Nonlinear conductance, rectification and mechanosensitive channel formation of lipid membranes
NNonlinear conductance, rectification and mechanosensitive channelformation of lipid membranes
Karis A. Zecchi and Thomas Heimburg ∗ Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark
ABSTRACT
There is mounting evidence that lipid bilayers display conductive properties. However, when interpret-ing the electrical response of biological membranes to voltage changes, they are commonly considered as inert insulators.However, lipid bilayers under voltage-clamp conditions do not only display current traces with discrete conduction-steps in-distinguishable from those attributed to the presence of protein channels. In current-voltage (I-V) plots they may also displayoutward rectification, i.e., voltage-gating. Surprisingly, this has even been observed in chemically symmetric lipid bilay-ers. Here, we investigate this phenomenon using a theoretical framework that models the electrostrictive effect of voltageon lipid membranes in the presence of a spontaneous polarization, which can be recognized by a voltage offset in electricalmeasurements. It can arise from an asymmetry of the membrane, for example from a nonzero spontaneous curvature of themembrane. This curvature can be caused by voltage via the flexoelectric effect, or by hydrostatic pressure differences acrossthe membrane. Here, we describe I-V relations for lipid membranes formed at the tip of patch pipettes situated close to anaqueous surface. We measured at different depths relative to air/water surface, resulting in different pressure gradients acrossthe membrane. Both linear and nonlinear I-V profiles were observed. Nonlinear conduction consistently takes the form ofoutward rectified currents. We explain the conductance properties by two mechanisms: One leak current with constant con-ductance without pores, and a second process that is due to voltage-gated pore opening correlating with the appearance ofchannel-like conduction steps. In some instances, these nonlinear I-V relations display a voltage regime in which dI/dV isnegative. This has also been previously observed in the presence of sodium channels. Experiments at different depths revealchannel formation that depends on pressure gradients. Therefore, we find that the channels in the lipid membrane are bothvoltage-gated and mechanosensitive. We also report measurements on black lipid membranes that also display rectification.In contrast to the patch experiments they are always symmetric and do not display a voltage offset.
Keywords: permeability, ion channels, rectification, lipid membrane, flexoelectricity, thermodynamics, voltage-gating, mechanosensitivity ∗ corresponding author, [email protected]. The permeability of biological membranes is of immense bi-ological importance. The biological membrane separates in-side and outside of cells and has to be selectively permeableto ions and substrates in order to establish well defined chem-ical potential gradients of the components between inside andoutside of the cells. Since this is a formidable task, it is be-lieved that nature must control this by an appropriate “smart”mechanism, in particular by providing selective ion channelsand pumps to cell membranes (1). The picture is that of anintelligent pump station with many switches, in which theopening and closing of individual pipes is controlled by sub-strates or system parameters such as transmembrane voltage,mechanical membrane tension or temperature. Channels thatrespond to these variables are called voltage-gated channels,mechano-sensitive channels or heat- and cold receptors. Acomplete field has dedicated its research to the investigationof the molecular nature of the switches. Since there are manysubstrates and ions, the whole machinery of the biologicalmembrane is complex. In order to understand the working ofa membrane with such a complex composition of “intelligent”components, one imagines a network of sequential (mostlybinary) molecular interactions called pathways. This pictureis inherently non-thermodynamic. Instead of making use ofthermodynamic variables that act on a complete system withenergy, entropy and distributions of states, the channels andreceptors seemingly act as receptors to voltage and other in-tensive variables on the level of single molecules. This picturethat does not account for the thermodynamic nature of com-plex biological ensembles, which must undoubtably exist.It comes as a profound surprise that appearance of channel- like conduction events can also be seen in pure lipid mem-branes in the absence of any proteins and macromolecules,i.e. in the complete absence of any single molecule that couldact as a channel (e.g., (2–9)). These channel events are indis-tinguishable from those of proteins in so far as the current-traces alone do not provide any indication of whether theevents originate from proteins or pure lipid membranes. Theirsingle channel conductance, open-lifetime distributions andvoltage dependence are very similar to those reported for pro-teins (8). We have called the channels found in lipid mem-branes “lipid ion channels” (7) in order to stress these simi-larities. Lipid channels are thought being due to pores in thelipid membrane that open and close as a consequence of ther-modynamic fluctuations. Due to the fluctuation-dissipationtheorem, fluctuations become large close to melting transi-tions. Therefore, in this temperature regime lipid channelsand lipid membrane conductance are strongly temperaturesensitive (5, 10–12). The lipid membrane permeability isvoltage-gated and can display rectified behavior, i.e., the con-ductance can be largely different at positive and negative volt-age (8, 9, 13, 14), especially when measured on patch pipettes.Since pure lipid membranes do not contain single macro-molecules that could account for the formation of pores, thesecurrent fluctuations must be controlled by the thermodynam-ics of the membrane as a whole. This is striking because onecan define a self-consistent macroscopic thermodynamic the-ory that describes these channels (7) without any need formacromolecules.Such findings represents a serious problem for the inter-pretation of electrophysiological data. It is easy to demon-strate that quantized conduction events exist in lipid mem-branes in the absence of proteins. However, it is practically1 a r X i v : . [ phy s i c s . b i o - ph ] A ug mpossible to investigate channel proteins in the absence ofmembranes. A common approach in electrophysiology is toconsider the lipid membrane as an insulator with very high re-sistance and attribute all discrete opening- and closing eventsto channel proteins. This is obviously not permissible if themembrane itself can display channels with similar appear-ance. Many publications have shown that the lipid membraneis not generally an insulator (e.g.,(5, 10–12)). A completefield exists that describes the formation of nano pores in lipidmembranes by voltage pulses (electroporation), e.g. (15, 16).This has found clinical applications in drug-delivery and thetreatment of cancer (17, 18). Thus, the interpretation of cur-rent traces in electrophysiological experiments rests on as-sumptions that are provably not generally true.While the body of research on protein channels is huge,the permeability of pure membranes is still under-investigated.However, it seems unlikely that on one hand lipid pores rep-resent the sole possible permeation mechanism in syntheticmembranes but that on the other hand this mechanism is com-pletely absent in cell membranes. It is interesting to ask thequestion whether including the thermodynamics of lipid chan-nels into a picture for the biological membrane will help toelucidate the function of cell membranes. Most importantly,it is not known to which degree lipid pores and protein chan-nels may share a similar mechanism or may even be the same.In (9) we have proposed that proteins could act as catalysts forlipid pore formation, a view that is in line with the experimen-tal finding that truncated proteins that cannot span through themembrane nevertheless can induce pores in biomembranes(19).Besides the fact that lipid pores display a similar appear-ance as protein channels, it is not known how they actuallylook like. (20) have proposed that there exist hydrophobicand hydrophilic pores with openings on nanoscale, a viewthat is consistent with molecular dynamics simulations (16).In this paper we study I-V profiles of synthetic lipid mem-brane patches using patch-clamp recordings. We use the droplet-technique, in which the membrane is formed across a patchpipette that is in contact with the aqueous surface of a buffer(21, 22). In this setup, the depth of the pipette can be altered.This will influence the pressure gradients across the mem-brane. We study the depth dependence, analyze the theoryof the I-V profiles and combine it with theoretical consider-ation about the equilibration processes directly after a volt-age jump. We compared the patch experiments with blacklipid membrane (BLM) experiments which are performed onmuch larger membranes. Finally, we compare our findingswith potassium channels. sn -glycero-3-phosphocholine (DMPC), 1,2-dilauroyl- sn -glycero-3-phosphocholine (DLPC) and choles-terol were purchased from Avanti Polar Lipids (Alabaster/AL, US), stored in a freezer and used without further purifica-tion. Lipid patches consisted of DMPC:DLPC=10:1 (mol:mol)for the patch clamp experiments and of DMPC:DLPC:choles-terol = 77.3:7.7:15 (mol:mol:mol) for the black lipid mem- brane experiment. Each lipid was suspended separately inchloroform and then mixed to the desired ratio. The mixturewas then dried under vacuum. In the patch experiments, thedry lipids were resuspended in Hexane:Ethanol=4:1(mol:mol)to a final concentration of 2mM for the patch clamp experi-ment. The cholesterol mixture used in the BLM experimentswas dissolved in decane to a final concentration of 10mg/mL.In the patch clamp experiment, the electrolyte solutionused on both sides of the membrane consisted of 150 mMKCl, 150 mM NaCl and it was buffered with 50 mM TRISto a final pH of 7.6. All water used in the experiments waspurified with a Direct-Q Water Purification System (MerckMillipore, Germany) and had a resistivity larger than 18.1M Ω · cm. In the BLM experiments we used 150 mM KCl,150 mM NaCl, 2 mM HEPES and 1 mM EDTA (both fromSigma-Aldrich, Germany), pH was adjusted to 7.4Experiments were performed at a temperature at the upperend of the melting regime for all lipid mixtures used (see Fig.1).Figure 1: Calorimetric profiles of the two lipid mixtures used. Thevertical dashed line indicates the experimental temperature at whichI-V profiles and currents were measured.
