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IV. IMPEDANCE ANALYSES ON PORE-SPANNING MEMBRANES

IV. IMPEDANCE ANALYSES ON PORE-SPANNING MEMBRANES

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276



E.K. Schmitt and C. Steinem



These data show that nano-BLMs are a powerful membrane

system that overcomes the disadvantage of poor long-term stability

of classical BLMs. However, classical BLMs have also been developed further in recent years in order to diminish their drawbacks such as long-term stability and applicability in chip based

assays. Glass supports with a single pore of 100-400 nm in diameter served as supports for BLMs, which are stable for up to two

weeks.30 In another approach, giant unilamellar vesicles are sucked

on a single hole by means of low pressure, which ruptures the vesicle and generates a bilayer within seconds.31 Nevertheless, these

systems still only provide a bilayer covering one single hole,

whereas nano-BLMs are composed of more than 109 individual

bilayers.

2.



Pore-Suspending Membranes on CPEO3



(i) Impedance Analysis of Pore-Suspending Membranes on

Porous Alumina with Fully Opened Pore Bottoms

Nano-BLMs proved to be a robust system for the investigation

of ion channels on a single channel level (see Section III). Due to

the method of preparation, nano-BLMs still contain some organic

solvent, which is reflected in the mentioned fluctuations in membrane resistance and the obtained lateral diffusion coefficients.28

Several membrane proteins lose activity in the presence of organic

solvents such as n-decane and hence bilayers prepared without addition of solvent are highly desirable. For BLMs this has been realized by the method of Montal and Mueller, who established solvent-free lipid bilayers by the membrane folding method.32

Already some years ago, we followed a strategy to form poresuspending bilayers starting from large unilamellar vesicles

(LUVs).22,33,34 With this method, it is not only possible to gain solvent-free pore-spanning membranes, but in addition it holds the

potential for establishing lipid bilayers with high protein density.

As a starting point, porous substrates were functionalized with a

thiol-component to chemically distinguish between the upper surface and the inner pore walls, which should prevent the fusion of

vesicles within the pores. Yet, these membranes proved to be rather leaky, as shown by EIS.34 To achieve highly insulating pore-



Ion Channels and Transporters in Pore-Suspending Membranes



277



suspending membranes, it turned out to be advantageous to functionalize the gold-covered porous substrate with cholesterylpolyethylenoxy thiol (CPEO3), a cholesterol derivative with a hydrophilic linker terminated with a thiol group, which renders the upper

surface hydrophobic.35 CPEO3 was already successfully used by

others to establish solid supported membranes on gold electrodes.36,37 To generate pore-suspending membranes, LUVs composed of 1,2-diphytanoyl-sn-glycero-3-phosphocholine (DPhPC)/

1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) (6:4) were

spread and fused on CPEO3-functionalized porous alumina, leading to a pore-suspending membrane, whose electrical characteristics could be monitored by EIS. The setup was a three-piece Teflon chamber with the porous substrate horizontally fixed between

the two upper parts (Fig. 1B). Sealing rings allow insulating the

substrate area from its environment. However, to prevent leak currents, a small amount of n-decane was applied in the sealing ring

region prior to the addition of liposomes. The organic solvent did

not alter the electrical properties of the sample. A characteristic

course of the absolute value of the impedance |Z|(f) after 30 hours

of incubation with LUVs is depicted in Fig. 4 A (open squares). To

extract the electrical parameters of the membrane system, again

the equivalent circuit depicted in Fig. 2 A (inset) was used.

Good accordance between model and experimental data is

found with a membrane capacitance of Cm = 4 nF and a membrane

resistance Rm = 82 Mȍ. Taking the porous area into account, the

absolute capacitance value translates into a specific capacitance of

0.4 μF cm-2. From independent experiments, a mean specific

membrane capacitance of (0.5 r 0.1) μF cm-2 (n = 5) was determined. This is in agreement with values found for solvent-free

BLMs, which are 0.5–1.0 μF cm-2.27 The membrane resistance Rm,

which varied between 106–108 ȍ, is still lower than those obtained

for nano-BLMs. However, it is already sufficiently high to monitor

channel activities in an integral manner,38 as will be shown in detail in Section IV.

