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Influence of Polylysine on the Rupture of Negatively Charged Membranes Anke Diederich,* Gu¨nther Ba¨hr, and Mathias Winterhalter Department of Biophysical Chemistry, Biozentrum of the University of Basel, Klingelbergstrasse 70, CH-4056 Basel, Switzerland Received March 5, 1998. In Final Form: May 13, 1998 We investigate the stability and rupture kinetics of planar lipid membranes covered with electrostatically adsorbed polyelectrolytes. After black lipid membranes were formed from negatively charged lipids, polylysines (PLs) of different molecular weights (MW) were added on one or on both sides of the membrane. The adsorption of PL was detected by recording changes of the transmembrane voltage. Rupture was induced by applying short voltage pulses across the membrane. The voltage causing breakdown of the membrane gives information on its mechanical stability. Adsorption of PL on one side of the membrane leads to an asymmetric transmembrane potential, which adds to the externally applied voltage. High MW PL decreases the critical breakdown voltage of the membrane significantly but also increases the delay time between the voltage pulse and pore formation. It is further shown that PL alters the time course of pore widening in a molecular weight-dependent manner. Low MW PL-decorated membranes and undecorated membranes show a fast rupture determined by inertia. In contrast, adsorption of high MW PLs causes a dramatic decrease of the rupture velocity. In this case, the rupture velocity is determined by viscosity. An analysis of the rupture kinetics allows an estimate of the 2D viscosity.
Introduction The electrostatic interaction of polylysine (PL) with negatively charged membranes has been used in many studies as a model for the interaction of peripheral proteins with biological membranes. The polypeptide was shown to influence the structure of the membranes strongly. For example, it induces phase separation in mixed dipalmitoyl phosphatidic acid/dipalmitoyl lecithin bilayers1 or causes phase transitions in anionic lipid membranes.2,3 Short PL (MW ) 4000) was found to lower the gel-to-fluid phase transition temperature in dipalmitoylphosphatidylglycerol membranes, whereas long PL (MW ) 150 000) raised the phase transition temperature. Long PL also triggers fusion of negatively charged vesicles. An important biotechnological application of high MW PL is found in in vitro gene delivery experiments. In these experiments, rather large and positively charged cationic lipid DNA complexes are translocated into the cytoplasm.4,5 The in vitro transfection of these complexes probably occurs via endocytosis.6 Recently it was shown that high MW polymers such as PL can enhance the transfection efficiency of several types of cationic lipidDNA complexes up to 30-fold.7 The polycations probably reduce the complex size8 and protect the DNA from damage during endocytosis.9 It was shown that a 3-6-fold excess of cationic over anionic charges is necessary for efficient (1) Galla, H. J.; Sackmann, E. Biochim. Biophys. Acta 1975, 401, 509. (2) De Kruijff, B.; Rietveld, A. B.; Telders, N.; Vaandrager, A. Biochim. Biophys. Acta 1985, 820, 295. (3) Carrier, D.; Pezolet, M. Biochemistry 1986, 25, 4167. (4) Felgner, P. L.; Gadek, T. R.; Holm, M.; Roman, R.; Chan, H. W.; Wenz, M.; Northrop, J. P.; Ringold, G. M.; Danielsen, M. Proc. Natl. Acad. Sci. U.S.A. 1987, 84, 7413. (5) Gao, X.; Huang, L. Biochem. Biophys. Res. Commun. 1991, 179, 280. (6) Friend, D. S.; Papahadjopoulos, D.; Debs, R. J. Biochim. Biophys. Acta 1996, 1278, 41. (7) Gao, X.; Huang, L. Biochemistry 1996, 35, 1027. (8) Gershon, H.; Ghirlando, R.; Guttman, S. B.; Minsky, A. Biochemistry 1993, 32, 7143. (9) Abdallah, B.; Sachs, L.; Demeneix, B. A. Biol. Cell 1995, 85,1.
transfection in cell cultures. However, the question remains whether the excess PL in the complexes acts only to attach the lipid DNA complexes to negatively charged cell surfaces. Most likely, PL also induces changes in the mechanical properties of the cell membrane. Because the function of PL in transfection of a natural cell is exceedingly complex, a molecular understanding of the function of the polycation in the transfection process is still poor. We reduce the number of parameters and investigate a model membrane system consisting of a negatively charged black lipid membrane (BLM) and a PL-containing aqueous phase. This allows us to quantify the mechanical stability and rupture kinetics of the surface-decorated membrane under well-defined conditions. We use an adapted electroporation technique in combination with the inner field compensation (IFC) technique.10,11 The latter method is sensitive to changes in the boundary potential (sum of surface potential and dipole potential of BLM)10 and is, therefore, an ideal tool to sense binding of polyelectrolytes. First, we detect the adsorption of the polyelectrolyte by recording changes in the boundary potential. The mechanical stability and rupture kinetics of the surface-decorated membranes are then determined by inducing irreversible breakdown of the membrane.12,13 This is accomplished by applying short voltage pulses. Measurement of the rapid voltage decay during rupture yields information on the kinetics of the rupture process. Earlier measurements on the rupture kinetics were performed on macroscopically large soap films. The kinetics was recorded with a high-speed camera. A linear increase of the defect in time was reported.14-16 More (10) Winterhalter, M. In Nonmedical Application of Liposomes; Lasic. D. D., Barenholz, Y., Eds.; CRC Press: Boca Raton, 1996; p 285. (11) Sokolov, V. S.; Kuz’min, V. G. Biofizika 1980, 25, 170. (12) Wilhelm, C.; Winterhalter, M.; Zimmermann, U.; Benz, R. Biophys. J. 1993, 64, 121. (13) Lindemann, M.; Steinmetz, M.; Winterhalter, M. Prog. Colloid Polym. Sci. 1997, 105, 209. (14) Evers, L. J.; Shulepov, S. Y.; Frens, G. Faraday Discuss. 1996, 104, 335.