Patch clamp experiments:
Glass micropipettes were pulledfrom borosilicate capillaries with a vertical PC-10 puller (Nar-ishe Group, Japan) following the two-steps procedure explai-ned in (23). They were then fire-polished using a NarishigeMF-900 Microforge, which created pipette openings on theorder of 10 μ m.Lipid membrane patches were reconstituted on the tip ofglass pipettes following the method introduced by (21) anddescribed in detail in (22, 23). According to the protocol adroplet of lipid solution is placed on the outer wall of a glassmicropipette filled with the electrolyte. The pipette standsvertically with its tip in contact with the liquid/air interface ofa buffered electrolyte filled glass beaker. As the lipid dropletflows down to the pipette tip, it gets sealed by a spontaneouslyformed lipid bilayer.Two Ag/AgCl electrodes were placed one inside the pipet-te and the other one in the bulk electrolyte, the latter acting asground electrode. They were both connected to a patch clampamplifier (Axopatch 200B, Molecular Devices, US) througha headstage to which the pipette was also secured. The am-plifier was run in whole cell mode, the signal was sampled2t a frequency of 10 kHz and filtered with a 2 kHz low passBessel filter. The headstage was allowed to move verticallywith the aid of a micromanipulator (Luigs & Neumann, Ger-many), with which the vertical position of the tip relative tothe electrolyte surface could be monitored.
Black lipid membrane experiments:
A DMPC:DLPC:cholesterol = 77.3:7.7:15 (mol:mol:mol) mixture was dissol-ved in decane to a final concentration of 10 mg/mL. Blacklipid membranes were formed on a circular aperture in a 25 μ m thick Teflon film. We used commercially available hori-zontal bilayer slides (Ionovation GmbH, Germany) made oftwo microchambers (filled with approx 150 μ l of the sameelectrolyte solution) separated by an horizontal Teflon film.The upper and lower chambers are connected only throughthe 120 μ m aperture in the film. Once a small droplet ( ≈ μ l) of lipid solution is placed in the upper chamber close to theaperture, a bilayer is formed automatically by a microfluidicperfusion system (Ionovation Explorer, Ionovation GmbH,Germany). The membrane formation was monitored with ca-pacitance measurements and was automatically repeated un-til the membrane capacitance was stable above a minimumthreshold value of 40 pF. The bilayer slide was placed onthe work stage of a in inverted microscope (IX70, Olympus,Japan) which allowed for optical monitoring of the bilayerformation. See (24) for more details. Differential scanning calorimetry:
Heat capacity pro-files were obtained using a VP scanning-calorimeter (Micro-Cal, Northampton, MA) at a scan rate of 5 ◦ /h. All experiments are representative and qualitatively repro-ducible. However, membranes break easily. In patch clampmeasurements, voltage-jumps were performed between 200mV and -200 mV in steps of 25 mV (Fig. 2). Each step lasts3.1 seconds for 17 different voltage-clamp traces needed forone I-V profile. Thus, each series lasts about 53 seconds.Only few membranes are stable long enough for a completeseries of voltage jumps that lead to a single I-V profiles. Evenless membranes allow for recording several I-V profiles tocheck for reproducibility and the variation of pipette depth.The typical interval between two I-V profiles recorded on thesame membrane is 1–5 minutes. The series of I-V profilesshown in Fig. 6 (top) contains 5 traces for one single depthof the pipette in the aqueous medium, which corresponds to10–25 minutes. Since we could measure on this membrane at3 different depths, the membrane was stable for a total of ∼
30 min - 1 hour. For this reason, all patch clamp data shown inthis paper originate from two different membrane patches thatwere sufficiently stable to not break during many I-V record-ings. We name them membrane 1 and membrane 2 through-out the text. However, we have many more experiments thatare consistent with our results, where the membranes did notlast long enough for an extended series of recordings.The voltage-jump protocol for the BLM measurementsshown in Fig. 10 was different. Here, we changed the voltagefrom +10 mV to -10 mV, then to 20 mV and -20 mV and soon (not shown). Figure 2:
Protocol of the voltage steps used in the I-V measurement.The lower bar indicates the duration of each part of the protocol.The arrow shows the direction of voltage steps, which ranged from mV to − mV in steps of − mV. After a voltage jump, all the current traces measured showedan initial transient decay of about 10 ms from a current peakat t = 50 ms (the time of the voltage step, see Fig.3) to theirsteady state value (the current value at t = 3 s). The transientpart of the current contains information about the chargingof the pipette (and electrodes), the charging of the membraneand any relaxation phenomena in the membrane which canlead to changes in resistance, capacitance and polarization.Figure 3: Initial phase of a voltage jump from 0 V to 0.175 V (left)and back (right) from the experiment shown in Fig. 4 B and D. Theprofiles are reasonably well fitted by a biexponential function withthe same two relaxation times for the jump in both directions. Thetwo exponential functions are shown in the inserts.