Pore-spanning membranes feature a high degree of mechanical and long-term stability. The membrane resistance Rm was extracted by impedance data analysis and given as a function of time

(Fig. 4 B). Up to 50 hours after preparation, Rm remains almost

constant followed by a decrease, which is attributed to the rupture

of single pore-suspending membranes. It turned out that adding



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|Z| / W



E.K. Schmitt and C. Steinem



10



8



10



7



10



6



10



5



10



4



Rm / W



10



10



6



10



5



10



4



10



3



A



-3



10



-1



10



1



f / Hz



10



3



10



5



B



100



t/h



200



300



Figure 4. A) Absolute value of the impedance |Z|(f) of a

functionalized porous alumina substrate prior the addition of the vesicle suspension (Ŷ). (Ƒ) depicts the impedance data obtained 30 hours after vesicle addition. The

solid line is the result of a fitting routine using the equivalent circuit shown in Fig. 2 A (inset) with Cm = 4 nF and

Rm = 82 Mȍ. B) Change in membrane resistance Rm as a

function of time as a measure of long-term stability of a

pore-suspending bilayer preparation. After the poresuspending membrane had been established, impedance

spectra were taken every hour and the membrane resistance was extracted from the impedance data. Around

50 hours after vesicle addition, rupturing of the membranes becomes discernable as a decrease in membrane

resistance. Electrolyte: 0.1 M NaCl.35



Ion Channels and Transporters in Pore-Suspending Membranes



279



LUVs to established pore-spanning membranes, which are partially ruptured and thus leaky, refurbished the insulating properties.

We demonstrated that the absolute value of the impedance of porespanning lipid bilayers increased by one order of magnitude four

hours after LUVs were added.35

Interestingly, not all pore-spanning membrane preparations

resulted in an impedance spectrum as shown in Fig. 4 A. In many

cases, two dispersions were monitored that changed during the

vesicle incubation process, as observed in the impedance spectra

shown in Fig. 5 A.

To analyse these data, three degenerate networks are conceivable (Fig. 5 C). Two Ohmic resistors and capacitors, respectively,

account for the two observed dispersions in series to a resistor that

reflects the electrolyte resistance Rel. Data analysis based on the

three networks provided very similar values for each parameter

and, hence, they cannot be distinguished. Over the course of an

incubation period of 22 hours, as indicated by the arrow in Fig. 5

A, the two dispersions merge into one. We hypothesize that, within

the first stage of bilayer formation, the LUVs fuse only partially

(Fig. 5 B). This intermediate state of hemi-fused liposomes could

be modelled by two RC-elements in series to each other (Fig. 5 B),

characterising the electrical properties of the membrane interfaces.

(ii) Impedance Analysis of Pore-Suspending Membranes on

Porous Alumina with Partially Opened Pore Bottoms

Despite the promising electrical properties and long-term stability of these pore-spanning membranes, they suffered from very

long formation times of up to 24 hours. Especially when proteoliposomes are applied, a fast preparation is desired, as some proteins denature, thus losing their function within a few hours. We

assumed that the area where the sealing ring contacts the porous

substrate is crucial for current leakage. Thus, we altered the surface of the porous substrates with a total area of 0.314 cm2 in a

way that only a small fraction of the barrier oxide within the sealing ring area is fully removed (0.079 cm2), while the rest of the

pores remain sealed with alumina (Fig. 6).



