Membrane electroporation and electromechanical deformation of vesicles and cells Eberhard Neumann Sergej Kakorin and Katja Toensing Physical and Biophysical Chemistry Faculty of Chemistry University of Bielefeld P.O. Box 100 131 D-33501 Bielefeld Germany Received 17th August 1998 Analysis of the reduced turbidity (*T ~/T and absorbance *A~/A relaxations of 0) ( 0) unilamellar lipid vesicles doped with the diphenylhexatrienyl[phosphatidylcholine (b- DPH pPC) lipids in high-voltage rectangular electrical –eld pulses demonstrates that the major part of the turbidity and absorbance dichroism is caused by vesicle elongation under electric Maxwell stress. The kinetics of this electrochemomechanical shape deformation (time constants 0.1Oq/lsO3) is determined both by the entrance of water and ions into the bulk membrane phase to form local electropores and by the faster processes of membrane stretching and smoothing of thermal undulations.Moreover the absorbance dichroism indicates local displacements of the chromophore relative to the membrane normal in the –eld. The slightly slower relaxations of the chemical turbidity (*T `/T and absorbance *A`/A modes are both associated with the entrance of 0) ( 0) solvent into the interface membrane/medium caused by the alignment of the dipolar lipid head groups in one of the lea—ets at the pole caps of the vesicle bilayer. In addition (*T `/T indicates changes in vesicle shape and volume. The results for lipid vesicles 0) provide guidelines for the analysis of electroporative deformations of biological cells.1 Introduction The method of membrane electroporation is widely applied in cell biology and medicine to introduce eÜector substances and genes into biological cells and tissue.1 The mechanisms of electric pore formation in lipid bilayer membranes and the resulting transport facilitation for macromolecules are not yet well understood. Basic elements of the electric –eld eÜects have already been derived from electro-optic and conductometric data for model systems such as unilamellar lipid vesicles doped with optical membrane probes.2,3 Here the lipid probe 2-[3-(diphenylhexatrienyl propanoyl]-1-hexadecanoyl-sn-glycero-3-phosphocholine (b-DPH pPC) has been used where one of the hydrocarbon chains of the PC is replaced by the DPH residue.DPH[doped bilayer membranes exhibit characteristic absorbance changes in polarized light when subjected to electric –elds.4 Previously the negative absorbance dichroism of DPH-doped lipid vesicles was analysed in terms of structural rearrangements of lipids and of DPH molecules in the wall of electropores assuming the DPH site to be the origin of pore formation.5 On the other hand the electro-optic data with b-DPH pPC can only be rationalized quantitatively if the major part of the absorbance dichroism is attributed to global vesicle deformation under the electric Maxwell stress.2,6 Here we develop the theoretical and analytical framework to diÜerentiate the contributions of the –eld-induced membrane structural changes and of the vesicle shape deformation to the tur- 111 Faraday Discuss.1998 111 111»125 bidity and absorbance dichroisms. It appears that the two characteristic turbidity *T ~ and absorbance *A~ modes associated with orientational processes are rate-limited by the electric pore formation whereas the chemical turbidity *T ` and absorbance *A` modes reveal further details such as the entrance of water and ions into the interface regions of the lipid head groups.7,8 Additionally *A~ re—ects local chromophore displacements in the membrane. where *Ip\Ip(E)[Ip is the light *C (1) (2) (3) 2 Materials and methods 2.1 Vesicle suspensions Large unilamellar phospholipid vesicles and vesicles doped with the optical lipid probe b-DPH M pPC r\782 were prepared by the extrusion method as described by Toensing et al.9 The vesicle mean diameters determined by dynamic light scattering measurements (data not presented) are U\100^36 nm after extrusion through the 100 nm –lter ; in line with the size distribution of extruded vesicles determined by Mayer et al.10 During vesicle preparation and the following electro-optic relaxation measurements care was taken to protect the DPH samples from photolysis.The –nal total lipid concentration used for the optical and electro-optical measurements was app [LT]\1 mM corresponding to a vesicle density of ca. 7.4]1015 L~1 for vesicles of radius a\50 nm. Under these conditions the average distance between the anionic surfaces of single vesicles is about ca. 0.53 lm qualifying the suspension as dilute with practically no vesicle»vesicle contacts.Actually at the maximum –eld E\8 MV m~1 and at the eÜective permittivity of vesicle et eff e BeL\2.5 where L is the permittivity of the lipid membrane the minimum characteristic time of approach of vesicles due to induced dipole forces taking vesicle»vesicle hydrodynamic appB610 t interactions into account is ls.11,12 Therefore at the pulse duration of tE\10 ls and at –eld strengths EO8 MV m~1 we may safely neglect vesicle»vesicle interactions. 