The relaxation processes are well described by a biexpo-nential function (Fig.3). We decided to not include the firstdata point in the fit. This corresponds to the first 100 μ s whichis the time resolution of our experiment.The current response of the membrane after a voltage jumpwas measured. As an example, we show two sets of record-ings in Fig.4 A, B. Possible voltage offsets were correctedby subtracting the mean value of the current at the holdingvoltage from the corresponding current trace during the stepprotocol.In order to obtain steady state currents for the I-V profiles,3igure 4: A-B:
Detail of the last . s of two representative current responses to the voltage pulses shown in Fig. 2 recorded from thesame membrane. The graph shows the response to only every other voltage step for clarity. Current traces were corrected for the initialoffset at zero voltage. Currents in A were measured with the tip of the pipette at the air/water interface. Traces in B were measured with thetip of the pipette mm below the water surface. C-D:
Current-voltage relationship for the traces in A-B, respectively. All points of all thecurrent traces between . s and s were plotted and fitted. The model used for the fit were a linear relation in panel C, and eq. 5 in panelD as outlined in the Theory Section. The fit gives a conductance of g L = 372 ± pS for the recording in A and C , and a voltage offset of V = 209 mV for the recording in B and D . Solid circles show the average values of the current. The measurements were performed at atemperature of T = 297 . K. we restricted ourselves to determine averages of the secondhalf of the current traces corresponding to the last 1.5 s aftereach voltage step (open circles in Fig.4 C, D). Both recordings in Fig.4 A and B were obtained from thesame membrane (membrane 1). Nevertheless, they show dis-tinct features that are representative of all the recordings madeon the two membranes used in the patch clamp measurementsdescribed in this work. These are outlined below.Fig.4 A shows the current response of the membrane whenthe tip of the pipette was at the air/water interface. The cur-rent traces are symmetric with respect to voltage and theirrelatively small value indicates a large membrane resistance.This can be quantified by inspection of the correspondentcurrent-voltage relationship (Fig.4 C). A linear fit to the datain Fig.4 C gives a value for the conductance of g L =(372 ± R =2.69G Ω . The conductance in this case is constant and independentof voltage.A different scenario is shown in the traces plotted in Fig.4B, measured for the same membrane at a different depth withrespect to the water surface (3mm). Here, the current re-sponse to positive and negative voltage-jumps is clearly dif-ferent, as confirmed by the asymmetric and nonlinear I-Vcurve in Fig.4 D. The membrane appears to be more conduc-tive at positive voltages, showing a fairly constant conduc-tance of about g = 1 . nS (or resistance of roughly R = 500 M Ω ), as obtained by a linear fit to the positive voltage range. Thus, it is almost five times larger than the linear I-V profileshown in Fig.4 C. The response to negative voltages, in con-trast, is slightly nonlinear and less pronounced, comparablein magnitude to the linear case.The data point at mV in Fig.4 D has not been includedin the fit. In our protocol this is the first datapoint. The corre-sponding current trace shows a transient behaviour and doesnot equilibrate fully in the 3 seconds of the test pulse. Thistransient behaviour of the current starting from a low con-ductance value and increasing without reaching a steady statewas not uncommon. It was only observed at positive highvoltages, and under few instances (in case of reversed volt-age protocol) at high negative voltages. In the absence of anysatisfactory explanation, in this work traces showing similarbehaviors were discarded from steady-state analysis. Further,we generally find that the first datapoint in each I-V profileis an outlier with respect to an otherwise systematic behavior.This might also be related to an equilibration of the mem-brane patch after the first voltage jump of a series.The two sets of recordings shown in Fig.4A and B havebeen performed at different depths of the pipette tip with re-spect to the bath surface. Different vertical positions of thepipette relative to the surface correspond to different valuesof hydrostatic pressure at the bath-facing leaflet of the mem-brane. Since the pressure at the inner leaflet is constant, thiscorresponds to different pressure gradients across the mem-brane. A pressure difference between the two leaflets can re-sult into a net curvature according to the Young-Laplace law.Curvature in a chemically symmetric membrane can breakthe otherwise symmetric charge and dipole distribution, and4herefore produce a voltage offset, as outlined in (13). The general tendency of a membrane to display a higher con-ductance at positive as compared to negative voltages is knownas outward rectification. In the case of biological membranes,it’s customary to ascribe electrical rectifications like the oneshown here to the voltage dependent behaviour of certain protein-channels spanning the membrane. However, outward recti-fied I-V curves like the one of Fig.4 D have already beenobserved earlier in protein-free membranes (8, 23). In thesepublications, the rectified behavior was explained on the ba-sis of a capacitor model like the one introduced below. Itrequires the formation of membrane pores and a spontaneouselectrical membrane polarization as caused from an asymme-try between the two monolayers of a bilayer (14). This could,for instance, originate from membrane curvature that changesthe relative lipid dipole density on the two monolayers of themembrane.We will describe the conductance of a membrane by usinga description from (13).We assume that the membrane contains pores with anopen probability that display a quadratic voltage dependence(8, 25). The free energy of an open pore is given by ∆ G = ∆ G + α (cid:2) ( V + V ) − V (cid:3) (1)Here, ∆ G is the free energy of a pore at a voltage of V =0 V, and α is a coefficient. ∆ G displays a minimum at V = − V , where V is the voltage offset that originates from apolarization of the membrane. Its origin will be discussed be-low. Defining an equilibrium constant K = exp( − ∆ G/kT ) between a closed and an open pore, we obtain for the prob-ability of finding an open or a closed pore, P open or P closed ,respectively: P open = K K and P closed = 11 + K (2)which sum up to one. If we assume that conduction oc-curs exclusively via open pores in the membranes, the overallcurrent through the membrane pores will be given by I p = g pore N P open V ≡ g p P open V , (3)where g pore is the conductance of a single open pore, N is the total number of pores, and g p = N g pore is the conduc-tance of N open pores.In the experimental section we find that there exist cur-rent traces that do not display any open pore events. Thisis mostly the case when the current-voltage relation is linear.It is therefore possible that there exists a voltage-independentleak current, I L , and voltage-dependent current through poresin a membrane, I p . If this were the case, the current-voltagerelation in eq. 3 would be given by I = I L + I p = ( g L + g p P open ) V (4)where g L is a constant leak-conductance of the membranein the absence of pores. This equation assumes identical ion concentrations on both sides of the membrane (Nernst poten-tial E is zero). If the ion concentrations were different fromzero, we would obtain I = ( g L + g p P open ) ( V − E ) (5)with E = ( RT /zF ) ln( c out /c in ) for an ion with charge z and the concentrations c out and c in outside and inside ofthe pipette, respectively. Since we use the same buffer in thepipette and in the external medium, the Nernst potential inour experiments is E = 0 V.Fig. 5 shows the non-linear rectified I-V profile from Fig.4 D and three attempts to describe it. We expect the I-V pro-file to pass through zero ( E = 0 ) because we have the sameion concentrations on both sides of the membrane. We cor-rected for slight deviations in the current at zero voltage. Forthe fit in Fig. 5 A we assumed that there is only one sin-gle permeation process by pores and no leak-conductance (ie, g L = 0 in eq. 5). The fit is reasonable but not perfect. Theinsert shows the calculated pore open-probability. It displaysa minimum at − mV corresponding to a spontaneous po-larization of the membrane that leads to a voltage offset of V = +162 mV. The minimum open-probability at this volt-age is about . which requires 27 % of all pores being open.However, we will see below that no open pores can be de-tected at this voltage. For this reason we decided that this isnot the most likely scenario. Fig. 5 C shows a free fit allow-ing for a variation of the leak conductance g L . The straightline in this panel corresponds to the leak currents I L = g L V .In this fit, the open probability of the pores reaches a mini-mum at -208 mV and the minimum open probability of poresis below 1 %. Since there is one more fit parameter, it is notsurprising that