrophysiological patch is highly variable and can be 10–100 times higher than estimates of the tension in a typical cell membrane. This suggests that electrophysiological experiments may be systematically altering channel-gating characteristics and querying the channels under conditions that are not the same as their physiological counterparts. Third, we show that reversible adhesion leads to a predictable change in the population response of gating channels in a bilayer patch.     

The structure and dynamics of patch-clamped membranes: a study using differential interference contrast light microscopy

We have developed techniques for micromanipulation under high power video microscopy. We have used these to study the structure and motion of patch-clamped membranes when driven by pressure steps. Patch-clamped membranes do not consist of just a membrane, but rather a plug of membrane-covered cytoplasm. There are organelles and vesicles within the cytoplasm in the pipette tip of both cell-attached and excised patches. The cytoplasm is capable of active contraction normal to the plane of the membrane. With suction applied before seal formation, vesicles may be swept from the cell surface by shear stress generated from the flow of saline over the cell surface. In this case, patch recordings are made from membrane that was not originally present under the tip. The vesicles may break, or fuse and break, to form the gigasealed patch. Patch membranes adhere strongly to the wall of the pipette so that at zero transmural pressure the membranes tend to be normal to the wall. With transmural pressure gradients, the membranes generally become spherical; the radius of curvature decreasing with increasing pressure. Some patches have nonuniform curvature demonstrating that forces normal to the membrane may be significant. Membranes often do not respond quickly to changes in pipette pressure, probably because viscoelastic cytoplasm reduces the rate of flow through the tip of the pipette. Inside-out patches may be peeled from the walls of the pipette, and even everted (with positive pressure), without losing the seal. This suggests that the gigaseal is a distributed property of the membrane-glass interface.     

Free energy potential for aggregation of giant, neutral lipid bilayer vesicles by Van der Waals attraction.

Here, we report the first direct observation of Van der Waals' attraction between biomembrane capsules using measurements of the free energy reduction per unit area of membrane-membrane contact formation. In these studies, the membrane capsules were reconstituted neutral (egg phosphatidylcholine) lipid bilayers of giant (greater than 10(-3) cm diam) vesicles. Micromanipulation methods were used to select and maneuver two vesicles into proximity for contact; after adhesion was allowed to occur, the extent of contact formation was regulated through the vesicle membrane tensions that were controlled by micropipette suction. The free energy reduction per unit area of contact formation was proportional to the membrane tension multiplied by a simple function of the pipette and vesicle dimensions. The free energy potential for Van der Waals attraction between the neutral bilayers in 120 mM NaCl solutions was 1.5 X 10(-2) ergs/cm2. Also, when human serum albumin was added to the medium in the range of 0-1 mg/ml, the free energy potential for bilayer-bilayer adhesion was not affected. Using published values for equilibrium spacing between lipid bilayers in multilamellar lipid-water dispersions and the theoretical equation for van der Waals attraction between continuous dielectric layers, we calculated the value for the Hamaker coefficient of the Van der Waals attraction to be 5.8 X 10(-14) ergs.     

Role of the membrane cortex in neutrophil deformation in small pipets.

The simplest model for a neutrophil in its "passive" state views the cell as consisting of a liquid-like cytoplasmic region surrounded by a membrane. The cell surface is in a state of isotropic contraction, which causes the cell to assume a spherical shape. This contraction is characterized by the cortical tension. The cortical tension shows a weak area dilation dependence, and it determines the elastic properties of the cell for small curvature deformations. At high curvature deformations in small pipets (with internal radii less than 1 micron), the measured critical suction pressure for cell flow into the pipet is larger than its estimate from the law of Laplace. A model is proposed where the region consisting of the cytoplasm membrane and the underlying cortex (having a finite thickness) is introduced at the cell surface. The mechanical properties of this region are characterized by the apparent cortical tension (defined as a free contraction energy per unit area) and the apparent bending modulus (introduced as a bending free energy per unit area) of its middle plane. The model predicts that for small curvature deformations (in pipets having radii larger than 1.2 microns) the role of the cortical thickness and the resistance for bending of the membrane-cortex complex is negligible. For high curvature deformations, they lead to elevated suction pressures above the values predicted from the law of Laplace. The existence of elevated suction pressures for pipets with radii from 1 micron down to 0.24 micron is found experimentally. The measured excess suction pressures cannot be explained only by the modified law of Laplace (for a cortex with finite thickness and negligible bending resistance), because it predicts unacceptable high cortical thicknesses (from 0.3 to 0.7 micron). It is concluded that the membrane-cortex complex has an apparent bending modulus from 1 x 10(-18) to 2 x 10(-18) J for a cortex with a thickness from 0.1 micron down to values much smaller than the radius of the smallest pipet (0.24 micron) used in this study.     