2.2 Electro-optical relaxation spectrometry Rectangular pulses of –eld strength up to 8 MV m~1 and of duration up to tE\10 ls are applied by cable discharge to the sample cell equipped with parallel planar graphite electrodes thermostatted at T \293.0^0.1 K (20 °C).The –eld-induced changes in the transmittance of planepolarized light were measured at the wavelength j\365 nm (Hg-line ; highest accuracy). The light intensity change *Ip caused by the electric pulse and measured at the polarization angle p relative to the direction of the applied external –eld vector E is related to the optical *Cp\Cp(E)[C density change by 0 p \[log(1]*Ip/Ip) intensity change from Ip (at E\0) to Ip(E) in the presence of E Cp(E) and C are the optical 0 p densities at E and at E\0 respectively. Generally C\A]lT comprising both absorbance (A) and turbidity (T ) along the light path length l. The absorbance Ap of the reporter lipids b-DPH pPC in the bilayer of the vesicles is given by the diÜerence *Cp between Cp(V,D) of the doped vesicles and Cp(V) of the vesicles without the reporter lipid but at the same total lipid concentration and vesicle size Ap\Cp(V,D)[Cp(V).The –eld-induced optical change may be decomposed into a deformational/orientational part OR p and a structural/chemical part *CCH p according to *Cp\*COR p ]*CCH p The –eld-induced changes *CA and *CM at the two light polarization modes p\0° (p parallel to the external –eld vector E) and p\90° (o perpendicular to E) are given by *CA\CA[C and 0 *CM\CM[C0 respectively. As outlined for the absorbance dichroism7 both the consumptive dichroism (*A) and the conservative scattering dichroism (*T ) are originally de–ned for optical density changes of purely deformational/orientational origin.13,14 In the notation used here the optical density dichroism is classically de–ned by *C\*COR A [*COR M On the other hand the diÜerence *C~ either *A~ or *T ~ of the actually measured changes *CA and *CM is given by *C~\*CA[*CM\*C](*CCH A [*CCH M ) Faraday Discuss.1998 111 111»125 112 *CCH A B*CCH M we may approximate the diÜerence In the case of small chemical contributions or if mode *C~ by the dichroism *C i.e. :7 *C~\*C (4) The equations *A`\*ACH and *T `\*T CH are straightforward ; analogous to the expression 7,8 *A for *CCH\(*CA]2*CM)/3 . Therefore *CCH generally refers to changes in we obtain CH the scattering cross-section or the immediate environment of the absorbing chromophore due to entrance of water and small ions. Note that if the scattering contribution is negligibly small we have *C\*A and outside the absorbance bands we use *C\l *T .The absorbance dichroism is a quantitative measure of rotational displacements comprising both global shape deformations as well as local chromophore shifts in the lipid bilayer. The turbidity term *TCH/T0 re—ects changes in the refractive index of the membrane due to entrance of water and ions as well as changes in vesicle shape and volume. 3 Results The b-DPH pPC membrane probes greatly increase the absorbance of light in the doped vesicles in the light wavelength range 300\j/nm\400 (Fig. 1). The optical density and the absorbance both increase linearly with the concentration of b-DPH pPC suggesting that at zero external –eld there are no optically detectable interactions between the ììreporter lipids œœ in the vesicle membrane (Fig.2). In the electric –eld pulse the very rapid (ca. 1 ls) increases in the *A`/A *A~/A and *T `/T absorbance terms *T ~/T and (Fig. 3) and the turbidity modes 0 0 0 0 (Fig. 4) are followed by similarly rapid –eld-oÜ relaxations. Outside the absorption band the electro-optic relaxations of labelled and non-labelled vesicles are practically identical (Fig. 5). These data show that the membrane probes incorporated in the lipid molecules change neither membrane electroporatability nor mechanical properties such as bending rigidity or membrane spontaneous curvature. At larger b-DPH pPC concentration there is a weak dependence of the chemical and dichroitic absorbance modes on the probe content in the membrane especially at higher –eld strengths (Fig.6). However no