this describes the measured I-V profile better.However, what also speaks in favor of this description is thatone does not expect open pores at negative voltages. Onlyat positive voltages, the open probability of pores is signifi-cantly different from zero. The fit in Fig. 5 C is composedof a leak current I L and a pore current I p , which are indepen-dently shown in the figure.In our experiments we sometimes find linear I-V relationsand sometime outward rectified profiles. It is not exactly clearwhy both cases occur with the same experimental settings forthe same membrane. Interestingly, the linear I-V profile (Fig.4 C and Fig. 5 B) yields a quite similar conductance g L asleak current I L in Fig. 5 C. This supports our assumptionthat the conductance of the lipid membranes is a phenomenondescribed by two different processes: A voltage-independentleak conductance and a voltage-gated pore formation process.Therefore, we tentatively assumed that the two cases areonly distinguished by the presence or absence of prepores thatare ready to open but that the leak conductance of the mem-brane is identical in all experiments. Fig. 5 B shows a fitwhere the leak conductance g L was obtained from the linearI-V profile shown in Fig. 4 C. Its value was kept constant forfitting the rectified profile. We see that this describes the I-Vprofile quite well. In Fig. 3 one could see that the initial current during equili-bration displays more than one exponential component. Time-5igure 5:
Three different scenarios to fit the nonlinear current-voltage relations. A: conductions by pores only ( g L = 0 ). B: Conductionby voltage-dependent pores and a voltage-independent fixed leak current taken from the experiment in Fig. 4 C. C: Same as B but the leakcurrent was not fixed. The latter fit describes the data best. The inserts show the pore open probability for the three different scenarios.The minimum of P open represents the offset voltage − V . See text for details. dependent changes of the membrane current can have two ori-gins. The first is the charging of the membrane capacitor, ofpipette walls and electrodes. The charge on a capacitor isgiven by q = C m V + A · P , (6)where C m is the capacitance, A is the area of the capacitorand P is its spontaneous polarization (13), which is related tothe voltage offset V described above. The capacitive currentis therefore given by I c ( t ) = C m dVdt + V C m dt + ddt ( A · P ) (7)The first term on the right hand side is considered in elec-trophysiology, while the second and third term are neglected.Thus, in the textbooks it is assumed that the capacitance ofthe membrane and all membrane properties are constant af-ter a voltage jump. This assumption requires that the mem-brane structure is independent of voltage, which is practicallyimpossible for a soft molecular layer the will deform in thepresence of electrostatic forces. The time constant of charg-ing a constant capacitor in an electrolyte solution, τ , is typ-ically fast because it is dominated by the low resistance ofthe electrolytic medium. The second term in eq. 7 repre-sents the time-dependent change in capacitance caused by avoltage-induced structural change in the membrane, and thethird term is the related voltage-induced change in the spon-taneous polarization of the membrane, for instance caused bychanges in lipid head-group orientation or changes in curva-ture. Due to electrostriction, the capacitance of membranes isvoltage-dependent (13, 14, 26). The capacitance of a mem-brane is given by C m = ε εA/D where A is the membranearea and D is the membrane thickness. Electrostriction re-duces the membrane thickness and increases the membranearea. Both effects lead to an increase in capacitance, ∆ C m .This effect is most pronounced close to melting transitions inmembranes because here the membranes are softest. This isthe situation treated in this paper (see Fig. 1). In this paper we assume that the slow timescale of capacitance and polar-ization changes, τ m , results from the relaxation processes inmembranes, which are in the millisecond regime (27, 28).A further time-dependent change in the membrane cur-rent may originate from voltage-induced changes in the mem-brane conductance, ∆ g , due to changes in membrane struc-ture. It is known that membranes are more permeable intheir melting transitions (5, 10–12). Therefore, a voltage-induced change in membrane structure as caused by elec-trostriction will also change the conductance of the mem-brane. In the presence of a spontaneous voltage-offset (polar-ization) of the membrane, this effect will be different for pos-itive and negative voltages, i.e., it will be rectified. Since it isrelated to structural changes in the membrane, the time-scaleof its changes will also be dictated by the relaxation time-scale in the membrane, τ m , where we have assumed a single-exponential relaxation process (as described in (27, 28)).For the total membrane current we obtain for a jump fromvoltage V b before the jump to a voltage V a after the jump: I ( t ) = C m,b τ ∆ V e − tτ + (∆ C m V a + ∆( AP )) e − tτm τ m + (cid:16) g b + ∆ g (cid:16) − e − tτm (cid:17)(cid:17) V a = (8) = g a V a + C m,b τ ∆ V e − tτ + (cid:18) ∆ C m V a + ∆( AP ) τ m − ∆ gV a (cid:19) + e − tτm == g a V a + A e − tτ + A m e − tτm , where the term related to charging the capacitor is de-scribed by the timescale τ and the amplitude A . All termsrelated to changes in membrane structure change with thetime constant τ m and amplitude A m . C m,b , C m,a , g b and g a are the steady-state capacitance and conductance beforeand after the voltage jump, respectively. ∆ V = V a − V b , ∆ C m = C m,a − C m,b , ∆ g = g a − g b and ∆( AP ) = ( AP ) a - ( AP ) b are the differences of the respective functions in6teady state before and after the voltage change. We see thatthe steady-state current after a jump is given by I ( V a ) = g a V a . (9)The time-dependent current contributions are dominatedby two time-scales. One of them, τ , is related to charginga constant capacitor, while the second one, τ m , is slow anddominated by the relaxation process of conductance, capaci-tance and polarization of the membrane. In order to better understand the appearance of the nonlin-ear behaviour and the origin of the voltage offset, I-V mea-surements were performed on the same membrane at differ-ent positions of the tip in the water bath. This is an indirectattempt of controlling the hydrostatic pressure gradient acrossthe membrane, which increases linearly with the depth, h .With the aid of a micromanipulator, the tip of the pipettewas lowered from its initial position (close to the water sur-face) down to different depths inside the water bath. Fig. 6shows two series of I-V curves measured for the same mem-brane (membrane 1) at different positions, i.e., at 1 and 3 mmbelow the water surface, corresponding to a pressure differ-ence of about 98 and 294 Pa. The numbers close to each curveindicate the temporal order of the recording in each sequence.The time interval between subsequent recording was not fixedbut was never more than 5 minutes (with an average of 1minute and a half). Fits for the I-V profiles were generatedby using eq. 4 and the procedure used in Fig. 5C. The twocontributions to the conductance are displayed separately inthe small panels. No qualitative differences can be observedbetween the recordings at 1 and 3 mm. Both positions pro-duce consistently both linear and nonlinear responses, the lat-ter being always in the form of outward rectified I-V curves.Interestingly, during each voltage-jump sequence, one behav-ior was consistently maintained while in the next sequenceone can observe a different behavior. For instance, in Fig. 6top left, the first trace was outward rectified, the second waslinear, the 3rd and 4th trace were rectified and finally the 5thwas linear. The reason for this behavior is not clear. It seemsthat the linear contribution of the conductance is the same inboth, linear and rectified profiles - but that it is not alwayspossible to activate pores. The values of the voltage offsetas obtained from the fit vary slightly from one recording tothe other, but they are comparable between the two differentpositions. On average, it is 243 ( ±
34) mV at 1 mm depthand 221 ( ±