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recently, a linear increase was also observed for silicone oil films covering a wafer.17 Conductance measurements on BLMs indicated again a linear increase of the defect size in time.12,13 In contrast, thin films made of highly viscous polymers show an exponential increase as predicted by theoretical considerations.12,18 Previously, it was shown that the pore widening velocities of BLMs are reduced by covalently bound poly(ethylene glycol) and polymerized surface attached actin.10,13 Actin, for example, led to an exponential increase of the pore radius with time. In this case, a measurement of the rupture velocity allowed determination of the 2D viscosity of the surface-decorated membrane.13 To our knowledge, this was the first time that the 2D viscosity of an isolated polymer-decorated membrane located in an aqueous phase of high ionic strength was determined. Another important parameter measured in our experiments is the voltage leading to rupture of the film. This so-called breakdown voltage was widely investigated using planar lipid membranes24,25 and showed a qualitative agreement with measurements on the mechanical stability of bilayer vesicles.26 Micromanipulation on giant liposomes in an externally applied electric field showed the equivalent action of a mechanical tension and the electrically induced tension.27 However, these measurements require the formation of giant liposomes, which is, in many cases, difficult or even impossible. In contrast, BLMs can be made under a wide range of experimental conditions. In this work, we study the influence of the degree of polymerization (DP) of the polyelectrolyte and the influence of bulk ion concentration on the rupture behavior of negatively charged BLMs. Materials and Methods Diphytanoylphosphatidylserine (DPhPS) was obtained from Avanti Polar Lipids (Alabaster, AL) with a purity >99%. Pentalysine and all poly-(L-lysines) hydrobromide (PL) with DPs of 38, 251, and 2007 were purchased from Sigma (St. Louis, MO). They had average MWs of 8000, 52 000, and 420 000 with polydispersities of 1.25, 1.1, and 1.1, respectively. Poly-(DL-lysine) hydrobromide (DL-PL) from Sigma had a DP of 194, an average MW of 41 000, and a polydispersity of 1.2. The unbuffered electrolyte was prepared from KCl (purchased from Merck, Darmstadt, Germany) and deionized, filtered water (NANO-pure, Barnstead, England) with specific resistivity >17 MΩ-cm. Olefine-free n-decane was obtained from Fluka (Buchs, Switzerland) with a purity >98%. All substances were used as delivered without further purification. Formation of Black Lipid Membranes. BLMs were made according to Mueller et al.21 from a 1% (wt/wt) solution of DPhPS in n-decane. We used a custom-made Teflon cuvette separated into two 5-mL compartments by a septum with a ∼1 mm2 hole. The front side of one compartment contained a glass window, (15) Pandit, A. B.; Davidson, J. F. J. Fluid Mech. 1990, 212, 11. (16) McEntee, W. R.; Mysels, K. J. J. Phys. Chem. 1969, 73, 3018. (17) Redon, C.; Brochard-Wyart, F.; Rondelez, F. Phys. Rev. Lett. 1991, 66, 715. (18) Debregeas, G.; Martin, P.; Brochard-Wyart, F. Phys. Rev. Lett.1995, 75, 3886. (19) Babakov, A. V.; Ermishkin, L. N.; Liberman, E. A. Nature 1966, 210, 953. (20) Carius, W. J. Colloid Interface Sci. 1976, 57, 301. (21) Mueller, P.; Rudin, D. O.; Tien, H. T.; Wescott, W. C. J. Phys. Chem. 1963, 67, 534. (22) Hiemenz, P. C. Principles of Colloid and Surface Chemistry; Marcel Dekker Inc.: New York, 1986. (23) Winterhalter, M.; Helfrich, W. J. Phys. Chem. 1992, 96, 327. (24) Chernomordik, L. V.; Melikyan, G. B.; Chizmadzhev, Y. A. Biochim. Biophys. Acta 1987, 906, 309. (25) Abidor, I. G.; Arakelyan, V. B.; Chernomordik, L. V.; Chizmadzhev, Y. A.; Pastushenko, V. F.; Tarasevich, M. R. Bioelectrochem. Bioenerg. 1979, 6, 37. (26) Teissie, J.; Tsong, T. Y. Biochemistry 1981, 20, 1548. (27) Needham, D.; Hochmuth, R. M. Biophys. J. 1989, 55, 1001.