Membrane tension directly shifts voltage dependence of outer hair cell motility and associated gating charge.

The unique electromotility of the outer hair cell (OHC) is believed to promote sharpening of the passive mechanical vibration of the mammalian basilar membrane. The cell also presents a voltage-dependent capacitance, or equivalently, a nonlinear gating current, which correlates well with its mechanical activity, suggesting that membrane-bound voltage sensor-motor elements control OHC length. We report that the voltage dependence of the gating charge and motility are directly related to membrane stress induced by intracellular pressure. A tracking procedure was devised to continuously monitor the voltage at peak capacitance (VpkCm) after obtaining whole cell voltage clamp configuration. In addition, nonlinear capacitance was more fully evaluated with a stair step voltage protocol. Upon whole cell configuration, VpkCm was typically near -20 mV. Negative patch pipette pressure caused a negative shift in VpkCm, which obtained a limiting value near the normal resting potential of the OHC (approximately -70 mV) at the point of cell collapse. Positive pressure in the pipette caused a positive shift that could reach values greater than 0 mV. Measures of the mechanical activity of the OHC mirrored those of charge movement. Similar membrane-tension dependent peak shifts were observed after the cortical cytoskeletal network was disrupted by intracellular dialysis of trypsin from the patch pipette. We conclude that unlike stretch receptors, which may sense tension through elastic cytoskeletal elements, the OHC motor senses tension directly. Furthermore, since the voltage dependence of the OHC nonlinear capacitance and motility is directly regulated by intracellular turgor pressure, we speculate that modification of intracellular pressure in vivo provides a mechanism for controlling the gain of the mammalian "cochlear amplifier".     

A novel micropipet method for measuring the bending modulus of vesicle membranes.

A theoretical model and an experiment are presented for determining the bending modulus of a bilayer vesicle membrane. The vesicle is held with a pipet having a radius between 1 and 2 microns, and the tension in the membrane is changed by changing the suction pressure. Then the vesicle membrane is deformed by aspirating it into a smaller pipet having a radius on the order of 0.5 microns. The relationship between the suction pressures in the two pipets is found to be linear, as predicted by the theoretical model. The curvature of the vesicle membrane at the pipet orifice and the bending modulus are found with the help of the model from the slope and the intercept of the linear experimental relationship between the suction pressures in the two pipets. The bending modulus for the two SOPC membranes studied in these experiments was found to be either 0.6 or 1.15 x 10(-19) J, which is similar to the values measured previously.     

Detailed mechanics of membrane-membrane adhesion and separation. I. Continuum of molecular cross-bridges

The mechanics of membrane-membrane adhesion are developed for the approximation that the molecular cross-bridging forces are continuously distributed as a normal stress (force per unit area). The significance of the analysis is that the finite range of the cross-bridging forces and the microscopic contact angle are not assumed negligible. Since the cross-bridging and adhesion forces are finite range interactions, there are two membrane regions: a free zone where the membranes are not subject to attractive forces; and an adherent zone where the membranes are held together by attractive stresses. The membrane is treated as an elastic continuum. The approach is to analyze the mechanics for each zone separately and then to require continuity of the solutions at the interface between the zones. Final solution yields the membrane contour and stresses proximal to and within the contact zone as well as the microscopic contact angle at the edge of the contact zone. It is demonstrated that the classical Young equation is consistent with this model. The results show that the microscopic contact angle becomes appreciable when the strength of adhesion is large or the length of the cross-bridge is large; however, the microscopic contact angle approaches zero as the membrane elastic stiffness increases. The solution predicts the width of the contact zone over which molecular bonds are stretched. It is this boundary region where increased biochemical activity is expected. In the classical model presented here, the level of tension necessary to oppose spreading of the contact is equal to the minimal level of tension required to separate the adherent membranes. This behavior is in contrast with that derived for the case of discrete molecular cross-bridges where the possibility of different levels of tension associated with adhesion and separation is introduced. The discrete cross-bridge case is the subject of a companion paper.     