20) mV on average at a depth of 3 mm. The leakconductance g L and the pore conductance g p were larger atlarger depth of the patch pipette. For membrane 1, the con-ductance g L increased by 32% and the pore conductance g p by 37% when going from 1 to 3 mm depth.It is interesting to note that trace 1 in the top left panel ofFig. 6 displays a voltage regime around − mV, in whichthe dependence of the current on voltage, dI/dV , is negative.This is impossible without a voltage-dependent conductance.It can be explained if one considers that around -200 mV, allpores are closed while at -50 mV some pores are open. Forthis reason, one can find a larger negative current at -50 mVthan at -200 mV. Nonlinear I-V curves and outward rectification are not theonly properties of the lipid membranes studied here that re-sembled those of biological membranes. We also find thatseveral recordings of membranes showed current fluctuationsand quantized steps that are typical of ion channel activity.Fig.7 shows two current responses of membrane 2 to thesame voltage protocol as describe in section 2.3. The mem-brane had the same lipid composition as the one of Fig.4 -6. The two recordings shown here were obtained with themembrane at mm (left) and mm (right) below the watersurface.One can recognize that the I-V profiles in both cases arenon-linear. They display a larger conductance at positive volt-ages, which is more pronounced at the depth of 8 mm as com-pared to the 4 mm recording. Further, one recognizes discon-tinuous conduction steps in both experiments, which are alsomore pronounced at 8 mm depth. The fits to the I-V profileare performed as in Figs. 5 and 6.A continuous recording of this membrane at 4 mm depthand a fixed holding voltage allowed to observe consistentchannel-like activity for a longer period of time. Fig. 8 showsthe first s of the raw current trace. The trace shows clearquantized steps from a baseline at pA that was slightlydrifting to a set value of about pA. The step-size wasabout 13 pA, corresponding to a single lipid channel conduc-tance of about ∼ pS, very similar to the single channelconductance in the same experiment at 150 mV and 125 mV.Thus, the single channel conductance is probably indepen-dent of voltage, as already found in (8). The step size at 200mV for the 8 mm depth recording in Fig. 7 (right, top) yieldsa single channel conductance of about 137 pS, which is twiceas high as in the 4 mm recording in the left panels. The cur-rent traces in Fig. 7 indicate that at high positive voltage,pores can be open most of the time.The above recordings were observed when the pipette tipwas mm and mm below the water surface, so slightly lowerthan the recordings shown for membrane 1 in Fig.6.We observed channels at high positive voltages and at dif-ferent depths. In membrane 2 (Fig. 7 and Fig. 8), channelactivity seemed to increase with increasing depth of the tipin the water bath. At the same time, the voltage thresholdfor activity onset seemed to decrease with increasing depth/pressure. However, we have only three data points in thissense (i.e. three different depths). Note that the depths hereare larger than those for the previous membrane. Interest-ingly, also the first membrane showed current fluctuationswhen brought mm below the air-water interface. This isshown in Fig. 9. The current traces correspond to voltagesteps in the range − mV (we did not record traces fornegative voltage because at 0 V the membrane ruptured).The membrane in Fig.9 ruptured at mV. Indeed, mem-brane rupture at large depths was one of the main obstaclesto investigating this phenomenon further. In fact, membraneinstability seemed to increase with increasing depth.Summarizing, it seems that larger depth of the pipette en-hances channel activity, and they occur at lower voltage. Inthe previous section, we have also found large conductances g L and g p at larger depth. This suggests that the lipid mem-brane channels are mechanosensitive.7igure 6: I-V recordings of the same membrane as Fig.4 (membrane 1) at different depths below the air/water interface.
Top:
Tip mmbelow the surface. Bottom:
Tip mm below the surface. Both sets of recordings show two different electrical behaviors, with both linearand nonlinear I-V relationships. The curves were measured in sequence and are numbered in order of appearance. Only the average valuesof the current are displayed for clarity. The dotted lines are fit to all current data points. Current response of membrane 2 at mm ( Left ) and mm ( Right ) below the water surface. The current response to negativevoltages doesn’t show current fluctuations.
Left:
The membrane current at high positive voltages shows quantized steps to a lower currentvalue before jumping down to it and staying there for the lower voltages. The current response at mV shows a constant drift in thebaseline and is not shown here.
Right:
The current responses to , and mV have been shifted to the top panel for clarity as theyoverlap. The membrane shows current fluctuations for increasing voltages. They end up in well-defined quantized steps at high voltageswhen pores are open most of the time. Continuous current recording for the same membrane asFig. 7 (membrane 2) at a holding voltage of mV 4mm belowthe water surface ( T = 297 . K). The graph shows 5 consecutiveseconds of recording, starting from the top row. The time-intervalsare presented as a stack for clarity.
Figure 9:
Current response of the same membrane as Fig.5-6 (mem-brane 1) at a depth of 10 mm below the water surface. The mem-brane ruptured at mV. Hence only the positive range is shown. Left : Current traces at different voltages. The top trace is the re-sponse to the first jump of the protocol (from to mV), and ithas been plotted separately for clarity. At this voltage, the mem-brane shows a step-wise increase in conductance, from an initialvalue of about . nS to a final one of roughly . nS. In the bot-tom panel, the other traces are shown. Current fluctuations startto appear in the form of spikes already at mV, and increase innumber and duration at higher voltages. Right : Current-voltage re-lationship for the traces shown at the left. A linear fit gives a valueof the conductance of . nS. This is in line with the final value ofconductance for the trace at mV. Due to its transient behaviour,however, this trace has not been included in the fit. In a previous publication (24) we suggested that the offsetvoltage responsible for the asymmetry and the apparent out-ward rectification of the I-V profiles is caused by flexoelec-tricity. Bending of the membrane creates an electrical po-larization that is roughly proportional to the curvature (14,29, 30). The tip diameter of a patch pipette is small. Themaximum curvature possible is that of a half sphere witha radius that corresponds to the radius of the tip opening.For a pipette with 1 μ m diameter, the maximum curvatureis c = 1 / nm . However, if one uses black lipid mem-branes spanning a hole with a diameter of about 100 μ m, themaximum possible curvature is 100 times smaller (see (24)for details about this argument). If the voltage offset werein fact caused by flexoelectricity, the voltage offset wouldbe practically absent in black lipid membrane measurements.This means that patch pipettes allow for high curvature, whileblack lipid membranes rather imply membranes without orwith low curvature.Fig. 10 shows a black lipid membrane experiment madewith the Ionovation Explorer (see Material and Methods sec-tion). The aperture in this experiment had a diameter of about120 μ m. In the patch experiment it was 8 ∼ μ m, i.e., about 15times smaller. We used a membrane with 77.3 % DMPC, 7.7% DLPC and 15 % cholesterol and a temperature of 32 ◦ C atthe upper end of the melting transition of this membrane (Fig.1). Cholesterol is known for largely broadening the meltingtransitions of membranes, thus reducing domain formationand fluctuations. This renders membranes more stable. Thisis an important factor in black lipid membrane measurementsbecause of the notorious instability of the membranes closeto transitions.We found an I-V profiles that is completely symmetric,i.e., it does not display a significant voltage offset (the fityields ∼ -5 mV). We found a leak conductance of g L = 270 pS and a pore conductance of g p = 863 pS when fitting itwith eq. (4). The conductance steps at 100 mV correspond to78 pA, comparable to a single channel conductance of ∼ pS. This is similar to the single channel conductance of thetraces in Fig. 6 where we found ∼ pS. This indicates thatthe magnitude of the conductance steps does not depend onthe size of the membrane. Most interestingly though, the nearabsence of a voltage offset allows seeing that the rectificationpattern is also symmetric, and that channel activity appearsboth at positive and negative voltages in the nonlinear part ofthe I-V profile that we attribute to pore formation. This sup-ports our interpretation of having two conduction processespresent. In section 3.3.2 we described how after a voltage jump onefinds transient equilibration processes that consist of capaci-tive currents and time-dependent changes in conductance (Fig.3). We have argued that one expects (at least) two relaxationprocesses. One is related to charging the capacitor via theelectrolyte and a second one is coupled to changes in mem-brane structure with effects both on conductance and capaci-tance. In the present set of experiments, we performed volt-age jumps from zero to a fixed voltage, and back to zero. The10igure 10:
Recordings on a DMPC:DLPC:chol.= 77.3 : 7.7 : 15 BLM measured at 32.4 ◦ C. Left: Current traces. For better visibility,they are evenly spaced on the vertical axis. Note, the current traces in the linear regime of the I-V profile are not shown. Right: I-V-profile.The solid line is a fit of the I-V profile to eq. (5). The insert represents the pore open probability. Note that for the BLM, the I-V profile issymmetric and the channel activity occurs at both higher positive and higher negative voltages.
