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DOI 10.1140/epje/i2013-13009-0 Regular Article Eur. Phys. J. E (2013) 36:9 T HE EUROPEAN P HYSICAL JOURNAL E Bilayer properties of giant magnetic liposomes formed by cationic pyridine amphiphile and probed by active deformation under magnetic forces O. Petrichenko 1 , K. ¯ Erglis 1 , A. C¯ ebers 1, a , A. Plotniece 2 and K. Pajuste 2 , G. B´ ealle 3 , Ch. M´ enager 3 , E. Dubois 3 , and R. Perzynski 3 1 University of Latvia, Zel ¸l ¸u-8, R¯ ıga, LV-1002, Latvia 2 Institute of Organic Synthesis, Aizkraukles 21, R¯ ıga, LV-1006, Latvia 3 UPMC University Paris 6 - PECSA UMR CNRS 7195, case 51, 4 place Jussieu, 75005 Paris, France Received 15 October 2012 and received in final form 4 January 2013 Published online: 30 January 2013 – c EDP Sciences / Societ`a Italiana di Fisica / Springer-Verlag 2013 Abstract. We synthesize giant magnetic liposomes by a reverse-phase evaporation method (REV) using a new self-assembling Cationic Pyridine Amphiphile (CPA) derived from 1,4-dihydropyridine as liposome- forming agent and a magnetic ferrofluid based on γ-Fe 2O3 nanoparticles. Having in view the potential interest of CPA in targeted transport by magnetic forces, the mechanical elastic properties of such bilayers are here directly investigated in vesicles loaded with magnetic nanoparticles. Bending elastic modulus K b 0.2 to 5kBT and pre-stress τ0 3.2 to 12·10 6 erg/cm 2 are deduced from the under-field deformations of the giant magnetic liposomes. The obtained K b values are discussed in terms of A. Wurgers’s theory. 1 Introduction Mechanical elastic properties of bilayers based on a new Cationic Pyridine Amphiphile (CPA) derived from 1,4-dihydropyridine (1,4-DHP) are here explored via the under-field deformation of giant magnetic liposomes formed with this liposome-forming agent. Indeed cationic amphiphiles synthesized on the basis of 1,4-DHP deriva- tives are known to spontaneously self-assemble into nanoaggregates in an aqueous environment, as lipid-like compounds, due to the presence of both a hydrophobic and a hydrophilic part in the molecule. The liposomes resulting from this self-association can be used for DNA transfection into cells [1]. Indeed the positively charged surface of these cationic liposomes easily interacts with the negatively charged cell surface and makes them effi- cient cargos for material introduction inside cells [2]. It has been shown in [1] that dodecyloxycarbonyl sub- stituents as hydrophobic moiety at positions 3 and 5 of the 1,4-DHP ring are optimal for high transfection efficiencies in vitro. In particular 1,1 -[(3,5-didodecyloxycarbonyl- 4-phenyl-1,4-dihydropyridine-2,6-diyl)dimethylen]- bispyridinium dibromide (called CPA further on) derived from 1,4-DHP which is used here (see fig. 1), is actually more active than the commercially available cationic lipid DOTAP (N-(1-(2,3-dioleoyloxy)propyl)-N,N,N- trimethylammonium methylsulfate) and cationic polymer a e-mail: [email protected] PEI 25 (polyethyleneimine of 25 kDa) for the transfer of β-galactosidase gene into fibroblasts (CV1-P) and retinal pigment epithelial (D 4O7) cell lines in vitro [1, 3, 4]. In addition 1,4-dihydropyridine cycle acts as active linker in this molecule. According to [5], 1,4-DHP nucleus is a privileged structure with intrinsic characteristics adapted for transport of pharmacologically active compounds and commercial drugs, some in vivo tests being in progress. For example 1,4-DHP derivatives are known as calcium channel blockers in the therapy of cardiovascular dis- eases [6,7]. They possess a broad range of other biological activities, for example, antioxidant [8], antiradical [9] anticancer [10], neuroprotective [11], antibacterial [12] and reversal of multidrug resistance [13, 14]. However mechanical elastic properties of such bilayers based on these cationic amphiphiles are not yet known, while they are key parameters for the cellular internalisation processes as quoted in [15]. Indeed in this latter work [15], it is shown that the cellular uptake of liposomes may largely depend on the liposome bending elasticity and pre-stress tension. Moreover the very unusual large size of the polar head of these cationic amphiphiles with C 12 hydrophobic chains leads us to hypothesize unusually small bending rigidity modulus if to follow A. Wurger’s theory developed in [16, 17]. Magnetic liposomes for their part are liposomes filled up with a magnetic fluid. They are attracting the interest of bioresearchers due to their numerous applications [18], for example ultra small and small ones (typically 10 to