Minimum energy analysis of membrane deformation applied to pipet aspiration and surface adhesion of red blood cells.

An experimental procedure is demonstrated which can be used to determine the interfacial free energy density for red cell membrane adhesion and membrane elastic properties. The experiment involves micropipet aspiration of a flaccid red blood cell and manipulation of the cell proximal to a surface where adhesion occurs. A minimum free energy method is developed to model the equilibrium contour of unsupported membrane regions and to evaluate the partial derivatives of the total free energy, which correspond to the micropipet suction force and the interfacial free energy density of adhesion. It is shown that the bending elasticity of the red cell membrane does not contribute significantly to the pressure required to aspirate a flaccid red cell. Based on experimental evidence, the upper bound for the bending or curvature elastic modulus of the red cell membranes is 10-12 ergs (dyn-cm). Analysis of the adhesion experiment shows that interfacial free energy densities for red cell adhesion can be measured from a lower limit of 10-4 ergs/cm2 to an upper limit established by the membrane tension for lysis of 5-10 ergs/cm2.     

The ultrastructure of patch-clamped membranes: a study using high voltage electron microscopy

We have developed techniques for studying patch-clamped membranes inside glass pipettes using high voltage electron microscopy (HVEM). To preserve the patch structure with the least possible distortion, we rapidly froze and freeze dried the pipette tip. The pipette is transparent for more than 50 microns from the tip. HVEM images of patches confirm light microscopy observations that the patch is not a bare bilayer, but a membrane-covered bleb of cytoplasm that may include organelles and cytoskeleton. The membrane that spans the pipette is commonly tens of micrometers from the tip of the pipette and occasionally as far as 100 microns. The structure of patches taken from a single cell type is variable but there are consistent differences between patches made from different cell types. With suction applied to the pipette before seal formation, we have seen in the light microscope vesicles swept from the plasmalemma up the pipette. These vesicles are visible in electron micrographs, particularly those made from chick cardiac muscle. Colloidal gold labeling of the patch permitted identification of lectin-binding sites and acetylcholine receptors. In young cultures of Xenopus myocytes, the receptors were diffuse. In 1-wk-old cultures, the receptors formed densely packed arrays. The patch pipette can serve, not only as a recording device, but as a tool for sampling discrete regions of the cell surface. Because the pipette has a constant path length for axial rotation, it is a unique specimen holder for microtomography. We have made preliminary tomographic reconstructions of a patch from Xenopus oocyte.     

Adhesivity and rigidity of erythrocyte membrane in relation to wheat germ agglutinin binding

Binding of the plant lectin wheat germ agglutinin (WGA) to erythrocyte membranes causes membrane rigidification. One of our objectives has been to directly measure the effects of WGA binding on membrane rigidity and to relate rigidification to the kinetics and levels of WGA binding. Our other objective has been to measure the strength of adhesion and mechanics of cell separation for erythrocytes bound together by WGA. The erythrocyte membrane rigidity was measured on single cells by micropipette aspiration. The slope of the suction pressure-length data for entry into the pipette provided the measure of the membrane extensional modulus. Data were collected for cells equilibrated with WGA solutions in the range of concentrations of 0.01- 10 micrograms/ml. Erythrocyte-erythrocyte adherence properties were studied by micropipette separation of two-cell aggregates. First, a "test" cell was selected from a WGA solution by aspiration into a small micropipette, then transferred to a separate chamber that contained erythrocytes in WGA-free buffer. Here, a second cell was aspirated with another pipette and maneuvered into close proximity of the test cell surface, and adhesive contact was produced. The flaccid cell was separated from the test cell surface in steps at which the force of attachment was derived from the pipette suction pressure and cell geometry. In addition, we measured the time-dependent binding and release of fluorescently labeled WGA to single erythrocytes with a laser microfluorometry system. The results showed that the stiffening of the erythrocyte membrane and binding of fluorescently labeled WGA to the membrane surface followed the same concentration and time dependencies. The threshold concentration for membrane stiffening was at approximately 0.1 microgram/ml where the time course to reach equilibrium was close to 1 h. The maximal stiffening (almost 30-fold over the normal membrane elastic modulus) occurred in concentrations greater than 2 micrograms/ml where the time to reach equilibrium took less than 1 min. The WGA binding also altered the normal elastic membrane behavior into an inelastic, plastic-like response which indicated that mechanical extension of the membrane caused an increase in cross-linking within the surface plane. Similar to the stiffening effect, we observed that the membrane adhesivity of cells equilibrated with WGA solutions greatly increased with concentration greater than 0.1 microgram/ml.(ABSTRACT TRUNCATED AT 400 WORDS)     