280



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E.K. Schmitt and C. Steinem

10



6



10



5



10



4



A

t



f





-75

-50



t



-25

0

10



-1



10



0



10



1



10



2



10



3



10



4



10



5



10



6



f / Hz



B

Cm2



Rm2



hemifused

liposome

cis



Cm1



Rm1

Rel



trans



C



C2



C1



Rel



Rel

Rm1

Rm2



Cm2



Cm1 Rm1

Cm1



Rm2



Cm2



Figure 5. A) Absolute value of the impedance |Z|(f) and

phase angle I(f) of a pore-spanning membrane on CPEO3functionalized porous alumina in the presence of a vesicle

suspension composed of DPhPC/DOPC 6:4 (Ŷ) 4 hours,

(Ƒ) 9 hours, (Ɣ) 12 hours, (ż) 15 hours and (Ÿ) 22 hours

after the addition of LUVs. The arrow indicates the time

course of the experiment. Of the two discernable dispersions at the beginning, only one dispersion is found at the

end of the incubation period. Electrolyte: 0.1 M NaCl.35 B)

Scheme depicting the hypothesized intermediate state during pore-spanning membrane formation, which leads to

two dispersions in the impedance spectra together with an

equivalent circuit representing the two membranes (Rm1,

Cm1 and Rm2, Cm2) and the electrolyte resistance Rel. C) Alternative equivalent circuits to model the impedance data,

which feature two discernable dispersions with Rm1, Rm2,

Cm1 and Cm2 and the electrolyte resistance Rel.



Ion Channels and Transporters in Pore-Suspending Membranes



barrier oxide



B



A



281



A2



A1

1 μm



open pore bottoms



8



Rel



|Z| / W



10



C



7



10



Rox



6



Cox



10



5



10



4



10



-2



10



-1



10



0



10



1



10



2



3



10 10

f / Hz



4



10



5



10



6



10



Figure 6. A) Scanning electron microscopy image of the porous alumina substrate

after partial opening of the pores, and B) schematic drawing of the substrate. C)

Impedance spectra of a porous alumina layer (Ŷ) before and (Ƒ) after pore bottom

opening. The solid lines are the results of the fitting procedures. For (Ŷ), the

equivalent circuit shown in the inset was used with the following results: Rox = 0.3

Gȍ, Cox = 2.6 nF and Rel = 5400 ȍ. For (Ƒ), an equivalent circuit comprising the

electrolyte resistance Rel in series to a CPE-element, representing the non-ideal capacitive properties of the platinised platinum electrodes, was used with the following results: Rel = 4300 ȍ, A = 0.6 mF sĮ-1 and Į = 0.80. Inset: Equivalent circuit

composed of a parallel connection of a resistance Rox and a capacitance Cox representing the aluminium oxide in series to the electrolyte resistance Rel.38



As only the porous area fraction of the substrate (p = 33 ± 3

%) is considered electrically active,25 these areas translate into A1

= 0.0026 cm2 and A2 = 0.0078 cm2, respectively. However, alumina is not an ideal insulator, as shown by EIS. The mean specific

capacitive values Cox,sp of the remaining barrier oxide is (1.1 ± 0.3)

μF cm-2 (n = 16), the specific resistance Rox,sp varies from 104–107



282



E.K. Schmitt and C. Steinem



ȍ cm2. Hence, the electrical properties of the partially remaining

barrier oxide need to be considered in data analysis.

On these particular alumina substrates that were again functionalized with CPEO3, the fusion process of LUVs leading to insulating lipid bilayers was finished after 3 hours, which is significantly faster. Also the success rate of the preparation increased to

80 %. We suggest that the process is driven by the bilayer that is

formed on the solid part of the alumina substrate, which then acts

as a nucleation site for membrane formation in the adjacent region.

It was shown by others that the border of a lipid bilayer catalyzes

the growth of bilayers in adjacent regions when liposomes are

added.39,40

To analyse the impedance data, an equivalent circuit was developed that takes the two different areas (A1 and A2) of the porous

substrate into account (Fig. 7).