changes are observed in the turbidity terms *T ~/T0 and *T `/T outside the absorbance band with increasing concentration of b-DPH pPC in the 0 vesicle membrane (Fig. 7). At the –eld strengths 2OE/MV m~1O8 the chemical turbidity and Fig. 1 Optical density of a suspension of unilamellar vesicles composed of L-a-phosphatidyl-L-serine (PS) and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) in the molar ratio PS POPC of 1 2 (» » ») and the M same suspension doped with the optical probe b-DPH pPC r\782 at the concentrations [b-DPH pPC]/ lM\2.5 3.3 5 10 20 (from bottom to top) as a function of the wavelength j. Vesicle radius a\50 nm vesicle density ov\7.4]1015 L~1; total lipid concentration [LT]\1.0 mM; 0.66 mM HEPES-Na (pH 7.4) 0.13 mM CaCl2 T \293 K (20 °C).113 Faraday Discuss. 1998 111 111»125 Fig. 2 Optical density C365 (D V) at j\365 nm (Ö) of a doped PS POPC (1 2) vesicle suspension as a function of the total concentration of b-DPH pPC. The absorbance A365 (>) of the ììreporter lipid œœ b-DPH pPC at j\365 nm is given by the diÜerence of the doped (D V) vesicle system and the non-doped (V) one A365\*C365\C365 (D V)[C365(V) ; experimental conditions as in Fig. 1. Both C365 and A365 are linear in [b-DPH pPC] hence there is no optically visible interaction between the reporter molecules. Fig. 3 Field-on and –eld-oÜ relaxations of the absorbance terms *A`/A and *A~/A0 at the two extreme 0 –eld strengths E\2 (thin line) and E\8 MV m~1 (thick line) [b-DPH pPC]\5 lM.One rectangular electric pulse of –eld strength E and pulse duration tE\10 ls at T \293 K. Note the change in the timescale for tP20 ls. Experimental conditions as in Fig. 1. Faraday Discuss. 1998 111 111»125 114 *T ~/T and Fig. 4 Field-on and –eld-oÜ relaxations of the turbidity terms *T `/T (j\365 nm) for non- 0 0 doped vesicles at the two extreme –eld strengths E\2 (thin line) and E\8 MV m~1 (thick line). Wavelength j\365 nm. Experimental conditions as in Fig. 3. Visual inspection shows that there are at least two kinetic modes I and II in the presence of E. *T `/T0 *A`/A0 are 10-fold smaller than the dichroitic modes (*T ~/T0 justifying the approximations *T /T absorbance terms *A~/A 0\*T ~/T0 and *A/A0\*A~/A0 respectively. 0) 4 Theory and data analysis 4.1 Vesicle orientation If the vesicles shortly after extrusion were slightly elongated,15 they can be oriented in an electric –eld.However the very rapid (ca. 1 ls) after-–eld relaxations of the major part of the absorbance *A~/A (Fig. 3) and the turbidity *T ~/T (Fig. 4) modes exclude the possibility that the optical 0 0 signals are due to orientation of non-spherical vesicles in an external –eld. After-–eld disorientation of slightly elongated vesicles may be described by rotational diÜusion of a sphere of radius a\50 nm with the rotational relaxation time given by16 qrot\4nga3/(3kT ) where g is the viscosity of the solvent here water k the Boltzmann constant and T is the absolute temperature. With g\10.02]10~4 kg m~1 s~1 at T \293 (20°) qrot\130 ls.If the vesicles were modelled by ellipsoids q should be even slightly larger. In any case the time constants of the after-–eld dichroisms (ca. 1 ls) are appreciably smaller than qrot . Since the after-–eld rotational relaxation is rot independent of the –eld strength comparison of the time constants suggests that the major parts of the *T ~/T and *A~/A relaxations are caused by a mechanism diÜerent from the vesicle 0 0 orientation namely electric pore formation as well as membrane stretching and smoothing of thermal undulations under Maxwell stress. 4.2 Hydrophilic pore model If the reduced absorbance mode *A~/A is directly due to the electropores pore formation can be 0 115 Faraday Discuss. 1998 111 111»125 0 *C~/C of a doped vesicle suspension [b-DPH pPC]\5 lM; at wavelengths j\281 (» » ») and 436 Fig.5 Comparison of the reduced dichroitic (turbidity) modes (a) *T ~/T of an unlabelled vesicle suspension with (b) 0 (»») nm outside the b-DPH-residue absorption band (see Fig. 1). The extent and the rate of the turbidity dichroisms are independent of both the wavelength [*T ~/T (281 nm)B*T ~/T (436 nm)B*C~/C (281 0 0 0 nm)B*C~/C (436 nm)] and the presence or absence of the reporter lipid b-DPH pPC (b). One rectangular 0 electric pulse of –eld strength E\5 MV m~1 and pulse duration t Experimental conditions as in Fig. 1. E\10 ls was applied at T \293 K. described in terms of local lipid phase transitions involving cooperative clusters L of n lipids in n the pore edge. During this transition the membrane probes together with lipid molecules are locally rotating (Fig.8). The entrance of the highly polarizable aqueous solvent (water and ions) modi–es the local environment of the chromophores and is described by the term *A`/A0 . Based *A`(t Fig. 6 Dependence of the absorbance terms E)/A0 (open symbols) and *A~(tE)/A0 (–lled symbols) at tE\10 ls and j\365 nm on the b-DPH pPC concentration at –eld strengths E/MV m~1\2.0 (» @); 2.8 4.0 ( ) K ( C) ; 5.0 L ( 7) ; 6.5 +) ; 8.0 (« OP). One rectangular electric pulse –eld strength E and (| >); pulse duration tE\10 ls at T \293 K. Experimental conditions as in Fig. 1. Faraday Discuss. 