Analysis of adhesion of large vesicles to surfaces.

An experimental procedure that can be used to measure the interfacial free energy density for the adhesion of membranes of large vesicles to other surfaces is outlined and analyzed. The approach can be used for both large phospholipid bilayer vesicles and red blood cells when the membrane force resultants are dominated by isotropic tension. The large vesicle or red cell is aspirated by a micropipet with sufficient suction pressure to form a spherical segment outside the pipet. The vesicle is then brought into close proximity of the surface to be tested and, the suction pressure reduced to permit adhesion, and the new equilibrium configuration is established. The mechanical analysis of the equilibrium shape provides the interfacial free energy density for the surface affinity. With this approach, the measurable range of membrane surface affinity is 10(-4)-3 erg/cm2 for large phospholipid bilayer vesicles and 10(-2)-10 erg/cm2 for red blood cells.     

Estimating the sensitivity of mechanosensitive ion channels to membrane strain and tension

Bone adapts to its environment by a process in which osteoblasts and osteocytes sense applied mechanical strain. One possible pathway for the detection of strain involves mechanosensitive channels and we sought to determine their sensitivity to membrane strain and tension. We used a combination of experimental and computational modeling techniques to gain new insights into cell mechanics and the regulation of mechanosensitive channels. Using patch-clamp electrophysiology combined with video microscopy, we recorded simultaneously the evolution of membrane extensions into the micropipette, applied pressure, and membrane currents. Nonselective mechanosensitive cation channels with a conductance of 15 pS were observed. Bleb aspiration into the micropipette was simulated using finite element models incorporating the cytoplasm, the actin cortex, the plasma membrane, cellular stiffening in response to strain, and adhesion between the membrane and the micropipette. Using this model, we examine the relative importance of the different cellular components in resisting suction into the pipette and estimate the membrane strains and tensions needed to open mechanosensitive channels. Radial membrane strains of 800% and tensions of 5 10(-4) N.m(-1) were needed to open 50% of mechanosensitive channels. We discuss the relevance of these results in the understanding of cellular reactions to mechanical strain and bone physiology.     

Detachment of agglutinin-bonded red blood cells. II. Mechanical energies to separate large contact areas.

As detailed in a companion paper (Berk, D., and E. Evans. 1991. Biophys. J. 59:861-872), a method was developed to quantitate the strength of adhesion between agglutinin-bonded membranes without ambiguity due to mechanical compliance of the cell body. The experimental method and analysis were formulated around controlled assembly and detachment of a pair of macroscopically smooth red blood cell surfaces. The approach provides precise measurement of the membrane tension applied at the perimeter of an adhesive contact and the contact angle theta c between membrane surfaces which defines the mechanical leverage factor (1-cos theta c) important in the definition of the work to separate a unit area of contact. Here, the method was applied to adhesion and detachment of red cells bound together by different monoclonal antibodies to red cell membrane glycophorin and the snail-helix pomatia-lectin. For these tests, one of the two red cells was chemically prefixed in the form of a smooth sphere then equilibrated with the agglutinin before the adhesion-detachment procedure. The other cell was not exposed to the agglutinin until it was forced into contact with the rigid cell surface by mechanical impingement. Large regions of agglutinin bonding were produced by impingement but no spontaneous spreading was observed beyond the forced contact. Measurements of suction force to detach the deformable cell yielded consistent behavior for all of the agglutinins: i.e., the strength of adhesion increased progressively with reduction in contact diameter throughout detachment. This tension-contact diameter behavior was not altered over a ten-fold range of separation rates. In special cases, contacts separated smoothly after critical tensions were reached; these were the highest values attained for tension. Based on measurements reported in another paper (Evans et al. 1991. Biophys. J. 59:838-848) of the forces required to rupture molecular-point attachments, the density of cross-bridges was estimated with the assumption that the tension was proportional to the discrete rupture force x the number of attachments per unit length. These estimates showed that only a small fraction of agglutinin formed cross-bridges at initial assembly and increased progressively with separation. When critical tension levels were reached, it appeared that nearly all local agglutinin was involved as cross-bridges. Because one cell surface was chemically fixed, receptor accumulation was unlikely; thus, microscopic "roughness" and steric repulsion probably modulated formation of cross-bridges on initial contact.(ABSTRACT TRUNCATED AT 400 WORDS)     