Figure 1. (A) Scheme of IFC setup used to detect changes in the boundary potential of BLMs. (B) Scheme of the chargepulse instrumentation used to induce and measure irreversible breakdown of BLMs. which allowed for optical observation of the membrane and its annulus. The thinning of the membranes could be observed through a microscope (60-fold magnification). In the early stage, the film appeared colored due to interference patterns of the reflected light at the two membrane-water interfaces. Generally, the colors turned to homogeneous black within a few minutes. One compartment is grounded and called cis, and the other compartment is called trans (compare Figure 1). The bulk solution in both compartments was stirred gently with two small magnetic stirrers. All experiments were performed at room temperature (295 ( 2 K). Inner-Field-Compensation Technique. The adsorption of PL was controlled by means of an IFC apparatus similar to the one described by Sokolov and Kuz’min.11 The principle scheme is shown in Figure 1A. The lock-in amplifier (SR830 DSP, Stanford Research Instruments, Stanford, CA) provides a sine wave voltage with amplitude 45 mV and frequency ω/2π ) 1062 Hz. This voltage is applied to the membrane via the summator and causes a small oscillating compression of the membrane. Due to this compression the capacitance of the BLM changes with the voltage.19 The capacitive current also contains harmonics higher than the fundamental frequency. The amplitude of the second harmonic 2ω component is proportional to the difference in the boundary potential of both sides of the membrane.20 The transmembrane current is converted to a voltage via the current amplifier (Keithley 427), and the amplitude of the second harmonic is detected with the lock-in amplifier. The lock-in amplifier provides a dc voltage dependent on the amplitude of the second harmonic of the current and on the relative phase φ between the internal reference signal and the second harmonic signal from the membrane. The phase φ
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is adjusted such that the lock-in amplifier feeds a voltage back to the membrane via the summator to compensate for the difference in the boundary potential of the membrane. The detected difference of the boundary potential is independent from the amplitude of the applied sine wave. Electroporation Setup. The rupture of the membranes was triggered and detected according to Wilhelm et al.12 The experimental setup is shown in Figure 1B. It contains two Ag/ AgCl electrodes, one is connected to a fast pulse generator (Tektronix PG 507) through a diode (reverse resistance . 1011 Ω); the other is grounded. The voltage between the two electrodes is measured by a digital storage oscilloscope (LeCroy 9354A) connected through a passive oscilloscope probe and is further analyzed on a computer. To achieve a fast charging of the membrane, the presence of a 50 Ω resistance is necessary. The membrane capacitance is calculated from the RC-time constant of the exponential discharge of the membrane across the 10 MΩ resistance of the passive oscilloscope probe. The time-dependent membrane conductivity G(t) is obtained from the voltage curve stored in the oscilloscope. If the membrane resistance becomes smaller than the external 10 MΩ resistance due to defect formation, the discharge occurs mainly across the defect. As long as the defect is small relative to the total area, one can consider the capacitance of the membrane as constant. In this case the membrane conductance is described by
G(t) )
I(t) 1 -d(CU(t)) -C dU(t) 1 dQ(t) ) ) ) ) dt U(t) U(t) dt U(t) U(t) dt -C d(ln U(t)) (1) dt
where I(t) is the current, U(t) the transmembrane voltage, Q(t) the charge, and C the capacitance of the membrane. IFC and Electroporation Experiments. The BLM experiments were generally performed as follows: 20 min after painting the DPhPS membrane, the electrodes were connected to the IFC setup (Figure 1A). Usually, the compensation voltage was near zero, indicating the same boundary potentials on both sides of the membrane due to symmetrical conditions. Subsequently, we added PL to a final concentration of 20 µg/mL to either the cis or the trans compartment. PL adsorption caused a change in the compensation voltage. Titration curves performed in control measurements indicated that a PL concentration of 20 µg/mL saturates the membrane surface under the experimental conditions chosen in this study (data not shown). Symmetrically PL-decorated membranes were formed by adding PL to a final concentration of 20 µg/mL to both compartments of the cell. The compensation voltages of these symmetrically decorated membranes were around zero, as expected. After stabilization of the compensation voltage we switched to the electroporation apparatus (Figure 2B). To measure the membrane capacitance, the membrane is charged with a short rectangular pulse of 1 µs duration to an initial voltage of about 100 mV. To initiate the irreversible breakdown, the membranes are charged with single rectangular pulses of 10 µs duration to voltages in the range of 250 to 700 mV. To produce only single defects, we begin charging the membrane with a 250 mV pulse. Then we raise the applied voltage in 20 mV steps, applying five pulses per step until the membrane disrupts. In a typical experiment, about 20 to 100 pulses are applied prior to membrane rupture. Note that the rupture curves of well-thinned membranes with a capacitance above 0.6 nF usually show no significant dependence on the frequency of the applied voltage pulses. CD Spectra of DPhPS/PL-Vesicles. DPhPS (10 mg/mL in chloroform) was dried by evaporating the solvent under vacuum. Subsequently, the DPhPS film was dispersed in water containing 100 mM KCl to a final concentration of 10 mg/mL and vortexed for 5 min. Then a freeze-thaw cycle was repeated five times. The opaque suspension was extruded 10 times using a 100-nm polycarbonate filter (Nuclepore Corp Pleasanton, CA). CD spectra were recorded on a Jasco J-720-spectrometer (Japan Spectroscopic Co., Tokyo, Japan). The samples contained 300 µg DPhPS vesicles and/or 30 µg PL per mL of solution. The vesicles and PL were mixed 10 min prior to measurement.
Figure 2. (A) Time course of the membrane voltage during electric field-induced irreversible rupture of a DPhPS membrane in the presence of short PL (DP ) 38, curve a) or long PL (DP ) 2007, curve b). The length of the applied voltage pulse was 10 µs. The aqueous phase contained 100 mM KCl; T ) 295 K. (B) Time course of the conductivity calculated from the two voltage versus time curves of Figure 2A. The symbols indicate the experimental data. The solid lines are linear fits.
Theory In this study, we investigate the mechanical stability of charged lipid membranes interacting electrostatically with ions in solution, e.g., monovalent ions or polyelectrolytes. The dissociated charges from the lipid headgroups induce a surface potential ψ0 at the membranewater interface which depends on the concentration of the ions in solution. The potential of a planar surface is given by a solution of the Poisson-Boltzmann equation22,23
ψ0 )
2kT σ*e ln(p + x1 + p2) and p ) λ e 20kT Debye λDebye )
x
0kT 2n0e2
(2)
where k is the Boltzmann constant, T the temperature, e the elementary charge, σ* the surface charge density, the dielectric constant of the electrolyte, 0 the dielectric permittivity of the vacuum, and n0 the bulk ion concentration.