1998 111 111»125 116 tE 6 ) ) ; 4.0 (K ( C) ; 5.0 L ( 7) ; 6.5 +) ; 8.0 (« OP). Experimental Fig. 7 Dependence of the turbidity terms *T ~(tE)/T0 (open symbols) and *T `(tE)/T0 (–lled symbols) at the end of the pulse at j\436 nm i.e.outside absorbance band on the b-DPH pPC concentration at –eld strengths E/MV m~1\2.0 (» @) ; 2.8 (| conditions as in Fig. 6. on the original concept of HO and HI pores,17 a speci–c scheme for electropore formation has been proposed:5 The state transitions from the closed membrane state (C) to hydrophobic (HO) and hydrophilic (HI) pore states are associated with the rotation of the lipids and chromophores in the HI-pore Fig. 8 HI pore model and vesicle geometry relative to the –eld direction E. Scheme for the molecular rearrangements of the lipids in the pore edges of the lipid vesicle membrane. C denotes the closed bilayer state. The induced membrane –eld leads to entrance of water into the membrane to produce pores (P) cylindrical HO pores or inverted HI pores.In the pore edge of the HI pore states the lipid molecules are rotated into the pore region to minimize the hydrophobic contact with water. In the pole caps the rotation of DPH lipids leads to a negative absorbance dichroism ([) and in the equatorial region to a positive contribution to the dichroism (]). 117 Faraday Discuss. 1998 111 111»125 wall edge. The speci–c structural organization of the lipids and DPH in the HI pore states is modelled by a 90° rotation of the optical transition moment l of the chromophore with respect to the membrane normal (Fig. 8). For the chromophores the scattering component of the molar absorption coefficients is negligibly small compared with the absorbance component.Therefore a change in the scattering of the rotated chromophores is negligible. Perpendicular to the optical transition moment of chromophore the absorbance is zero.18 Hence the absorbance is associated predominantly with the vector l. In the C and HO states l predominantly shows positions parallel to the membrane normal. The orientational distribution of the chromophores around the membrane normal in the C and HO states and around the orthogonal direction in the HI state decreases the amplitude of the dichroitic signal. Because of axial symmetry about the –eld direction and free orientation of the chromophores around the HI-pore axis the Lambert»Beer formalism –nally yields an expression for the absorbance mode (*A~/A (6) 4 *A~ \ 3 A Pn Ab]3 HI[bfHOB(1[3 cos2 h) sin h dh 0) f 2 0 and for the chemical mode (7) 0 (*ACH/A0\*A`/A0) accordingly *A` \ b 2 HI]fHO) sin h dh Pn ( f h h HO(h)\[HO]h/[C0] and fHI(h)\[HI]h/[C0] respectively where and [HI] are the DPH probe concentrations of HO and HI pores respectively at h and f is the total probe concentration.Mass conservation suggests HI(h)]fHO(h)]fC(h)\1 A0 0 where h is the positional angle of the chromophore (Fig. 8) relative to the –eld direction. The relative molar absorption coefficient diÜerence is de–ned by the molar absorption factor b\(e*[eC)/eC. For simplicity we assume that in state C the microscopic molar absorption coefficients of the chromophore in the presence (eE C) and in the absence (eC) of the –eld are equal (eEC\eC).In contrast to C the membrane probes in HO and HI pore edges are partially exposed to water and ions ; hence eHI and eHODeC. We assume equal molar extinction coefficients of membrane probes in HO and HI pore edges respectively eHI\eHO4e*. Similar to the orientation distribution function for chromophores in a solution the angular distribution functions representing the probabilities of –nding chromophores in HO or HI membrane states at an angle between h and h]dh are de–ned by f [HO] [C0] where fC(h)\[C]h/[C0]. Here it is recalled that o*A~/A0 oAo*A`/A0 o (Fig. 6 and Fig. 3) hence the molar absorption factor b is practically zero and the approximation *A~\*A is valid.Substitution of b\0 in eqn. (6) yields the absorbance dichroism (due to the local rotation of the membrane probes in HI pore edges) (8) 8 *A \ 9 A Pn f 0 0 The distribution function is speci–ed as (9) fHI(h)\ 0 f * h*\h\n[h* n[h*OhOn 7HI f ( * h)(1[3 cos2 h)sin h dh 0OhOh* where f * is the fraction of chromophores in HI pore edges in the vesicle pole caps. The h f -average fraction 6 of chromophores in HI pores is then given by (10) f6 \ 1 n fHI(h)sin h dh\f *(1[cos h*) 2 P0 Substitution of eqn. (9) in eqn. (8) and integration yields (11) 4 f * cos h*(cos2 h*[1) *A \ 9 A0 *A/A Analysis of eqn. (11) shows that at a given value of f * has a minimum at h*\ 0 Actually the rotation of chromophores in HI pores at arccos(J1/3)\54.7°.Faraday Discuss. 