Assessment of potential stimuli for mechano-dependent gating of MscL: effects of pressure, tension, and lipid headgroups

MscL is a mechanosensitive channel of large conductance that serves as an "emergency relief valve", protecting bacteria from acute hypoosmotic stress. Although it is well-accepted that the MscL protein and an adequate membrane matrix are necessary and sufficient for the function of this channel, the exact role of the membrane has yet to be elucidated. Here, we address the role of the membrane matrix through in vitro reconstitution of the MscL protein in defined lipid bilayers. We have applied Laplace's law to visualized membrane patches where we can measure patch curvature as described in previous studies. Here, by comparing patches with different curvatures, we demonstrate that the MscL channel senses tension within the membrane and that the pressure across it plays no detectable role as a stimulus. In addition, gating only occurs when the smallest radius of curvature is nearly achieved, suggesting that the lateral tension rather than membrane curvature is the important biophysical parameter. Finally, we have examined the contribution of specific headgroups by measuring their effect on the membrane tension required to gate the channel. We have found that the addition of neither anionic nor endogenous lipids to a non-native membrane effected a leftward shift in the activation curve. In fact, the major endogenous lipid of the Escherichia coli membrane, phosphatidylethanolamine, led to a channel activity at a higher tension threshold, suggesting that this lipid effects altered activity through changes in the biophysical properties of the membrane, rather than through an MscL-specific interaction.     

Biophysics and Structure of the Patch and the Gigaseal

Interpreting channel behavior in patches requires an understanding of patch structure and dynamics, especially in studies of mechanosensitive channels. High resolution optical studies show that patch formation occurs via blebbing that disrupts normal membrane structure and redistributes in situ components including ion channels. There is a 1-2 μm region of the seal below the patch where proteins are excluded and this may consist of extracted lipids that form the gigaseal. Patch domes often have complex geometries with inhomogeneous stresses due to the membrane-glass adhesion energy (E_a), cytoskeletal forces, and possible lipid subdomains. The resting tension in the patch dome ranges from 1-4 mN/m, a significant fraction of the lytic tension of a bilayer (∼10 mN/m). Thus, all patch experiments are conducted under substantial, and uneven, resting tension that may alter the kinetics of many channels. E_a seems dominated by van der Waals attraction overlaid with a normally repulsive Coulombic force. High ionic strength pipette saline increased E_a and, surprisingly, increased cytoskeletal rigidity in cell-attached patches. Low pH pipette saline also increased E_a and reduced the seal selectivity for cations, presumably by neutralizing the membrane surface charge. The seal is a negatively charged, cation selective, space with a resistance of ∼7 gigohm/μm in 100 mM KCl, and the high resistivity of the space may result from the presence of high viscosity glycoproteins. Patches creep up the pipette over time with voltage independent and voltage dependent components. Voltage-independent creep is expected from the capillary attraction of E_a and the flow of fresh lipids from the cell. Voltage-dependent creep seems to arise from electroosmosis in the seal. Neutralization of negative charges on the seal membrane with low pH decreased the creep rate and reversed the direction of creep at positive pipette potentials.     

Free energy potential for aggregation of mixed phosphatidylcholine/phosphatidylserine lipid vesicles in glucose polymer (dextran) solutions.