Bilayer properties of giant magnetic liposomes formed by cationic pyridine amphiphile and probed by active deformation under magnetic forces

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DOI 10.1140/epje/i2013-13009-0

Regular Article

Eur. Phys. J. E (2013) 36: 9 THE EUROPEANPHYSICAL JOURNAL E

Bilayer properties of giant magnetic liposomes formed by cationicpyridine amphiphile and probed by active deformation undermagnetic forces

O. Petrichenko1, K. Erglis1, A. Cebers1,a, A. Plotniece2 and K. Pajuste2, G. Bealle3, Ch. Menager3, E. Dubois3, andR. Perzynski3

1 University of Latvia, Zellu-8, Rıga, LV-1002, Latvia2 Institute of Organic Synthesis, Aizkraukles 21, Rıga, LV-1006, Latvia3 UPMC University Paris 6 - PECSA UMR CNRS 7195, case 51, 4 place Jussieu, 75005 Paris, France

Received 15 October 2012 and received in final form 4 January 2013Published online: 30 January 2013 – c© EDP Sciences / Societa Italiana di Fisica / Springer-Verlag 2013

Abstract. We synthesize giant magnetic liposomes by a reverse-phase evaporation method (REV) using anew self-assembling Cationic Pyridine Amphiphile (CPA) derived from 1,4-dihydropyridine as liposome-forming agent and a magnetic ferrofluid based on γ-Fe2O3 nanoparticles. Having in view the potentialinterest of CPA in targeted transport by magnetic forces, the mechanical elastic properties of such bilayersare here directly investigated in vesicles loaded with magnetic nanoparticles. Bending elastic modulusKb ∼ 0.2 to 5kBT and pre-stress τ0 ∼ 3.2 to 12·10−6 erg/cm2 are deduced from the under-field deformationsof the giant magnetic liposomes. The obtained Kb values are discussed in terms of A. Wurgers’s theory.

1 Introduction

Mechanical elastic properties of bilayers based on anew Cationic Pyridine Amphiphile (CPA) derived from1,4-dihydropyridine (1,4-DHP) are here explored viathe under-field deformation of giant magnetic liposomesformed with this liposome-forming agent. Indeed cationicamphiphiles synthesized on the basis of 1,4-DHP deriva-tives are known to spontaneously self-assemble intonanoaggregates in an aqueous environment, as lipid-likecompounds, due to the presence of both a hydrophobicand a hydrophilic part in the molecule. The liposomesresulting from this self-association can be used for DNAtransfection into cells [1]. Indeed the positively chargedsurface of these cationic liposomes easily interacts withthe negatively charged cell surface and makes them effi-cient cargos for material introduction inside cells [2].

It has been shown in [1] that dodecyloxycarbonyl sub-stituents as hydrophobic moiety at positions 3 and 5 of the1,4-DHP ring are optimal for high transfection efficienciesin vitro. In particular 1,1′-[(3,5-didodecyloxycarbonyl-4-phenyl-1,4-dihydropyridine-2,6-diyl)dimethylen]-bispyridinium dibromide (called CPA further on) derivedfrom 1,4-DHP which is used here (see fig. 1), is actuallymore active than the commercially available cationiclipid DOTAP (N-(1-(2,3-dioleoyloxy)propyl)-N,N,N-trimethylammonium methylsulfate) and cationic polymer

a e-mail: [email protected]