1998 111 111»125 118 54.7°\h\(180°[54.7°) contributes to the dichroism positively reducing the total amplitude of the negative absorbance dichroism. Substitution of h*\54.7° in eqn. (11) and in eqn. (10) yields (12) f *\[1.155 *A A0 and (13) f6 \[0.487 *A A0 respectively. 4.3 HI pore model and absorbance dichroism At the maximum –eld strength E\8 MV m~1 the amplitude value of the absorbance dichroism 0.225Oo*A/*A increases in the interval 0 oO0.28 with increasing concentrations of the membrane probe 2.5O[b-DPH pPC]/lMO20.0 (Fig. 6). Hence eqn. (12) and eqn. (13) yield 0.25Of *O0.32 and 0.11Of6 O0.135 respectively. Note the fractions of membrane probes in HI f *\[HI] /[C pores are de–ned as f6 \[HI]/[C 0] and 0] where [HI] is the concentration of p p b-DPH pPC in HI pores in vesicle pole caps (0OhOh*; n[h*OhOn) and [HI] is the haverage concentration of membrane probes in HI pores.Clearly eqn. (12) and eqn. (13) imply that *AP[HI] A0P[C0]\[b-DPH pPC]. Therefore at constant fraction of membrane p [HI] and area covered by HI pores f f * and 6 should not depend on [b-DPH pPC]. However the data show that there is a 28% increase in f f * and 6 accompanying an eight-fold increase in [b-DPH pPC] at E\8 MV m~1. The reporter lipids in the membrane might decrease the bending rigidity of the membrane and thereby increase the degree of vesicle deformation. However the analogous turbidity terms *T ~/T and *T `/T 0 0 measured outside the absorbance band are independent of [b- DPH pPC] (Fig.7) suggesting that the degree of the vesicle deformation is constant. In any case the fractions f f * and 6 are too large to be identi–ed with the fraction of porated membrane area. Actually 0.11Of6 O 0.135 implies that 11»13.5% of all membrane probes are in the HI pore edges. At random distribution of the chromophores in the membrane it would mean that 11»13.5% of the membrane surface area is covered by HI pores. However the upper limit for the fraction of membrane surface area covered by conductive pores has been estimated to be only ca. 0.002 which does not correlate with 0.11Of6 O0.135.19 Alternatively the b-DPH pPC molecules may locally change the ability of the membrane to be electroporated such that the pore formation is facilitated at the site of the probe.This assumption is in line with comparative —uorescence anisotropy and scanning calorimetry data suggesting that DPH pPC ììdisruptsœœ bilayer order in its near vicinity.20 In this case the electropores are concentrated at DPH sites. However at the maximum concentration [b-DPH pPC]\20 lM and at a lipid concentration of 1.0 mM there is on average one b-DPH pPC molecule per 50 lipid molecules in the two membrane monolayers. The surface area per lipid molecule in the liquid crystalline state of the membrane is about 0.6 nm2 .21 If we assume that the minimum HI pore radius is *S/S should lead to membrane rupture and to vesicle elongation. 0 rpBd/2\2.5 nm the minimum value of the relative increase in the membrane surface area is 0\0.11p]2.52/(0.6]50/2)\0.14 (or 14%).This fraction is again unreasonably large and Thus the absorbance dichroism does not directly re—ect HI pores. Rather the *A~/A mode must be predominantly due to global rotations of membrane probes caused by electroporative shape elongation of the vesicles under the electrical Maxwell stress. 