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If a symmetric membrane is exposed to the same bulk ion concentration on both sides, then the surface potentials are the same on both sides. A different ion concentration on both sides causes a difference in the surface potentials and, therefore, a transmembrane potential unequal to zero. It should be noted that a change in the dipole potential can also contribute to the transmembrane potential. External electric fields across membranes have a destabilizing effect24 and should add to internal transmembrane fields.10 The mechanical breakdown of a BLM can be understood as an activated process.25,28 The energy barrier Epore for rupture is determined by two opposite energy contributions which depend on the radius a of the defect12,25
Epore ) 2πaΓ - πa2σ
(3)
where Γ is the edge energy per unit length and σ is the surface tension of the membrane-water interface per unit area. The linear term in eq 3 describes the energy necessary to cut intermolecular links and to form a membrane edge. It dominates the expression for small pore radii and causes a pore to reseal. If a defect becomes larger than the critical radius a* ) Γ/σ, the quadratic term becomes dominant, and the pore will increase irreversibly. Previously, we suggested that external electric fields lower the energy barrier of a BLM by reducing the edge energy necessary to form a pore.29 An electric field pulse causes so-called Maxwell stresses, which depend quadratically on the applied field and compress the membrane. These stresses add to the mechanical stresses of the film prior to application of the field.10,12,25,30 In our measurements, we record the relaxation of an applied voltage across a membrane. The voltage versus time curves can be converted to conductance versus time according to eq 1. A previous study indicated that, under our specific conditions, we induced only one or, at most, very few pores by the voltage pulses.21 We derived this conclusion from the following observations: The frequent repetition of a rupture experiment under the same conditions yielded a distribution of the conductance increase around a minimal value and integer valued multiples of it. In a few cases, we observed a sudden doubling of the conductance increase during membrane rupture. This we interpreted as the occurrence of a second pore during the rupture process. If the conductance increase would be due to the widening of a large number of pores, no distinct minimal value but rather a wide distribution should be observed. Moreover, we observe a very broad distribution of the delay time until rupture occurred. This again suggests a single event rather than the formation of many pores. In case of a single pore, this pore has a large radius relative to the membrane thickness. Under these conditions, the conductance Gpore(t) of a pore can be approximated by the inverse access resistance
Gpore(t) )
1 ) 2κa(t) Rpore
(4)
where κ is the specific conductivity of the electrolyte.10,31 (28) Taupin, C.; Dvolaitzky, M.; Sauterey, C. Biochemistry 1975, 14, 4771. (29) Klotz, K. H.; Winterhalter, M.; Benz, R. Biochim. Biophys. Acta 1993, 1147, 161. (30) Winterhalter, M.; Helfrich, W. Phys. Rev. A 1987, 36, 5874. (31) Hille, B. Ionic channels of excitable membranes. Sinauer: Sunderland, MA, 1984.
The above equation relates the time dependence of the pore conductance to that of the pore radius. The pore widening in pure BLMs is driven by the finite surface tension and is limited by the inertia of the film.12,29 The viscosity of the lipid film can, in most cases, be neglected.10 Balancing the decrease in elastic energy by inertia and energy dissipation during the widening of the pore yields the following time dependence for a(t)
a(t) )
t ) Rt xΦσ dF
(5)
where Φ is a parameter depending on unknown material flow and on dissipation effects. Here, F represents the lipid density, d the thickness of the membrane, and R the velocity of the pore widening. As noted above, we can detect a pore only from the moment when its resistance becomes smaller than 10 MΩ. Then the conductance of the pore is much larger than that of the intact membrane. Therefore, we can equate in good approximation the conductance of the membrane G with the conductance of the pore Gpore. Combination of eqs 1, 4, and 5 then yields the following expression for the rupture velocity
R)
-C d ln U(t) 2κ dt
(
)
(6)
We have recently shown that surface-attached polymerized actin alters the rupture kinetics of a BLM significantly. Here, the increase of the pore radius does not show a linear time dependence but an exponential one. In this case, in the early stage of pore formation, the increase of a(t) is limited by the membrane viscosity η according to12
[ (4ησ )t - 1]
a(t) ∝ exp
(7)
Results In Figure 2A, we show two characteristic time courses of the voltage across the membrane during the rupture. Curve a corresponds to a DPhPS membrane in 0.1 M KCl electrolyte in the presence of short PL. The membrane is charged during 10 µs to a voltage of about 540 mV. In the following ∼50 µs, the voltage shows a rapid relaxation probably due to a rapid structural orientation of the membrane-attached polymer. This nonideal region is followed by the exponential decay of the voltage due to discharging of the membrane via the parallel 10 MΩ resistance of the passive oscilloscope probe. In this region, the RC-time constant yields information on the capacitance of the membrane. The defect formation is seen in the voltage curve a by a sharp kink after about 600 µs. This kink is followed by a superexponential voltage decay, indicating the rupture of the membrane. In general, we determine from this curve three independent quantities. The first is the so-called delay time which is the time interval between the end of the externally applied voltage pulse and the onset of the superexponential decay of the voltage curve. The second quantity is the so-called breakdown voltage causing irreversible rupture of the membrane. We define the amplitude of the voltage shortly after the pulse when the voltage decay starts to follow the RC behavior as breakdown voltage. For example, in Figure 2A the breakdown voltage is read about 50 µs after the voltage pulse. In our previous works, we defined the breakdown voltage at the onset of the superexponential decay. In most cases, membranes
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Table 1. Average Breakdown Voltages and Rupture Velocities of DPhPS BLMs in Water Containing Different KCl Concentrationsa membrane composition
av breakdown voltage (mV)
av rupture velocity (cm/s)
no. of expt
DPhPS (10 mM KCl) DPhPS (100 mM KCl) DPhPS (2000 mM KCl)
530 ( 28 530 ( 20 525 ( 25
20 ( 2 20 ( 2 43 ( 3
20 40 18
T ) 295 K. Errors given are standard errors.