PEI 25 (polyethyleneimine of 25 kDa) for the transfer ofβ-galactosidase gene into fibroblasts (CV1-P) and retinalpigment epithelial (D 4O7) cell lines in vitro [1, 3, 4]. Inaddition 1,4-dihydropyridine cycle acts as active linkerin this molecule. According to [5], 1,4-DHP nucleus is aprivileged structure with intrinsic characteristics adaptedfor transport of pharmacologically active compounds andcommercial drugs, some in vivo tests being in progress.For example 1,4-DHP derivatives are known as calciumchannel blockers in the therapy of cardiovascular dis-eases [6,7]. They possess a broad range of other biologicalactivities, for example, antioxidant [8], antiradical [9]anticancer [10], neuroprotective [11], antibacterial [12]and reversal of multidrug resistance [13, 14]. Howevermechanical elastic properties of such bilayers based onthese cationic amphiphiles are not yet known, whilethey are key parameters for the cellular internalisationprocesses as quoted in [15]. Indeed in this latter work [15],it is shown that the cellular uptake of liposomes maylargely depend on the liposome bending elasticity andpre-stress tension. Moreover the very unusual large sizeof the polar head of these cationic amphiphiles with C12

hydrophobic chains leads us to hypothesize unusuallysmall bending rigidity modulus if to follow A. Wurger’stheory developed in [16,17].

Magnetic liposomes for their part are liposomes filledup with a magnetic fluid. They are attracting the interestof bioresearchers due to their numerous applications [18],for example ultra small and small ones (typically 10 to

Page 2 of 7 Eur. Phys. J. E (2013) 36: 9

Fig. 1. Structure of 1,1′-[(3,5-didodecyloxycarbonyl-4-phenyl-1,4-dihydropyridine-2,6-diyl)dimethylen]-bispyridinium dibro-mide (CPA) [1].

100 nm in size) for their use as contrast agents in mag-netic resonance imaging [19] (MRI), hyperthermic treat-ments [20], magnetic guiding [21] and for targeted drugtransport [22,23]. With the purpose of using products witha low toxicity for applications in medicine, in particularfor hyperthermia and magnetic transport of drugs, thecurrent choice is to use a magnetic fluid based on γ-Fe2O3

nanoparticles (NPs) dispersed in an aqueous medium.Synthesizing cationic magnetic liposomes based on CPAderived from 1,4-DHP in the size range 50–100 nm, will bedone in a near future in order to associate the magneticproperties of the internalized magnetic nanoparticles andthe cationic properties of the external bilayer of the li-posome. However what we propose here, derives from aslightly different choice. Our study is motivated by thefact that an important issue for cellular targetting of li-posomes is their uptake by cells [24] and thus their elas-tic properties [15]. Since the size of liposomes used forgene delivery is typically around 100 nm [2] the measure-ment of their elastic properties is difficult. We propose tosynthesize giant magnetic vesicles of CPA and study theflattening of their thermal undulations in an applied mag-netic field by optical microscopy to determine the bendingelastic modulus of the membrane and its pre-stress. Thisactive method of measurement of the CPA membrane elas-ticity looks especially interesting due to the potential ap-plication of CPA in gene delivery by magnetofection [1], asvesicles already loaded with NPs are here probed under-field.

Since the pioneering work of [25], a well-known methodof measurement of the bending modulus of bilayers is tostudy the deformations of unswollen giant vesicles whileflattening the thermal undulations of their membrane. Asimilar active method has been developed later on, todeduce the properties of bilayers based on different am-phiphiles by filling up the vesicles with a dilute magneticfluid that does not interact with the membrane, thus pro-ducing a giant magnetic liposome and by applying mag-netic forces to the membranes [26–28]. This has been ex-tended to the case of smaller vesicles with strong magneticproperties, namely the magnetic endosomes formed by thepinocytosis pathway of incorporating magnetic nanopar-ticles in living cells [29].

We thus propose here to synthesize giant cationic mag-netic liposomes based on Cationic Pyridine Amphiphilederived from 1,4-DHP, which are much larger in size (ofthe order of 10 μm) than the ones obtained in [1] to quan-tify their under-field deformation and then reach the bend-

ing modulus and the pre-stress of their bilayer. We firstpresent our various experiments to synthesize, character-ize and follow the under-field deformation of our cationicmagnetic liposomes. Then we develop our analysis anddiscuss the experimental determinations in terms of thepredictions of [16]. Cationic magnetic liposomes based onthe Cationic Pyridine Amphiphile derived from 1,4-DHPemerge as a model system to test these predictions.