Figure 11:
Relaxation processes corresponding to the I-V profiles shown in Fig. 4C and D: A. Relaxation processes after a jump from 0volt to a fixed voltage for the rectified I-V profile shown in Fig. 4 D. The thin black lines represent the fits to a biexponential function. V. B. Relaxation processes after jump from a fixed voltage V to zero volts for the rectified I-V profile shown in Fig. 4 D. C. Bottom panel: The fitparameters of the relaxation processes corresponding to Fig. 4C. The top panel shows the corresponding I-V relation Both the amplitudesof the fast and the slow process, A and A m are linear as is the IV profile. D . Bottom panel: The fit parameters of the relaxation processescorresponding to Fig. 4D. Here, A m is linear in voltage and equal in magnitude in both experiments (blue lines). Amplitude A displaysa nonlinear voltage dependence for the rectified I-V profile (right). The solid lines at the bottom are the same in the panel C and D. In thepanel D they serve as a guide to the eye to demonstrate the nonlinearity of the voltage dependence for amplitude A . The current relaxationprofiles in panels A and B were not corrected for a slight current offset from zero. μ m) do not contribute much tothe observed currents.We describe the relaxation process by a bi-exponentialfunction (see Fig. 3 and Theory section): I ( t ) = g a V a + A e − tτ + A m e − tτm We fitted the relaxation profiles shown in Fig. 11 A and Bwith biexponential profiles. We found that one obtains goodfits of the relaxation profiles if the same relaxation times weretaken for a given membrane for all voltages jumps from zeroto a fixed voltage (Fig. 11 A, 0 → V) and back (Fig. 11 B,V → μ s (dominated by the digital filter time constant of theexperiment) and 1.74 ms for all profiles.What is fitted are theamplitudes A and A m of the two relaxation processes (Fig.11 C and D).We find that the bi-exponential relaxation profiles withfixed time constants describe the experimental data well. Theamplitude A m of the slow process displays a linear depen-dence on the voltage for both the linear and the rectified I-V-relation shown in the top panels of Fig. 11 C and D (bluesymbols). In contrast, the fast process with amplitude A (redsymbols) is similar to the voltage dependence of the IV rela-tion. It displays a linear behavior for the linear IV relationin Fig. 11 C, and a rectified behavior for the rectified I-Vrelation in Fig. 11 D. The analysis of the data in Fig. 7yields a similar result. Taking into account the similaritiesbetween the voltage-dependence of the fast process and thesteady state current, it seems plausible to assume that the fastrelaxation processes contains elements from the relaxation ofthe conductance after a voltage jump. Since we attributed thenon-linearity of the I-V profile to the opening of pores in theTheory section, we suggest that the fast process is related tothe timescale of pore opening. In this paper, we described the conductance of DMPC-DLPC=10:1 membranes subject to voltage jumps of different magni-tude and direction. The experiments had different aspects: 1.Studying I-V profiles at different depths of a patch pipette inthe aqueous buffer. 2. Studying discrete channel opening-and closing events. 3. Comparing BLMs with lipid patches4. Determination of the kinetics of membrane equilibrationafter a voltage jump.For each of the two membranes that were stable enoughfor an extended experimental sequence in the patch clamp ex-periments that we describe here, we found two quantitatively different current-voltage profiles. We either found linear I-Vrelationships or outward rectified I-V profiles, even under thesame conditions and for the same membrane. We could welldescribe these profiles with a model that allows for two elec-trical conduction processes: A voltage-independent leakageand a voltage-dependent pore-formation (i.e., the occurrenceof lipid ion channels). This is consistent with our observationthat membrane channels are usually found in the rectified pro-files at positive voltages. The asymmetry of the rectified I-Vprofile is a consequence of an offset potential V , i.e., a polar-ization of the membrane. The leakage-current of the rectifiedprofiles was within error identical to that of the linear I-V pro-files found for the same membrane in the absence of pores.One therefore has to conclude that the pore-formation some-times lacks the nucleation sites for pore formation (some-times called a pre-pore in the literature (16)). Sometimespores are present and sometimes they aren’t. Details of thissomewhat stochastic process remain to be explored. In con-trast, the leak current is always present. In our theory, weassumed that the voltage-dependence of the free energy ofthe pores is quadratic in voltage, which has been proposedearlier (8, 13, 25). In (25) it was also proposed that voltagemay stabilize the formation of pores with a given radius, i.e.,pores of fixed conductance, which we have also found here.Interestingly, the I-V relations of the BLM measurement wasnonlinear but symmetric, in agreement with previous findings(31).In the past, we have attributed an offset potential of themembrane to a spontaneous polarization of the membrane.Since our lipids are uncharged, the polarization may arisefrom membrane curvature due to an effect called flexoelec-tricity (13, 32). It arises from the asymmetric distribution oflipid dipoles in curved membranes. It may also arise fromthe asymmetric attachment of membranes to the glass pipetteor from a lipid asymmetry (not likely in the present experi-ments). The offset potential V results in the rectified profiles.The voltage dependence of the pore open probability is alsorelative to the voltage V .We have changed the depth of the pipettes in the aque-ous medium. This changes the pressure difference and mightpotentially lead to a change in the offset potential. For mem-brane 1 we found 243 ( ±
34) mV on average in 1 mm depth,while we found 221 ( ±
20) mV on average at a depth of3 mm. The difference of these two values of V is smallerthan the standard deviation. Similarly, for membrane 2 wefound V = 221 mV at 4 mm depth and V = 193 mV at 8mm depth. Thus, while it might be that the offset potential issmaller at larger depth, the error margin does not allow us tomake a trustworthy statement about its depth dependence. Itseems that the origin of membrane polarization is not primar-ily the pressure difference across the membrane. However,it was generally true that the leak conductance g L and thepore conductance g p were larger at larger depth of the patchpipette. For membrane 1, the conductance g L increased by32% and the pore conductance g p by 37%. For membrane 2, g L change by 43% upon going from 4mm to 8mm depth, and g p changed by 86%, respectively.Interestingly, one does not find a measurable offset poten-tial in black lipid membranes (Fig. ?? ). We attribute that tothe fact that the maximum possible curvature for a membrane12cross an aperture of 120 μ m in our BLMs is much smallerthat that of a lipid patch spanning a tip aperture of about 8 μ m.We reported that the rectified I-V relations are often ac-companied by the voltage-gated opening of single lipid ionchannels (see also (8, 9, 23)). This is surprising because it isusually believed that voltage-gated conduction-events are anexclusive feature of protein channels. In our experiments, theminimum pore open probability is found for V − V = 0 , i.e.,at a voltage around -200 mV. One expects opening of poresbelow about -400 mV (outside of our experimental range) andabove about 0 V. This has in fact been observed in Fig. 7. Inthe BLM measurements that do not display a voltage offset,the formation of channel events displays symmetric voltage-dependence, i.e., it occurs at both higher positive and negativevoltages. In patch experiments, we found a single channelconductance at 8 mm depth that was 2.0 times larger than thesingle channel conductance at 4 mm depth ( γ =