disrupt shortly after the onset of the pulse, and the differences in the definition are negligible. However, in this work, we observed long delay times between the voltage pulse and the rupture. These long delay times would lead, according to the previous definition, to apparently very small breakdown voltages. Control measurements showed that such small voltages usually cannot trigger membrane rupture even when applied over longer times. For the third characteristic quantity, we obtain the conductance increase due to defect formation by analyzing the voltage versus time curves (compare Figure 2, parts A and B) according to eq 1. From the conductance change, we conclude an apparent pore widening on the basis of eq 4. Effects of Ion Screening on the Rupture of Pure DPhPS Membranes. To elucidate the screening effect, we first investigated the influence of ionic strength on the breakdown voltage and rupture velocity of pure DPhPS bilayers. The aqueous phase contained 2, 0.1, and 0.01 M KCl, corresponding to different extents of surface-charge screening. The experimental results are summarized in Table 1. Surprisingly, the breakdown voltages of DPhPS membranes were independent of the ionic strength. The time course of the conductance showed for all membranes a linear increase during the rupture. The measured conductance is the sum of the individual pore conductivities. In the presence of large pores, eq 4 can be applied and gives a linear relationship between the conductance and the effective pore size. DPhPS membranes have comparable apparent rupture velocities in the presence of 0.1 and 0.01 M KCl. In the presence of 2 M KCl electrolyte, higher rupture velocities were found. Effects of Ion Screening on PL-Decorated DPhPS Membranes. In the following series of experiments, we formed membranes of DPhPS and adsorbed PL (DP ) 251) from an aqueous phase containing 0.01 M KCl. The polyelectrolyte was added only to the trans compartment resulting in one-sided adsorption of the polymer to the membrane. The IFC detected after ∼2 min an increasing compensation voltage, indicating the adsorption of PL. After 10-15 min, the compensation voltage reached a plateau of about +140 mV. The capacitance of the membranes did not change during PL adsorption. Disconnection of the IFC setup stopped the compensation of the transmembrane potential. In most cases, this triggered a spontaneous rupture of the membrane. As our setup could not follow the kinetics of such spontaneous rupture, these events were not included in our analysis. It is interesting to note that if a membrane was painted in the presence of polylysine, compensation voltages around zero were detected, indicating a symmetric membrane. Optical observation of these membranes revealed, in many cases, a silvery appearance or colored regions. The capacitance of these films was found to be only about 25% of the value of pure DPhPS membranes. Usually it was impossible to obtain optically black membranes by prolonged waiting under these conditions. Thinning of the membrane could only be forced by applying
Figure 3. Capacity discharge curves of a PL-decorated DPhPS membrane (DP ) 251) in an aqueous phase containing 10 mM KCl after a 1 µs voltage pulse, T ) 295 K. Curve a represents a typical RC-decay curve of a BLM painted in the presence of PL. The fast relaxation of the discharge process indicates a small capacitance of the membrane. Successive voltage pulses of increasing height and a duration of 10 µs caused the RCdecay curves to change from b to c to d and finally to e. Table 2. Average Compensation Voltage of DPhPS BLMs for One-Sided Adsorption of PL Having Various DPsa
polylysine L-PL
av MW
average compensation voltage (mV) of asymmetric no. of av DP DPhPS, PL BLMs expt
L-PL
600 8.000 42.000 52.000
5 38 194 251
L-PL
420.000
2007
L-PL DL-PL
35 ( 2 67 ( 2 74 ( 2 +79 ( 3 (trans) -77 ( 1 (cis) 76 ( 3
9 10 11 13 10 9
a
The aqueous phase contained in all experiments 100 mM KCl; T ) 295 K. Errors given are standard errors.
a series of voltage pulses of increasing pulse height. After each pulse, the RC-decay time increased, probably due to an increased capacitance of the film, indicating either a thinning of the film or an increasing film area. RC-decay curves of a typical pulse series are depicted in Figure 3. Due to the instability of the polymer-decorated membranes at low ionic strength, we used a 0.1 M KCl electrolyte for our systematic studies. The adsorption of PL (DP ) 251) to the trans side of the membrane caused a transmembrane potential of (79 ( 3) mV. In contrast to asymmetric DPhPS/PL membranes in the presence of 0.01 M KCl electrolyte, these BLMs were found to be stable. After the compensation voltage became constant, the IFC setup could be disconnected without causing spontaneous rupture of the asymmetric membrane. The capacitance of PL-free and PL-decorated bilayers was, in general, stable 20 min after painting of the membrane. Prior to rupture, the RC-decay times of DPhPS/PL membranes showed no significant dependence on the height, the frequency, or the sign of the external applied pulses. Repeated pulsing did not influence significantly the asymmetric transmembrane potential of the membrane. These observations indicate that the membrane structure and its solvent content as well as the structure and amount
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Table 3. Average Breakdown Voltages of DPhPS BLMs for Symmetrically and Asymmetrically Adsorbed PL (DP ) 251)a cis adsorption of L-PL (DP ) 251) to DPhPS membranes symmetric adsorption of L-PL (DP ) 251) to DPhPS membranes trans adsorption of L-PL (DP ) 251) to DPhPS membranes a
average breakdown voltage (mV)
number of experiments
590 ( 27 500 ( 26 425 ( 26
10 13 13
The aqueous phase contained 100 mM KCl; T ) 295 K. Errors given are standard errors. Table 4. Average Breakdown Voltages of DPhPS BLMs for Asymmetric and Symmetric Adsorption of PL Having Various Degrees of Polymerizationa
membrane composition (100 mM KCl)
average breakdown voltage (mV) for symmetric adsorption
number of experiments
average breakdown voltage (mV) for asymmetric adsorption
effective average breakdown voltage (mV) for asymmetric adsorption
number of experiments
DPhPS DPhPS, PL (DP ) 5) DPhPS, PL (DP ) 38) DPhPS, PL (DP ) 251) DPhPS, PL (DP ) 2007) DPhPS, DL-PL (DP ) 194)
530 ( 20 525 ( 15 540 ( 24 500 ( 26 426 ( 20 443 ( 21
40 10 11 13 14 10
552 ( 22 (cis) 485 ( 25 (trans) 425 ( 25 (trans) 334 ( 25 (trans) 398 ( 28 (trans)
517 ( 22 552 ( 25 504 ( 25 410 ( 25 472 ( 28
9 10 13 9 11
a The effective breakdown voltages listed in this table are corrected for the transmembrane potential of the BLMs. The aqueous phase contained in all experiments 100 mM KCl; T ) 295 K. Errors given are standard errors.