2 Materials and methods

2.1 Synthesis of the Cationic Pyridine Amphiphile

The self-assembling Cationic Pyridine Amphiphile derivedfrom 1,4-DHP of molar mass 925.94 g/mol (CPA) is ob-tained according to the method described by Pajuste et al.in [30]. The purity of the studied compound was at least98% according to high performance liquid chromatogra-phy (HPLC) data. This amphiphile molecule (see fig. 1),which presents two C12 chains has a length lC ∼ 17 A [31]with a rather large polar head a ∼ 120 A2, as measuredat pH = 7 and 10−2 M of KBr in a Langmuir-Blodgettmethod [32]. Its packing parameter is thus of the order of0.4–0.8 justifying its self-assembling in bilayers and lipo-somes.

2.2 Synthesis of the ferrofluid to be used for thepreparation of magnetic liposomes

An aqueous and acidic ferrofluid, based on γ-Fe2O3 nano-particles, is used to synthesize the magnetic liposomes(here also called vesicles). The magnetic nanoparticlesare produced by precipitating anionic magnetite (Fe3O4)from aqueous solutions of Fe2+ and Fe3+ chlorides usingammonium hydroxide [33]. After the precipitation step,the nanoparticles are further oxidized from Fe3O4 to γ-Fe2O3 with a Fe(NO3)3 solution [34]. The ferrofluid is thenobtained by peptizing the collected nanoparticles in anacidic aqueous medium at pH ∼ 1.5. The volume fractionΦFF = 1.8% of the dispersion is obtained by iron concen-tration colorimetric determination (with 5-Sulfosalicilicacid dihydrate) (Fe concentration 1.2 M) and the ferrofluiddensity is determined to be ρ = 1.07 g/cm3. The magneti-zation curve of this dispersion (see fig. 2) is obtained witha vibrating sample magnetometer (Lake Shore Cryotron-ics, Inc., model 7404 VSM) and the software for processingthe magnetization data. The most probable magnetic di-ameter of the nanoparticles is determined to be 14 nm byadjusting the magnetization curve of this dilute ferrofluidto a Langevin formalism weighted by the size distributionof the nanoparticles.

2.3 Preparation of the Cationic Magnetic Liposomes

The magnetic liposomes are synthesized using a REVmethod (reverse-phase evaporation) at room temperature,similar to that described in [35].

Eur. Phys. J. E (2013) 36: 9 Page 3 of 7

Fig. 2. Magnetization curve M(H) of the initial ferrofluid(ΦFF = 1.8%) used for the synthesis of the Cationic MagneticLiposomes.

In a first step, an emulsion is prepared. A mothersolution of the lipid (CPA dissolved in chloroform at10 mg/mL) is prepared. Then 0.3 to 1 mL of this mothersolution (corresponding to 3 to 10 mg of CPA) are intro-duced in 3 mL of ether and 2 mL of chloroform. Then 1 mLof the ferrofluid with Fe concentration 1.2 M and pH ∼ 1.5is added. This mixture is submitted to ultrasounds witha Bandelin Sonorex ultrasound bath (frequency 35 kHz)during 20 min.

In a second step, chloroform and ether are evaporatedfrom the emulsion in a rotary evaporator under reducedpressure and Cationic Magnetic Liposomes (vesicles) re-main dispersed in the solution. During the evaporationstep, the emulsion passes through a viscous gel form [36]and subsequently becomes an aqueous suspension. Theevaporation time may vary from 25 to 45 min. It dependson the volume of organic phase. At this step of the tech-nique, chloroform or ether are just remaining as very weaktraces, as attested by the in vivo experiments (which areextremely sensitive to such traces) performed in [35] withsmaller liposomes prepared with a different amphiphileand following the same pathway.

In a third step, the 0.5 mL of the dispersion are di-luted with 1 mL of water and a magnetic sorting of the bigmagnetic objects (the synthesized vesicles) is performedin a syringe above a strong permanent magnet. The freenanoparticles outside the vesicles are eliminated at thisstep of the synthesis.

Note that, at the end of the process, the ferrofluid en-closed inside the vesicles has the same size distribution ofnanoparticles as the initial ferrofluid but that it is dilutedby a factor α which is smaller than 1.