4.4 Electroporative deformation model Vesicles can be elongated if either the membrane area is increased or the intravesicular volume is decreased. However for the short duration of the electric pulse (10 ls) solvent transport through the membrane electropores is usually very small.2 If the optical transition moments of the membrane probes are predominantly aligned along the membrane normal the elongation of the vesicles leads to a global orientation of the membrane chromophores apart from the external –eld 119 Faraday Discuss.1998 111 111»125 direction leading to negative absorbance dichroism (Fig. 9). If chromophores are distributed at –nite angles around the membrane normal (Fig. 10) the amplitude of the dichroism is smaller than that for normal-parallel positions. At small deformations the shape of the elongated vesicles may be approximated by a spheroid.22 In view of iono-electrochromic eÜects or formation of electropores the molar absorption coefficient of the chromophores in the membrane may change.2 Formally we can describe the modi–ed molar absorption coefficients in terms of HO pores with the parameters fHO and eHO. If the water content of the membrane in the –eld is increased without pores because of –eld-induced orientation of the lipid head groups and isotropic penetration of water and ions into the membrane/solvent interface (Fig.10) the radius of the HO pores is theoretically zero. Because of axial symmetry about the –eld direction the reduced absorbance dichroism is given by *A~ \[ 8 3 M3 cos2 a[1N Pn [1]bfHO]M1[3 cos2[arctan(p2 tan h)]N sin h dh (14) is also dependent on h. The chemical absorbance term is given by eqn. (7). A0 0 where p\c/b is the axis ratio of the spheroid (c[b Fig. 9) and a is the average angle between the membrane normal and the optical transition moment of DPH pPC (Fig. 10). It is recalled that fHOApplying eqn. (14) for a\0 to the data in Fig.6 we obtain the axis ratio in the range at E\8 MV m~1). For small vesicle elongations 1.10OpO1.13 (for 0.225Oo*A~/A0 oO0.28 (pO1.13) the relative increase in the membrane surface area at constant vesicle volume is described by (15) 45 (p[1)2 *S B 8 S0 where S0\4na2 is the vesicle surface area. Substituting 1.10OpO1.13 in eqn. (15) we obtain 0.0018O(*S/S0)O0.0029 at 2.5O[b-DPH pPC]/lMO20.0 and E\8 MV m~1. Alternatively without electropore formation the membrane surface area could also increase due to membrane straining by the electrical Maxwell stress.23 Fig. 9 Rotational displacement of the optical transition moment l of the DPH chromophore in the membrane caused by vesicle shape deformation in the electric –eld E. If l is oriented predominantly perpendicular to the membrane surface the vesicle elongation changes the direction of l out of the parallel –eld direction leading to negative absorbance dichroism (*A).The elongated vesicle is modelled by a spheroid with the principal semiaxes c and b. Faraday Discuss. 1998 111 111»125 120 Fig. 10 Positions of the optical transition moments l of b-DPH pPC relative to the membrane normal N (perpendicular to the membrane surface S) characterized by the average angle a are diÜerent without electric –eld a (a) and in a –eld a(tE) (b). In the electric –eld the head-group dipole moments are partially oriented in the –eld direction. Entrance of water and ions in the head-group regions of the pole caps of the lipid mem- 0 brane is enhanced by the electric –eld (b) compared with zero –eld (a).In order to check the mechanism of vesicle elongation the reduced absorbance dichroism *A~/A is compared for vesicles of diÜerent radii a but at a constant transmembrane potential *r0 drop *r m . At constant m the free energy change associated with electroporation should be constant and the extent of membrane electroporation should not change with vesicle radius.5 Moreover vesicle elongation without pores should decrease with increasing curvature H\1/a. Axis ratio and curvature are related by:6,23 (16) p\1]G3 e0 ew(Ea)2 H 64 i H 1 where e e is the vacuum permittivity the relative permittivity constant of the solvent and i is the 0 w membrane bending rigidity. Note that the product (Ea) in eqn. (16) is a constant.Insertion of eqn. o*A~/A (16) in eqn. (14) shows that the absorbance term should decrease with increasing H. If 0 o vesicle deformation occurs without electropore formation controlled solely by the increase in surface area due to stretching of the membrane or reduction of membrane thermal undulations or the smoothing of a membrane super structure the decrease in p with increasing H should be even steeper because of the amplitude of the thermal undulations or superstructure decreases with decreasing vesicle radius.2,24 In any case increasing H should lead to a decrease in the vesicle elongation due to such elastic membrane stretching by the electrical Maxwell stress and thus to a decrease in o*A~/A0o in contrast to the experimental data (Fig. 11). On the other hand the increase in membrane surface area by electroporation is facilitated by the increase in the packing density diÜerence in the two membrane lea—ets due to increasing membrane curvature H.The enhanced formation of conical pores with increasing H is quanti–ed by the concept of the area diÜerence elasticity (ADE) energy25 and has been applied previously by Toensing et al.9 Clearly the experimental data suggest that vesicle elongation is rate limited by surface area increase due to pore formation. The increase in surface area (*S/S0) by the electropores can be readily transformed into the vesicle elongation under Maxwell stress. Moreover the largest increase in the membrane volume is in the pole caps of the vesicle facilitating the vesicle elongation. 