The barrier oxide layer is represented by a resistance Rox and a

capacitance Cox, on which a lipid bilayer characterized by a membrane resistance Rm,c and capacitance Cm,c is deposited. To get access to Rox and Cox, the electrical response of the substrate prior to

the selective removal of the barrier oxide layer was measured by

EIS for each individual substrate. To account for the electrical

properties of the lipid bilayer covering the open-pore array, a parallel RC-element with the membrane resistance Rm,o and capacitance Cm,o is added in series, whereas Rel represents the Ohmic behaviour of the electrolyte in the bulk and the open-pore array. This

equivalent circuit, however, contains too may parameters to be

able to fit all of them independently. Two approaches were followed to simplify the equivalent circuit and reduce the number of

parameters. For both, prior to the fitting routine, Rox and Cox were

individually determined and kept constant during the following

fitting routine. In approach (1), we assumed that the area related

values Rm,sp and Cm,sp obtained from lipid bilayers on gold electrodes are similar to those of membranes attached to the barrier

oxide. This approach implies that the barrier oxide is fully covered

by a lipid bilayer, whereas the coverage of the open pores is not

defined, thus the parameters Rm,o and Cm,o as well as Rel are free in

the fit routine. In approach (2), the specific membrane capacitance

and membrane resistance were assumed to be equal on the openpore array and on the barrier oxide. This was rationalized by the

electrical properties of CPEO3-DPhPC/DOPC bilayers on planar



Ion Channels and Transporters in Pore-Suspending Membranes



283



A

DPhPC/DOPC

CPEO3

gold

porous alumina



A2



A1



B

Rm,c



C



Rel



Rel

Cm,c

Rm,o



Rox



Cm,o Ra



CPE



Cox



A2



A1



Figure 7. A) Schematic drawing of the pore-suspending membrane on the porous

alumina substrate. B) Equivalent circuit representing the different elements of the

membrane system. Rox and Cox were independently determined by impedance analysis and kept constant during the fitting routine. C) Simplified equivalent circuit

according to the procedure described in the text.38



non-porous gold electrodes. Approach (2) results in Eqs. (1) and

(2):



Cm,o



Cm,c



A2



A1



Rm,o ˜ A2



Rm,c ˜ A1 ,



(1)



(2)



284



E.K. Schmitt and C. Steinem



which allow to replace Rm,o and Cm,o. Based on these considerations, the equivalent circuit shown in Fig. 7B contains only three

free parameters (Rel, Rm,c and Cm,c).

If active ion channels are incorporated in pore-suspending

membranes, solely the resistance of the bilayer covering the open

pores, Rm,o changes significantly. In this case, approach (2) is already too elaborate for data analysis and a more simple equivalent

circuit can be applied (approach 2’), which is depicted in Fig. 7 C.

Here, the resistance Ra represents the overall resistance at the limit

of low frequencies, which reads:



lim Z Re (Ȧ)

Ȧo0



Ra = Rm,o



Rox  Rm,c

Rm,o  Rox  Rm,c



lim Z Im (Ȧ)

Ȧo0



0



(3)



(4)



In the model shown in Fig. 7C, Ra is in parallel to a constant

phase element (CPE). The constant phase element was chosen instead of a capacitor to account for the non-ideal capacitive behaviour of the system. With the known parameter Rox, Rm,c and Rm,o

can be calculated from Eq. (3). In Fig. 8, the results of the two different approaches (2) and (2’) are compared.

The fitting results demonstrate that approach (2) (---) and (2’)

(—) reflect the course of the impedance data slightly better than

approach 1 (not shown). For approach (1), the parameter Rm,c is

three orders of magnitude larger than those determined by approach (2) and (2’), which is a result of the assumption of an ideal

membrane coverage on the solid area. However, this does not necessarily imply that approaches (2) and (2’) are more valid models

than (1). All of them are a compromise to minimize the number of

free parameters in data analysis. From four independent experiments we determined Cm,o,sp as 0.75-1.80 μF cm-2 and Rm,sp as