137 pS ver-sus γ =
68 pS, respectively). In the BLM experiment, thesingle channel conductance was γ =
78 pS.In the previous section, we outlined that the conductance g p of the I-V profile associated with open pores was about2 times larger at 8 mm depth than at 4 mm depth. Thesenumbers are well in agreement with the difference in sin-gle channel conductance. This indicates that interpreting aconduction process related to pore-formation is reasonable.The second conduction process that we called a leak-currentis voltage-independent and does not display discrete channelevents. Larger depth of the pipette enhances channel activity,and they occur at lower voltage. This suggests that the lipidmembrane channels are mechanosensitive.The conductance of the lipid pores is of a magnitude typ-ical for single channel proteins. (33) reported single potas-sium channel conductances of γ =
10, 20 and 40 pS in thesquid axon. (34) found that the so-called SLO-potassiumchannel family may have larger conductances, e.g. γ = γ = γ = γ = μ s (dominated by thelow pass-filter time constant of the experiment) and a slowtimescale of about 2 ms. The amplitude of the slow processwas linear with the magnitude of the voltage jump and didnot depend on whether the I-V profile was rectified or lin-ear. In contrast, the amplitude of the fast process reflectedthe voltage-dependence of the steady-state conductance of the membrane after the voltage jump. We conclude that there ex-ists a fast process altering the conductance by changing themembrane state. This could be reflected in a timescale ofchannel opening or of the overall membrane area. Usuallyone would assume that the membrane-related process is theslow process, which is opposite to the experimental evidenceshowing that the fast process reflects that rectification. Thereasons for this remain to be explained. It is further not clearwhy the I-V profiles are sometimes rectified and sometimesnot. Comparison of membrane conductance with the potas-sium channel of Hodgkin and Huxley
We have found that many of the I-V curves are recti-fied, which we we explained by the voltage-gated opening ofpores. These pores can be recognized in many of the currenttraces. Our analysis allows for a determination of the prob-ability of pore opening. We found that close to the offset-voltage V , the pores are mostly closed, while the open prob-ability increase as a function of ( V + 2 V V ) .Rectified behavior has usually been attributed to voltage-gated protein ion channels. These channels were originallyintroduced by Hodgkin and Huxley in order to explain theproperties of the nervous impulse in squid axons (36). In theirmodel they introduced two channels (or more accurately: twogating mechanisms) for the conduction of sodium and potas-sium. The conductances of the the potassium channel, g K ,and of the sodium channels, g Na were described by g K = g K, · n ( V, t ) g Na = g Na, · m ( V, t ) · h ( V, t ) (10)where n ( V, t ) , m ( V, t ) and h ( V, t ) are voltage and time-dependent functions describing single-exponential kinetics ofgate-opening in the channels. The potassium channel is de-scribed by 4 independent and identical gates. After a voltagejump from V to V , the conductance of the potassium channelis described by n ( V, t ) = n ∞ ( V ) − ( n ∞ ( V ) − n ∞ ( V )) · exp (cid:18) − tτ n ( V ) (cid:19) (11)where the relaxation time τ n ( V ) and the steady state val-ues of n , n ∞ ( V ) and n ∞ ( V ) are given by n ∞ ( V ) = α n ( V ) α n ( V ) + β n ( V ) and τ n ( V ) = 1 α n ( V ) + β n ( V ) (12)with α n ( V ) = 10 · ( V + 0 . − exp (cid:0) − V +0 . . (cid:1) ; β n ( V ) = 125 · exp (cid:18) − V + 0 . . (cid:19) V is given in units of [V]. The functions α n ( V ) and β n ( V ) were not derived from first principles butrather parametrized from experimental voltage-clamp data (37,38). The steady state open probability of the potassium chan-nel is then given by P open,K ( V ) = n ∞ ( V ) (13)This function is shown in Fig. 12 (solid black line). It isinteresting to compare it to the open probability of the purelipid membranes of the experiments described above (bluetraces).Figure 12: Comparison of the open probability of the K + -channelof (36) (fat line), the KvAP channel reconstituted into a POPE/POPC=3:1 membrane (39), and selected open probabilities fromFig. 6 and 7 in the voltage regime of physiological relevance. We took the calculated open probabilities of 5 selectedtraces from Figs. 6 and 7 and plotted them in comparisonto the steady state open probability of the K + -channel de-termined by Hodgkin and Huxley. While the curves are notidentical, they are in fact quite similar. Fig. 7er shows that theopen probability in fact goes along with the opening of pores.For comparison, we also added the normalized conductanceof the voltage-gated KvAP channel (red symbols, (39, 40))that displays a voltage-dependent conductance that is verysimilar to the HH-potassium channel and the lipid channelsfrom this publication. This demonstrates that many proper-ties of the potassium channel can be described be the recti-fied properties of the lipid membrane in the absence of anymacromolecules. The similarity of lipid membrane behaviorwith that of potassium channels has in fact been noticed be-fore (8, 9).Interestingly, (41) showed that the both mean conduc-tance and open channel life-times of the KcsA potassium chan-nels reconstituted into a synthetic lipid membrane are propor- Note that in (36) the voltage was defined relative to the resting potential. tional to the heat capacity of the lipid membrane. This behav-ior would be a logical consequence of membrane fluctuationsif the membrane conductance originated from the lipid mem-brane alone. Since the conductance of the membrane was stillproportional to the concentration of K-channels in the mem-brane, we have proposed in the past that the conductance inthe membrane originates from membrane pores that are cat-alyzed by the channel protein (9).
We describe the voltage-gated opening of channels in purelipid membrane. When the I-V profiles are outward rectified,in most cases one finds single channel events at high volt-age. When I-V profiles are linear, one does not see singlechannels. I-V profiles in BLMs are symmetric and show lipidchannels at higher voltage. We concluded that there are twoconduction processes: One leak current not related to mem-brane channels and with a conductance that is independent ofvoltage, and single channel events that are voltage-gated. Wereported evidence for that channel-opening is mechanosensi-tive. The properties of the membrane channels resemble thoseof potassium channels.
References
1. Hille B.
Ionic channels of excitable membranes (Cambridge:Cambridge University Press) (1992).2. Antonov VF, Petrov VV, Molnar AA, Predvoditelev DA, IvanovAS. The appearance of single-ion channels in unmodified lipidbilayer membranes at the phase transition temperature.
Nature (1980) 585–586.3. Kaufmann K, Silman I. The induction by protons of ion chan-nels through lipid bilayer membranes.