121 Faraday Discuss.1998 111 111»125 Fig. 11 Amplitude of the absorbance term *A~/A as a function of membrane curvature H\1/a at constant *rm\[1.5aE\[1.5]25 nm]8 MV m~1\[1.5]50 nm ]4 MV transmembrane voltage drop 0 m~1\[1.5]100 nm ]2 MV m~1\[1.5]200 nm]1 MV m~1\[0.3 V. The circles joined by a solid line are the experimental data. The dotted line corresponds to the vesicle elongation due to membrane stretching or smoothing of membrane undulations under the electric Maxwell stress. The increase in o*A~/A0 o with H suggests that in this case the electroporative vesicle deformation is predominant. Experimental conditions as in Fig. 1 and Fig. 3. The concept of electroporative vesicle elongation is also con–rmed by the increase in the conductivity of a suspension of salt-–lled vesicles exposed to an electric –eld pulse.2,4 Clearly the conductivity increase after the –eld pulse shows convincingly that electroporation causes permeabilization of the vesicle membrane i.e.there are electropores. Interestingly the reduced absorbance dichroism suggests a continuous increase in the electroporated surface area with increasing –eld strength whereas massive ion transport through the membrane only occurs above a threshold value. Therefore turbidity and absorbance electro-optics are suitable for an investigation of the very initial stages of membrane electroporation and global shape deformations. The relaxation time of vesicle deformation due to smoothing undulations can be estimated according to (17) qB[ 5 16 g i a3 lnA1[ 64 3 e ( 0 p e [ wE 1) 2a i 3B Inserting g\10.02]10~4 kg m~1 s~1 the vesicle radius a\50 nm a typical value for the membrane bending rigidity i\2.5]10~20 J and p\1.1 in eqn.(17) we calculate 0.8Pq/ lsP0.009 in the –eld strength range 1OE/MV m~1O8. The time constant of stretching is also small (2.5]10~10 s) ;26 the apparatus time constant is 20 ls and the –eld builds up rapidly (6]10~8 s). Since all the time constants are much smaller than those of electropore formation (3Pqp/lsP0.2) the slow mode (Fig. 4) of vesicle deformation is rate limited by and rapidly coupled to the primary electroporation process. Note that p\1.1 corresponds to a maximum change of 6.6% in the membrane curvature ; therefore the relative motion between monolayers may be neglected.Only a rapid ca. 1000-fold increase in curvature could lead to a retardation of the shape deformation due to viscous impedance arising from relative monolayer motion.27 It is recalled that the absorbance dichroism contains the ratio p and the angle a; see eqn. (14). For electroporative deformation the surface area increase *S(II) of the slow mode is proportional to the concentration [P] of electropores. In our chemical model for membrane electroporation [P]\[P] (CHP) the pore kinetics is described by =(1[exp[[t/qp]) where [P]= is the amplitude and q the time constant of the poration-resealing process. Both relaxation quantities are p dependent on the –eld strength and on the positional angle h (Fig. 8). Hence all measured parameters re—ect h-averages.Application of a Mie type numerical code for confocal coated spheroids28 to the –eld-on time course of the turbidity terms *T ~(t)/T and *T `(t)/T (see e.g. Fig. 4) yields 0 0 the dependence of the total increase *S on the –eld strength (Fig. 12). The increase in membrane = area in Fig. 12 is certainly large compared with 0.002 fraction of conductive pores reported by Hibino et al.19 However not all of *S= is due to electropores. Membrane stretching and smooth- Faraday Discuss. 