(2.3–6.9)·103 ȍ cm2. The differing area dependent values may reflect the error in the porous area, which was not individually determined for each substrate. Furthermore, hemifused vesicles could

still be present, although not resolved in impedance spectra as a

second dispersion. While for approach (2’) no information about



|Z| / W



Ion Channels and Transporters in Pore-Suspending Membranes



285



6



10



5



10



4



10



10



-1



10



0



10



1



10



2



10



3



10



4



10



5



10



6



f / Hz

Figure 8. Absolute value of the impedance |Z| of a pore-spanning bilayer from

LUVs (DPhPC/DOPC 6:4) on CPEO3-functionalized porous alumina with selectively opened pore-bottoms with Rox = 8.9 Mȍ und Cox = 6.7 nF, previously determined by EIS. The dashed line is the result of fitting the parameters of the

equivalent circuit shown in Fig. 7 B following approach (2): Rel = 2000 ȍ, Rm,o =

2.6 Mȍ, Cm,o = 1.9 nF, Rm,c = 0.89 Mȍ and Cm,c = 5.8 nF. The solid line is the

result of fitting the equivalent circuit shown in Fig. 7 C: Rel = 2000 ȍ, Ra = 2.3

Mȍ, Ca = 8.2 nF. Buffer: 10 mM TRIS, 100 mM TMA, pH 8.6.38



the capacitive properties of the membrane itself are obtained, the

overall resistance Ra and, after applying Eq. (3), Rm,c and Rm,o can

be accurately determined in a simple fit routine. This is a prerequisite for the analysis of impedance data obtained in the presence of

active ion channels, as further discussed in Section IV.

III. RECONSTITUTION OF PEPTIDES IN NANO-BLMS

As outlined in Section II, nano-BLMs are clearly advantageous

over classical BLMs, as they exhibit similar high membrane resistances, but are at the same time attached to a substrate, which

makes these membranes long-term and mechanically stable. In the

following paragraphs, several examples will be given to demon-



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E.K. Schmitt and C. Steinem



strate the applicability of nano-BLMs to monitor the activity of ion

channel peptides even down to the single channel level by voltage

clamp experiments.

1.



Peptidic Carriers and Ion Channels



To electrically monitor the activity of carriers and ion channel

forming peptides, the setup depicted in Fig. 1 A is routinely used.

For single channel recordings, two Ag/AgCl electrodes in the cis

and trans compartment were connected to an Axopatch 200B

patch clamp amplifier (Axon Instruments, Foster City, CA, USA)

in capacitive or resistive feedback configuration. The trans compartment was connected to ground and all potentials in the cis

compartment are given relative to ground. Data were collected

with a sampling rate of 10 kHz and filtered with a 4-pole low pass

Bessel filter with a cut-off frequency of 500 Hz-1 kHz.

(i) Reconstitution of the Ion Carrier Valinomycin

As a first example, the ion carrier valinomycin was investigated in nano-BLMs. Valinomycin is a cyclic depsipeptide from

Streptomyces fulvissimus consisting of three identical units. It mediates the transport of many alkali and alkaline earth cations in organic films or solvents of low polarity. It is highly selective for K+

and Rb+ over Li+, Na+, and alkaline earth cations by forming a

three-dimensional complex around the cation in order to increase

its solubility in nonpolar organic solvents or the interior of a biological membrane. In solid supported membranes, the transport

characteristics of valinomycin has been investigated in an integral

manner by means of impedance spectroscopy.41,42 However, the

ion transport is always hampered by the underlying capacitance of

the substrate. Impedance analysis of nano-BLMs doped with

valinomycin should, however, allow an immediate extraction of

the change in membrane resistance as a result of the valinomycin

transport activity. To reconstitute a nano-BLM system with

valinomycin, first a 1,2-diphythanoyl-sn-glycero-3-phosphocholine (DPhPC) nano-BLM on an octadecanethiol submonolayer

was prepared and then valinomycin dissolved in dimethylsulfoxide

was added in front of the membrane, which results in the spontaneous insertion of the depsipeptide. Impedance spectra were rec-



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