Several dispersions of Cationic Magnetic Liposomesare thus prepared following this method with differentamounts of CPA. Their characteristics are collected in ta-ble 1. The dispersions of Cationic Magnetic Liposomesare then observed by Transmission Electron Microscopy(TEM) (JEM-1230 TEM at 100 kV) (see fig. 3) and underan inverse micoscope Leica DMI13000 B. The typical sizesof magnetic liposomes observed by TEM are smaller than

Fig. 3. TEM images of the magnetic vesicles prepared usingREV method. (a) from sample A and (b) from B of table 1.

Table 1. Characteristics of the probed dispersions: CCPA num-ber of moles of CPA in the mother solution used during thesynthesis; α mean value of dilution factor α (see eq. (3) andfig. 5) of the ferrofluid in the Cationic Magnetic Liposomes asmeasured by magnetophoresis.

Sample CCPA (mol/l) α

A 9.72 · 10−3 0.104

B 8.64 · 10−3 0.098

C 7.56 · 10−3 0.100

D 3.24 · 10−3 0.085

those obtained by optical microscopy, the largest vesiclesbeing destroyed during the TEM processing. The typicaldiameter of the optically observed vesicles is of the order5–20 μm.

2.4 Deformations of the Cationic Magnetic Liposomesunder a uniform magnetic field

The dispersions containing the vesicles are put in an op-tical cell of thickness 65 μm. The deformation of the vesi-cles under a homogeneous field is followed by opticalmicroscopy at room temperature, by taking phase con-trast images with a further processing using ImageJ pro-gram [37]. The homogeneous magnetic field is created byfour coils with 368 turns of 0.7 mm wire for each coil,giving a total magnetic field H of strength in the range0–200 Oe. Typical images of the deformation of a vesicle(vesicle B1 from table 2) at different magnetic fields arepresented in fig. 4. In this experiment the deformationof the vesicles of table 2 is recorded as a function of the

Table 2. Characteristics of the studied Cationic Magnetic Li-posomes: D0 diameter; Kb bending elastic constant; τ0 pre-stress of the bilayer in zero applied field.

Vesicle D0 (μm) Kb/kBT τ0 (erg/cm2)

A1 11.3 2 5.0 · 10−6

B1 7.0 1.4 3.2 · 10−6

B2 12.5 4.8 4.6 · 10−6

C1 7.0 0.22 7.2 · 10−6

D1 11.9 0.77 1.2 · 10−5

Page 4 of 7 Eur. Phys. J. E (2013) 36: 9

Fig. 4. Deformation of a vesicle with apparent diameter D0 =7 μm. (Vesicle B1 from table 2.)

applied field H. Their individual deformation is here mea-sured, the main difficulty of the method resulting from thefrequent chaining of several vesicles during the slow fieldevolution.

2.5 Magnetophoresis of the Cationic MagneticLiposomes

A second experiment is performed under optical mi-croscopy to characterize the magnetic properties of theferrofuid enclosed in the Cationic Magnetic Liposomes anddetermine the dilution factor α. A magnetophoresis of thevesicles in a non-homogeneous magnetic field is carriedout at room temperature. The same optical cell contain-ing the dispersion of magnetic vesicles is placed in a fieldgradient dH/dx = 360 Oe/cm with a mean magnetic fieldstrength Hm = 630 Oe, which is created by a permanentmagnet. The velocity of the vesicle motion v is obtainedby taking images with the same inverted microscope andfurther processing by ImageJ. The analysis is performedfor different vesicles one by one and the magnetic momentmves of the studied vesicle at field Hm is deduced fromthe velocity of the vesicle motion in the non-homogeneousfield. It is determined by the balance of forces which re-sults from the field gradient mves(Hm)dH/dx [38] and thehydrodynamic drag given by the Stokes formula −3πηDv.As a result we obtain for the vesicle magnetic moment

mves(Hm) =3πηDv

dH/dx, (1)

where η is the viscosity of the carrier medium, here water,and D the hydrodynamic diameter of the vesicle, here as-similated to its apparent diameter D0 measured by opticalmicroscopy in zero field. The magnetization of a ferrofluidunder a given applied magnetic field H is directly propor-tional to the NPs volume fraction that it contains. Thedilution parameter α of the studied vesicle, ratio of the

Fig. 5. Dilution factor α = Mves/MFF as a function of thediameter D0 of the probed vesicles in sample D of table 1;mean value of the dilution factor α = 0.085.