The energetics of lipid vesicle-vesicle aggregation in dextran (36,000 mol wt) solutions have been studied with the use of micromechanical experiments. The affinities (free energy reduction per unit area of contact) for vesicle-vesicle aggregation were determined from measurements of the tension induced in an initially flaccid vesicle membrane as it adhered to another vesicle. The experiments involved controlled aggregation of single vesicles by the following procedure: two giant (approximately 20 micron diam) vesicles were selected from a chamber on the microscope stage that contained the vesicle suspension and transferred to a second chamber that contained a dextran (36,000 mol wt) salt solution (120 mM); the vesicles were then maneuvered into position for contact. One vesicle was aspirated with sufficient suction pressure to create a rigid sphere outside the pipette; the other vesicle was allowed to spread over the rigid vesicle surface. The aggregation potential (affinity) was derived from the membrane tension vs. contact area. Vesicles were formed from mixture of egg lecithin (PC) and phosphatidylserine (PS). For vesicles with a PC/PS ratio of 10:1, the affinity showed a linear increase with concentration of dextran; the values were on the order of 10(-1) ergs/cm2 at 10% by weight in grams. Similarly, pure PC vesicle aggregation was characterized by an affinity value of 1.5 X 10(-1) ergs/cm2 in 10% dextran by weight in grams. In 10% by weight in grams solutions of dextran, the free energy potential for vesicle aggregation decreased as the surface charge (PS) was increased; the affinity extrapolated to zero at a PC/PS ratio of 2:1. When adherent vesicle pairs were transferred into a dextran-free buffer, the vesicles did not spontaneously separate. They maintained adhesive contact until forceably separated, after which they would not read here. Thus, it appears that dextran forms a "cross-bridge" between the vesicle surfaces.     

The Purified Mechanosensitive Channel TREK-1 Is Directly Sensitive to Membrane Tension

Mechanosensitive channels are detected in all cells and are speculated to play a key role in many functions including osmoregulation, growth, hearing, balance, and touch. In prokaryotic cells, a direct gating of mechanosensitive channels by membrane tension was clearly demonstrated because the purified channels could be functionally reconstituted in a lipid bilayer. No such evidence has been presented yet in the case of mechanosensitive channels from animal cells. TREK-1, a two-pore domain K⁺ channel, was the first animal mechanosensitive channel identified at the molecular level. It is the target of a large variety of agents such as volatile anesthetics, neuroprotective agents, and antidepressants. We have produced the mouse TREK-1 in yeast, purified it, and reconstituted the protein in giant liposomes amenable to patch clamp recording. The protein exhibited the expected electrophysiological properties in terms of kinetics, selectivity, and pharmacology. Negative pressure (suction) applied through the pipette had no effect on the channel, but positive pressure could completely and reversibly close the channel. Our interpretation of these data is that the intrinsic tension in the lipid bilayer is sufficient to maximally activate the channel, which can be closed upon modification of the tension. These results indicate that TREK-1 is directly sensitive to membrane tension.     

Relationships among pressure, tension, and shape of the diaphragm

The shape of the diaphragm dome was calculated from transdiaphragmatic pressure and tension in the diaphragm. It was assumed that the muscle acts as a free membrane, attached at its edges to the inside of a vertical rib cage circular in cross section, that the attachments are inferior to the point at which the dome makes contract with the rib cage, and that the abdomen is filled with fluid with a hydrostatic gradient in pressure. The shape is different from a section of a sphere, with a radius of curvature substantially greater at the apex of the dome than at the sides. Observed shapes of human hemidiaphragm domes at functional residual capacity are not spherical but closely match the calculated shapes. Best-fitting shapes correspond to transdiaphragmatic pressures of about 3 cmH2O transdiaphragmatic pressure, suggesting that such a pressure and corresponding tension are present in the human diaphragm when it is at rest in an erect subject. In this model; as lung volume increases and the diaphragm shortens, its shape changes in such a way that the ratio between transdiaphragmatic pressure and tension in the diaphragm remains nearly constant, rather than increasing with volume. Such a model can explain the observation that the length-tension relationship of the muscle is much more important than curvature in determining the effectiveness of the diaphragm as a pressure generator.