Biophys. Chem. (1983) 89–99.4. Antonov VF, Anosov AA, Norik VP, Smirnova EY. Soft per-foration of planar bilayer lipid membranes of dipalmitoylphos-phatidylcholine at the temperature of the phase transition fromthe liquid crystalline to gel state. Eur. Biophys. J. (2005)155–162.5. Blicher A, Wodzinska K, Fidorra M, Winterhalter M, HeimburgT. The temperature dependence of lipid membrane permeabil-ity, its quantized nature, and the influence of anesthetics. Bio-phys. J. (2009) 4581–4591.6. Wunderlich B, Leirer C, Idzko A, Keyser UF, Myles V, Heim-burg T, et al. Phase state dependent current fluctuations in purelipid membranes. Biophys. J. (2009) 4592–4597.7. Heimburg T. Lipid ion channels. Biophys. Chem. (2010)2–22.8. Blicher A, Heimburg T. Voltage-gated lipid ion channels.
PloSONE (2013) e65707.9. Mosgaard LD, Heimburg T. Lipid ion channels and the role ofproteins. Acc. Chem. Res. (2013) 2966–2976.
0. Papahadjopoulos D, Jacobson K, Nir S, Isac T. Phase transitionsin phospholipid vesicles. fluorescence polarization and perme-ability measurements concerning the effect of temperature andcholesterol.
Biochim. Biophys. Acta (1973) 330–340.11. Nagle JF, Scott HL. Lateral compressibility of lipid mono- andbilayers. Theory of membrane permeability.
Biochim. Biophys.Acta (1978) 236–243.12. Sabra MC, Jørgensen K, Mouritsen OG. Lindane suppressesthe lipid-bilayer permeability in the main transition region.
Biochim. Biophys. Acta (1996) 85–92.13. Mosgaard LD, Zecchi KA, Heimburg T. Mechano-capacitiveproperties of polarized membranes.
Soft Matter (2015)7899–7910.14. Mosgaard LD, Zecchi KA, Heimburg T, Budvytyte R. Theeffect of the nonlinearity of the response of lipid membranesto voltage perturbations on the interpretation of their electricalproperties. a new theoretical description. Membranes (2015)495–512.15. Neumann E, Kakorin S, Tænsing K. Fundamentals of electro-porative delivery of drugs and genes. Bioelectrochem. Bioenerg. (1999) 3–16.16. B¨ockmann R, de Groot R, Kakorin S, Neumann E, Grubm¨ullerH. Kinetics, statistics, and energetics of lipid membrane electro-poration studied by molecular dynamics simulations. Biophys.J. (2008) 1837–1850.17. Gehl J. Electroporation: theory and methods, perspectives fordrug delivery, gene therapy and research. Acta Physiol. Scand. (2003) 437–447.18. Højholt KL, Muˇzi´c T, Jensen SD, Bilgin M, Nylandsted J, He-imburg T, et al. Calcium electroporation and electrochemother-apy for cancer treatment: Importance of cell membrane compo-sition investigated by lipidomics, calorimetry and in vitro effi-cacy.
Sci. Rep. (2019) 4758.19. Stoddart D, Ayub M, Hoefler L, Raychaudhuri P, Klingelhoe-fer JW, Maglia G, et al. Functional truncated membrane pores. Proc. Natl. Acad. Sci. USA (2014) 2425–2430.20. Glaser RW, Leikin SL, Chernomordik LV, Pastushenko VF,Sokirko AI. Reversible breakdown of lipid bilayers: Forma-tion and evolution of pores.
Biochim. Biophys. Acta (1988)275–287.21. Hanke W, Methfessel C, Wilmsen U, Boheim G. Ion chan-nel reconstruction into lipid bilayer membranes on glass patchpipettes.
Bioelectrochem. Bioenerg. (1984) 329–339.22. Gutsmann T, Heimburg T, Keyser U, Mahendran KR, Winter-halter M. Protein reconstitution into freestanding planar lipidmembranes for electrophysiological characterization. NatureProtocols (2015) 188–198.23. Laub KR, Witschas K, Blicher A, Madsen SB, L¨uckhoff A,Heimburg T. Comparing ion conductance recordings of syn-thetic lipid bilayers with cell membranes containing trp chan-nels. Biochim. Biophys. Acta (2012) 1–12.24. Zecchi KA, Mosgaard LD, Heimburg T. Mechano-capacitiveproperties of polarized membranes and the application to con-ductance measurements of lipid membrane patches.
J. Phys.:Conf. Ser. (2017) 012001. 25. Winterhalter M, Helfrich W. Effect of voltage on pores in mem-branes.
Phys. Rev. A (1987) 5874–5876.26. Heimburg T. The capacitance and electromechanical couplingof lipid membranes close to transitions. the effect of elec-trostriction. Biophys. J. (2012) 918–929.27. Grabitz P, Ivanova VP, Heimburg T. Relaxation kinetics of lipidmembranes and its relation to the heat capacity.
Biophys. J. (2002) 299–309.28. Seeger HM, Gudmundsson ML, Heimburg T. How anesthet-ics, neurotransmitters, and antibiotics influence the relaxationprocesses in lipid membranes. J. Phys. Chem. B (2007)13858–13866.29. Petrov AG. Flexoelectricity of model and living membranes.
Biochim. Biophys. Acta (2001) 1–25.30. Petrov AG, Sachs F. Flexoelectricity and elasticity of asymmet-ric biomembranes.
Phys. Rev. E (2002) 021905–1–021905–5.31. Wodzinska K, Blicher A, Heimburg T. The thermodynamicsof lipid ion channel formation in the absence and presence ofanesthetics. blm experiments and simulations. Soft Matter (2009) 3319–3330.32. Petrov AG. Electricity and mechanics of biomembrane sys-tems: flexoelectricity in living membranes. Anal. Chim. Acta (2006) 70–83.33. Llano I, Webb CK, Bezanilla F. Potassium conductance of thesquid giant axon. single-channel studies.
J. Gen. Physiol. (1988) 179–196.34. Salkoff L, Butler A, Ferreira G, Santi C, Wei A. High-conductance potassium channels of the slo family. Nat. Rev.Neurosci. (2006) 921–931.35. Sakmann B, Trube G. Conductance properties of single in-wardly rectifying potassium channels in ventricular cells fromguineapig heart. J. Physiol. London (1984) 641–657.36. Hodgkin AL, Huxley AF. A quantitative description of mem-brane current and its application to conduction and excitation innerve.
J. Physiol. London (1952) 500–544.37. Hodgkin AL, Huxley AF, Katz B. Measurement of current-voltage relations in the membrane of the giant axon of loligo.
J.Physiol. London (1952) 424–448.38. Hodgkin AL, Huxley AF. Currents carried by sodium and potas-sium ions through the membrane of the giant axon of loligo.
J.Physiol. London (1952) 449–472.39. Schmidt D, Jiang QX, MacKinnon R. Phospholipids and theorigin of cationic gating charges in voltage sensors.
Nature (2006) 775–779.40. Lee SY, Lee A, Chen J, MacKinnon R. Structure of the KvAPvoltage-dependent K + channel and its dependence on the lipidmembrane. Proc. Natl. Acad. Sci. USA (2005) 15441–15446.41. Seeger HM, Aldrovandi L, Alessandrini A, P Facci P. Changesin single K + channel behavior induced by a lipid phase transi-tion. Biophys. J. (2010) 3675–3683.(2010) 3675–3683.