of the surface attached PL are not irreversibly altered by the repeated application of voltage pulses. Influence of the MW and the Conformation of the Surface-Attached PL on the Boundary Potential. The sign of the voltage decay across the membrane depends on the side of PL addition. Addition of PL (DP ) 251) to the trans side of the BLM gave rise to an average compensation voltage of (+79 ( 3) mV. PL addition to the cis side yielded an average compensation voltage of (-77 ( 1) mV. The compensation voltages of asymmetric DPhPS/PL membranes usually varied by about 10% between individual experiments. To investigate the influence of the MW of PL on the compensation voltages, we added PL of various MW to only one compartment of the cell. The results of the experiments are summarized in Table 2. Trans adsorption of pentalysine causes a compensation voltage of (+35 ( 2) mV, immobilized PL (DP ) 38) exhibits potentials of (+67 ( 2) mV. High MW PL (DP ) 194, 251, 2007) yield potentials around +75 mV. Note that the PL with a DP of 194 is a DL-racemic mixture. Interestingly, adsorption of the DL-form results in a compensation voltage similar to that resulting from adsorption of the L-forms of comparable MW. CD measurements of dissolved L-forms in 0.1 M KCl show spectra typical of random coil conformations. In contrast, the DL-form does not yield an interpretable spectrum. The same is true for DPhPS/PL mixtures with DP ) 5 and 38 and for DPhPS/DL-PL mixtures with DP ) 194. DPhPS/PL mixtures containing high MW PL (DP ) 251, 2007) show spectra typical of R-helical polylysine. Influence of Surface-Attached PL on the Breakdown Voltage of DPhPS Membranes. In the following series of experiments, we investigated the influence of asymmetric boundary potentials on the breakdown voltage of BLMs. We applied a positive voltage pulse to a membrane where PL was attached on the cis side and compared its critical breakdown voltage to that of a membrane where PL was attached to the trans side. After cis adsorption of PL (DP ) 251), a breakdown voltage of (590 ( 27) mV was detected (Table 3). The trans adsorption caused a breakdown voltage of (425 ( 26) mV. BLMs with PL adsorbed to both sides of the membrane showed breakdown voltages of (500 ( 26) mV. In Table 4 we summarized the effect of PL adsorption on the breakdown voltages of BLMs.
Symmetrical adsorption of PL to the membranes has little effect on their breakdown voltages with the exception of the DL-form and the high MW L-form (DP ) 2007). The latter PL reduces the breakdown voltage by ∼100 mV. Moreover, it tends to induce spontaneous rupture. Interestingly, the DL-PL causes a destabilization, whereas the L-form of comparable MW (DP ) 251) does not show a similar effect. Moreover, the mechanical stability of a BLM seems to be affected already during the adsorption process, as noncompensated membranes frequently disrupted when PL started to adsorb to the membrane. Pore-Widening Kinetics of PL-Decorated DPhPS Membranes. The voltage curves of PL-decorated membranes were found to be dependent on the MW of the polyelectrolytes (compare Figure 2A). The conductivity calculated from the voltage curves changed more gradually in the presence of high MW PL than in the presence of low MW PL (compare Figure 2B). Figure 4 summarizes the apparent rupture velocities, which were calculated from our experimental data according to eq 4. The histograms for the rupture velocities are displayed in the left-hand panels (a to e) of Figure 4. The right-hand panels f to j show the histograms for the delay time of pore formation. The two histograms of each row are obtained from the same set of experiments. Panels a and f correspond to pure DPhPS membranes and panels b to e and g to j to polylysine-decorated membranes. The MW of the PLs is indicated in the figure legend. The left-hand panels show clearly the influence of the MW of the adsorbed polylysine on the apparent rupture velocities. Pure DPhPS membranes show an average velocity of 20 cm/s. PLs with DPs of 5 and 38 (panels b and c) increase the average velocity to 24 cm/s. The adsorption of high MW PL results in a significant decrease of the pore-widening kinetics. BLMs with adsorbed PL (DP ) 251, panel d) show a significantly reduced average rupture velocity of 11 cm/s and those covered with PL (DP ) 2007, panel e) show an even smaller value of 6 cm/s. For the sake of clarity, we have omitted the DL-form which has a high average rupture velocity of 16 cm/s. In the case of undecorated membranes, the rupture velocities average around 20 cm/s. The adsorption of PL shifts the average of the rupture velocities. The temporal evolution of all conductivity versus time curves of this study could be fitted linearly with the exception of those obtained from BLMs decorated with PL of the highest DP
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Figure 4. Distribution of the rupture velocities and the delay times for pure and PL-decorated DPhPS membranes in an aqueous phase containing 100 mM KCl; T ) 295 K. The left and right panels in each row are obtained from the same set of experiments. Histograms a and f show the frequency of the rupture events of pure DPhPS BLMs as function of the rupture velocities and delay times. Similar histograms are shown for the DPhPS/pentalysine membranes (b and g), for DPhPS/PL (DP ) 38) membranes (c and h), for DPhPS/PL (DP ) 251) membranes (d and i), and finally for DPhPS/PL (DP ) 2007) membranes (e and j). Note that the delay times of all the right-hand panels are plotted on a logarithmic scale.