NPs volume fraction Φves of the dilute ferrofluid enclosedin the vesicle to the NPs volume fraction ΦFF of the fer-rofluid initially used in the first synthesis step, can thusbe written as

α =Φves

ΦFF=

Mves(Hm)MFF(Hm)

, (2)

where Mves(Hm) is the magnetization of the dilute fer-rofluid enclosed in the vesicle at H = Hm. Moreover ifVves is the volume of the vesicle, its magnetic moment atH = Hm writes as mves(Hm) = VvesMves(Hm). The dilu-tion parameter α = Φves/ΦFF of the studied vesicle canthen be directly deduced from

α =mves(Hm)

VvesMFF (Hm). (3)

Using in eq. (3) the magnetization curve shown in fig. 2and eq. (1), the dilution factor α is obtained for severalvesicles of diameter D0 ranging between 5 μm and 20 μm,taken from the different dispersions of table 1. The resultsobtained with sample B are shown in fig. 5 demonstratingthe important diminution of the concentration of magneticnanoparticles in the Cationic Magnetic Liposomes withrespect to the concentration of the initial magnetic colloidused to synthesize these magnetic vesicles.

It is observed that the dilution factor α varies from onevesicle to another inside the same dispersion and that itsvalue is not correlated with the diameter D0 of the probedvesicle. In table 1, α the mean value of α is reported foreach of the probed dispersions. For all the dispersions,α is of the order of 10−1 meaning a volume fraction ofnanoparticles inside the vesicles Φves of the order of 0.2%.

3 Mechanical properties of Cationic MagneticLiposomes

The deformation in a homogeneous magnetic field ofunswollen giant magnetic liposomes based on more stan-dard phospholipids filled up with a dilute magnetic fluid

Eur. Phys. J. E (2013) 36: 9 Page 5 of 7

that does not interact with the membrane has been stud-ied in [25,27,28]. The obtained values of the bending mod-ulus Kb were in the range 10–20kBT . We develop herean analogous method of analysis, valid in large fields asin [29].

Assimilating the vesicle shape under a uniform appliedfield H with an ellipsoid of eccentricity e =

√1 − (b/a)2

(b and a, respectively, short and long axes of the ellip-soid) and homogeneous internal field Hint, the relationbetween the eccentricity e, the internal vesicle magnetiza-tion Mves(Hint) and the tension τ(Hint) of its bilayer wasderived in [39] by the virial method

M2vesD0

τ=

h(e) , (4)

where D0 is the apparent diameter of the vesicle and thefunction h(e) reads

h(e)=(3−2e2)(1−e2)1/2/e2 − (3 − 4e2) arcsin (e)/e3

(1 − e2)7/6((3 − e2) log ((1 + e)/(1−e))/e5− 6/e4).

The magnetization Mves of the vesicle and its ten-sion τ are both determined by the internal field Hint =H − 4πN(e)Mves in the ellipsoidal vesicle, where N(e) isthe demagnetization factor of the ellipsoid. However, sincethe magnetic properties of the vesicles are rather weak, weneglect here the correction for the demagnetizing field in-side the vesicles and we assume in the following Hint = H.

An important feature of the deformation of unswollenvesicles is the increase of the bilayer tension as the thermalundulations flatten [25,40]

τ = τ0 exp

(8πKb

kBT

ΔΣ

Σ0

)

. (5)

Here the tension τ0 expresses the pre-stress of the mem-brane in zero field while τ is the under-field tension, Σ0 isthe zero-field apparent surface of the vesicle and ΔΣ theunder-field increase of apparent surface. For an ellipsoidalshape, we get

ΔΣ

Σ0=

arcsin (e)/e + (1 − e2)1/2

2(1 − e2)1/6− 1 = f(e) . (6)

Thus expressing Mves as a function of the magnetizationMFF of the initial ferrofluid used in the synthesis processand of the dilution parameter α of the nanoparticles insidethe vesicle, we obtain from eqs. (4), (5) and (6)

M2FF =

h(e)πα2D0

τ0 exp

(8πKb

kBTf(e)

)

, (7)

where both e and MFF are field-dependent. Using the mag-netization curve MFF(H) of fig. 2, the data pair (e, H) isthen transformed in a data pair (e, MFF) to be fitted byeq. (7) with the function c1h(e) exp (c2f(e)).