1998 111 111»125 122 *S=/S0 of the relative change in the membrane surface area of a vesicle as a func- = *S Fig. 12 Amplitude value tion of the external –eld strength E. S is the total surface area of the vesicle membrane. *S is calculated from *T ~(t)/T and *T `(t)/T0 the –eld-on turbidity relaxations 0 assuming constant intravesicular volume.Note =\*S=(I)]*S=(II) is the total amplitude value of the electrochemomechanical surface area increase that 0 = *S\*S (I)(1[exp[[t/q(I)])]*S (II)(1[exp[[t/q(II)]). Experimental conditions as in Fig. = according to 4. *A~(t)/A using eqn. (14) with b\0 and a –nite value of a (Fig. 13) ing undulations in the electric –eld also contribute to *S=. Fortunately the turbidity terms *T ~/T and *T `/T are independent of the presence of the chromophores. Comparison of the p 0 0 values at diÜerent times calculated from the turbidity terms *T ~(t)/T and *T `(t)/T and from 0 0 the absorbance dichroism 0 *A`(t *A`/A0(B0) and *A~/A at the concentration of the membrane probes 0 E)/A0 *A~(tE)/A0 and *T ~(tE)/T0 *T `(tE)/T0 at the end of the Fig.13 Axis ratio p\c/b of the elongated vesicle as a function of the pulse time at the two extreme –eld strengths E/MV m~1\2 (Ö) and 8 (L). The circles are the values of p calculated from the turbidity terms *T ~/T and *T `/T at diÜerent times. The corresponding solid curves are the theoretical simulations with 0 0 *S\*S(I)]*S(II) for the kinetics of the increase in the membrane surface area *S. The dotted curves are calculated from the absorbance [b-DPH pPC]\5 lM. The values t pulse E\10 ls were used to calculate the average angle a(tE)\39.7° between the optical transition moment of b-DPH pPC and the membrane normal. Experimental conditions as in Fig. 3. 123 Faraday Discuss. 1998 111 111»125 Fig.14 Dependence of the angle a on b-DPH pPC concentration (Ö) the angle a extrapolated to the 0 beginning of the pulse (t\0) and (L) a(t t at the pulse end E) E\10 ls. Note for neither a0 nor a(tE) is there any dependence on the –eld strength in the range 2OE/MV m~1O8. Experimental conditions as in Fig. 3. indicates that the angle a also changes in the –eld strength range EP2 MV m~1. It is readily seen that unlike the turbidity dichroism the absorbance dichroism also contains information on the position of the lipid side chains here the DPH residue relative to the membrane normal. The –eld-induced increase in a and the dependence of a on the b-DPH pPC concentration (Fig. 14) cannot be rationalized unequivocally. One possible explanation is the rotational displacement of the chromophore residue caused by the alignment of the polar head group in the –eld direction (Fig.10). 5 Conclusion It appears that the concept of electrochemomechanical vesicle deformation can consistently rationalize the electro-optic data. However the local structural changes associated with the formation of HI pore edges cannot be directly identi–ed with electro-optics. The electropores are optically enhanced by vesicle deformation because the slow mode *S(II) of shape elongation under the electric Maxwell stress is caused by and rapidly coupled to the electroporative increase in the membrane area. This fundamental result of electroporative shape deformation also applies to biological cells and tissue. However the lipid-protein plasma membrane of cells is a part of a larger envelope structure comprising extracellular matrix components and intracellular cytoskeletal elements.29 Therefore the extent and rate of cell deformation will be determined by the elastic properties of this network.30 Acknowledgements We thank the Deutsche Forschungsgemeinschaft for the grant Ne227/9-2 to E.Neumann. References 1 E. Neumann and S. Kakorin Radiol. Oncol. 1998 32 7. 2 E. Neumann and S. Kakorin Curr. Opin. Colloid Interface Sci. 1996 1 790. 3 S. Kakorin E. Redeker and E. Neumann Eur. Biophys. J. 1998 27 43. 4 E. Neumann E. Werner A. Sprafke and K. Krueger in Colloid and Molecular Electro-Optics ed. B. R. Jennings and S. P. Stoylov Institute of Physics Bristol 1992 p. 197. 5 S. Kakorin S. P. Stoylov and E.Neumann Biophys. Chem. 1996 58 109. 6 S. Kakorin and E. Neumann Ber. Bunsen-Ges. Phys. Chem. 1998 102 670. Faraday Discuss. 1998 111 111»125 124 7 S. Kakorin and E. Neumann Ber. Bunsen-Ges. Phys. 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Garcia de la Torre Biophys. Chem. 1997 69 1. 22 B. Zeks and S. Svetina in Springer Proceedings in Physics ed. R. Lipowsky D. Richter and K. Kremer Springer-Verlag Berlin 1992 vol. 66 p. 174. 23 M. Kummrow and W. Helfrich Phys. Rev. A 1991 44 8356. 24 B. Kloesgen and W. Helfrich Eur. Biophys. J. 1993 22 329. 25 U. Seifert and R. Lipowsky in Structure and Dynamics of Membranes ed. R. Lipowsky and E. Sackmann Elsevier North-Holland Amsterdam 1995 vol. 1A p. 519. 26 S. Komura in V esicles ed. M. RosoÜ Marcel Dekker New York 1996 p. 197. 27 E. Evans and A. Yeung Chem. Phys. L ipids 1994 73 39. 28 V. G. Farafornov N. V. Voshcinnikov and V. V. Somsikov Appl. Opt. 1996 35 5412. 29 R. Lipowsky Encyclopedia Appl. Phys. 1998 23 199. 30 F. G. Schmidt F. Ziemann and E. Sackmann Eur. Biophys. J. 1996 24 348. Paper 8/06461J 125 Faraday Discuss. 1998 111 111»125