(DP ) 2007). Here the films show a wide range of rupture kinetics. Two typical conductivity curves which were obtained in the presence of high MW PL are presented in Figure 2B and Figure 5. The first part of the conductivity curves obtained from these experiments can be well described by an exponential function, whereas the second part can be described satisfactorily by a linear function. The exponential region yields time-dependent rupture velocities of a few mm/s and the linear region velocities of several cm/s. Delay Times of Pore Formation of PL-Free and PL-Decorated DPhPS Membranes. The delay times of pore formation are depicted in the right-hand panels of Figure 4. As shown in histogram f, ∼75% of PL-free DPhPS membranes disrupt within the first 100 µs after
the application of the pulse. PL-decorated BLMs in general have longer delay times between the applied pulse and the detection of pore widening. The average delay time increases from 85 µs for undecorated membranes to 220 µs in the presence of pentalysine. PL (DP ) 38) shifts the delay time to 870 µs, PL (DP ) 251) causes a shift to 930 µs, and PL (DP ) 2007) results in a pronounced shift of average value to 1700 µs. Moreover, the increase of the average delay times in the last three cases are not only due to a broadening of the delay time distribution but also due to rare rupture events in the 100 µs range. We infer that especially high MW polylysines are able to delay pore formation. A similar effect was observed by measuring the conductivity of DPhPS membranes in the presence of high MW PL (DP ) 2007). In this case, we detected,
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Figure 5. Time course of the conductivity of surface-decorated DPhPS/PL membrane (DP ) 2007) during irreversible rupture. The aqueous phase contained 100 mM KCl and 20 µg/mL of PL (T ) 295 K). Note the two kinetic regimes of the conductivity. The first one can be described satisfactorily by an exponential function and the second one by a linear function. The symbols indicate the experimental data. The solid lines are computed exponential and linear fits.
several seconds prior to spontaneous rupture, an increase of the membrane conductivity by several orders of magnitude (data not shown). Discussion The molecular area of DPhPS in a densely packed membrane is about 70 Å2.36 Inserting this value for the surface charge density into eq 2 yields a surface potential of about 130 mV in a 0.1 M KCl electrolyte. Neutralization of all surface charges on one side of the membrane should induce a transmembrane potential of the same value. However, we observed much smaller compensation voltages. This discrepancy between the measured potentials and the theoretical predictions by the Gouy-Chapmann theory is observed frequently not only in many systems but also with different techniques.37 Possible explanations are, for example, the binding of K+ ions, the bulky shape of PL, or an oversimplification within the Gouy-Chapmann theory.32 The dependence of the transmembrane potential on the MW of the surface-attached PL can be understood by the formation of polymer train-tail-loop structures on the membrane surface.33 The so-called trains of this structure (32) Ninham, B. W.; Yaminsky, V. Langmuir 1997, 13, 2097. (33) Hessellink, F. T. In Adsorption from Solution at the Solid/Liquid Interface; Parfit, G. D., Rochester, C. H., Eds.; Academic Press: New York, 1983; p 377. (34) Decher, G. Nachr. Chem., Tech. Lab. 1993, 41, 793. (35) Kim, J.; Mosior, M.; Chung, L. A.; Wu, H.; McLaughlin, S. Biophys. J. 1991, 60, 135. (36) Rand, R. P.; Parsegian, V. A. Biochim. Biophys. Acta 1989, 988, 351. (37) Ba¨hr, G., Diederich, A., Winterhalter, M., manuscript in preparation.
Diederich et al.
are lysine segments connected together, which are in contact with the membrane surface. The loops and tails extend into the surrounding medium. In the case of short PL, we expect the trains and tails to dominate the reduction of the surface-charge density. Long PL most likely develops relatively fewer tails but more trains and a larger number of loops per mole lysine. With these loops, long PL can change the surface potential of the membrane to a greater extent than with trains alone, because even if the 2D surface of the membrane is crowded with trains, loops can form in the third dimension. Moreover, in the case of R-helical PL, one cannot exclude additional dipole contributions to the change in potential. It was shown in this study that DPhPS films can be painted in the presence of PL in an aqueous phase containing 0.01 M KCl. Nevertheless, the thinning of these films to black membrane was found to be hindered. A possible reason could be the persistence of PL of longer length at lower ionic strength, and this longer length is conserved after PL adsorption to the charged membrane surface.32 In the case of a BLM, they may connect large regions of the bilayer, thus hindering the thinning process. If the asymmetric adsorption of PL causes a drastic curvature of the membrane, the film area should consequently increase significantly. However, under these experimental conditions, no changes in the membrane capacitance were observed. PL is known to trigger fusion of negatively charged vesicles as well as the formation of multilamellar chargeneutralized complexes.2 In this context, the question is raised whether single-sided adsorption of PL affects the mechanical stability of a lipid membrane which does not interact with other surface-decorated membranes. Note that the breakdown voltages of asymmetrically decorated membranes has to be corrected for the transmembrane potential due to PL adsorption. Theoretically, it should add to the external applied potential of the voltage pulse. This effect can be seen clearly by adding PL (DP ) 251) to the cis instead of the trans side of the membrane. As shown in Table 3, the average breakdown voltage of cisdecorated membranes is shifted by 165 mV compared to that of trans-decorated membranes. This is about double the transmembrane potential revealed by IFC. It is therefore possible to determine an asymmetric transmembrane potential by performing a series of rupture experiments. Interestingly, the breakdown voltage of a symmetrically decorated BLM of 500 mV is located about halfway between that of cis- and trans-decorated BLMs. From this observation, we infer that asymmetrically and symmetrically decorated membranes have similar mechanical stabilities. Moreover, comparison of the breakdown voltage of symmetrically decorated membranes with the breakdown voltage of asymmetrically decorated membranes which is corrected for the transmembrane potential (effective breakdown voltage in Table 4) suggests that this finding is valid for all PLs investigated in this study. Therefore, the well-known property of PL to induce fusion of negatively charged vesicles cannot be attributed to changes in the surface potential. Only PL of the highest molecular weight (DP ) 2007) leads to a change in the mechanical properties of the BLM and reduces the stability of the membrane. This indicates that the destabilization of the membrane may be due to the formation of an extensive and possibly entangled polyelectrolyte decoration on the surface of the BLM. This consideration is even more plausible since PL is known to bind in a multivalent manner to negatively charged
Rupture of Negatively Charged Membranes
membranes.35 One expects long PL to span large regions of the BLM, thus enhancing the membrane viscosity and membrane inertia. Our experimentally found dependency of the rupture velocity on the MW of the PL confirms these considerations. Undecorated membranes and those decorated with small MW PL disrupt quickly. As the DP increases, the inertia and viscosity of the membranes increase, too, and the membranes show reduced rupture velocities or, in the case of PL (DP ) 2007), even a viscous rupture behavior. In spite of this conclusive picture, one has to be careful with the comparison of rupture velocities obtained under different experimental conditions since our model assumes a single defect of circular shape during the detection of the pore widening. If more than one defect or different formed defects occur under certain experimental conditions, these defects are described by an equivalent and circular defect of an apparent radius a. In this case, our model yields only an apparent rupture velocity. In the early stage of the rupture process, one expects, in viscous films, an exponential widening of the pore radius in time. As soon as the widening becomes faster, the inertia should become the determining factor, and a transition to a linear rupture should occur. In this case, the conductivity curve should start with an exponential course which should become linear when the rupture proceeds. This seems to be the case for DPhPS-decorated membranes (DP ) 2007), compare curve b of Figure 2B. The wide range of rupture kinetics which was observed under these experimental conditions suggests, nevertheless, an inhomogeneous adsorption of the polymers to the membrane surface. For example, in Figure 5, a slow exponential increase of the conductance can be observed for more than 700 µs, which is followed suddenly by a fast linear rupture similar to that of undecorated membranes. This abrupt transition is possibly due to a large-scale inhomogeneity in the polymer decoration which leads to a sudden change in the kinetics when undecorated areas are reached by the defect. From the exponential part of the conductivity curve presented in Figure 2B and 5, the 2D viscosity of the decorated membrane can be estimated. Assuming the surface tension of a bilayer across a Teflon hole to be about σ ) 2 × 10-3 mN/m, we find that it yields membrane viscosities of (1-5) × 10-7 Ns/m.10 Another characteristic quantity of our rupture experiments is the delay time which starts after the membrane conductance becomes smaller than the external 10-MΩ resistance. Such a resistance corresponds to a single pore of ∼20-nm diameter in 100 mM KCl. On the basis of a constant pore widening velocity of 20 cm/s, such a defect requires only 100 ns to form. In addition, the delay times are hardly correlated with the rupture velocities of the membranes. The observation that PL causes delay times in the millisecond range implies a reduced ability of the lipid molecules to rearrange in a way which allows the pore to widen. If we assume that the defects are induced during the voltage pulse, which is at the point of maximal compression of the membrane, we can infer from our observations that the adsorbed PL prolongs the lifetimes of small defects.
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A recent study shows that the transfection efficiency of a cationic lipid-DNA complex into the cytoplasm can be enhanced up to 30-fold upon incorporation of high MW PL into the complex.7 It was speculated that the polyelectrolyte serves mainly to attach the complex electrostatically to the negatively charged target membranes. The results of the present study suggest that the excess PL influences the whole transfection process and not just the binding process of the lipid-DNA complex. Most probably, PL is capable of changing the mechanical properties of biological target membranes and BLMs alike. In this scenario, PL would decrease upon adsorption the mechanical stability of a target membrane and thus facilitate structural changes which are necessary for DNA transfection. Moreover, our findings suggest that high MW PL prolongs the lifetime of energetically unfavorable structural intermediates which may occur during transfection by enhancing the local viscosity of the target membrane. Conclusions We have demonstrated that asymmetric adsorption of polylysine causes an intrinsic transmembrane potential. This potential adds to the externally applied voltage and shifts the breakdown voltage of the membranes. We observe a dependence of the rupture behavior of PLdecorated BLMs on the MW of the polyelectrolyte. Adsorption of high MW PL (DP ) 2007) decreases the breakdown voltage of DPhPS membranes, whereas PL of lower MW does not cause significant changes in the breakdown voltages. One-sided adsorption of PL does not destabilize DPhPS membranes more than symmetrical adsorption. Adsorption of PL of high MW causes a decrease of the apparent rupture velocities and allows the determination of the 2D viscosity of the membrane. Moreover, the rupture curves of PL-decorated membranes (DP ) 2007) indicate a transition from the viscositydominated regime to the inertia-dominated one. Currently, a more detailed investigation concerning this transition is in progress. We suggest a simple theoretical model for the rupture behavior of BLMs, but a complete theoretical model is still lacking. Acknowledgment. We thank Dr. Yuri Ermakov (A. N. Frumkin Institute of Electrochemistry, Russian Academy of the Sciences, Moscow) for very fruitful discussions and advice concerning the construction of the IFC as well as our workshop for their qualified help in designing and building different parts necessary for the described setup. We express our gratitude to Professor Joel A. Cohen (Department of Physiology and Biophysics, University of the Pacific, San Francisco) for stimulating discussions and careful proofreading of the manuscript. For his support, we thank Professor Gerhard Schwarz. This work was sponsored by grants 31.042045.94 (to G.S.) and 7BUPJ048478 from the Swiss National Science Foundation. LA9802668