In this fitting process, the deduced parameters c1 andc2 are, respectively, related to the pre-stress of the mem-brane τ0 and to the bending modulus Kb, namely

Fig. 6. Under-field deformation e(H) of vesicle B1 with ap-parent diameter D0 = 7 μm (black circles) and vesicle D1 withapparent diameter D0 = 11.9 μm (empty circles) from table 2.Full lines is the adjustment by eq. (7) —see text and table 2for the adjusted values of Kb and τ0.

Kb =c2

8πkBT , (8)

τ0 = πD0c1α2 . (9)

As an illustration, the resulting fits of the data for vesi-cles B1 and D1 are compared to the experimental resultsin the plots e = f(H) presented in fig. 6. Table 2 col-lects the values of the deduced bending modulus Kb/kBTobtained from these fits for the various probed vesicles.These values of Kb ranging between 0.22 and 5kBT arerather low. They are discussed further on.

Table 2 also gives the obtained values of τ0, the pre-stress of the membrane in zero field. It is obtained byreplacing in eqs. (9), as said ahead, the unknown dilutionfactor α of the given vesicle by the mean value α measuredby magnetophoresis in the sample. The quite large disper-sion of α values around α imparts these values of τ0 with aquite large error bar. However the order of magnitude of τ0

is reliable. We find here τ0 ∼ 10−6–10−5 erg/cm2, whichis in perfect agreement with data obtained for differentbilayers of amphiphiles [40].

Let us note that the obtained values Kb and τ0 are con-sistent with the absence of NPs adsorption on the mem-brane. Indeed such a process would have considerably stiff-ened the membrane.

4 Discussion

The low values of the bending modulus obtained by ourmethod deserve further discussion. Similar values of thebending modulus were observed previously for giant vesi-cles with addition of non-ionic surfactant [28] or a catan-ionic one [41]. To obtain Kb of the order of kBT (or a frac-tion of it) in bilayers based on a single amphiphile moleculeis much more unusual [42]. This point has to be connectedwith the morphology of this bicatenary amphiphile witha rather large polar head and C12 hydrophobic chains.

Page 6 of 7 Eur. Phys. J. E (2013) 36: 9

Fig. 7. Kb/kBT versus a as deduced from eq. (11), from [16,17].

The bending modulus Kb of a bilayer strongly dependson the length of the hydrophobic chain L and on the po-lar head surface area a of the amphiphile [17]. Follow-ing A. Wurger’s description [16], mainly concerned withthe hydrophic tails contribution, Kb is related with themolecules configurations in the bilayer and their internaldegrees of freedom. Two terms enter in this description ofKb. The first term of entropic origin writes

K(1)b = kBT

L2

a, (10)

while the second contribution, related to the interactionpair potential between hydrophobic tails, writes

K(2)b =

L3

24adρ2u′′(ρ) (11)

with d = 1.27 A the length of a methyl group (here L =12d) and u(ρ) the energy density of the interaction definedper methyl unit, that can be described by a Lennard-Jonespotential. Using A. Wurger’s notations as in [17], Kb =K

(1)b + K

(2)b reads

kBTL2

a+

L3

24ad

εσ2

ρ20 − σ2

(1565

[1−

( σ

ρ0

)10]−42

[1−

( σ

ρ0

)4]),

(12)

where ρ0 =√

2a/√

3 is the nearest-neighbor distance inthe dense packing approximation, ε = 4.3 meV and σ =3.9 A being the Lennard-Jones parameters of a surfactantmethyl group (see [17]).

Figure 7 plots Kb/kBT as a function of the surfaceof the polar head a for L = 12d. Kb/kBT appears asa steeply decreasing function of a. For a = 120 A2, thesurface of the polar head of CPA experimentally derivedin [32], eq. (11) predicts Kb/kBT = 1.72, a value close tothe mean value 1.8 of our measurements. It would be inter-esting to probe this model with various CPA of differenthydrophobic chain lengths.

5 Conclusions

Giant cationic magnetic liposomes based on Cationic Pyri-dine Amphiphile derived from 1,4-DHP (CPA), with acharacteristic size 5–20 μm are synthesized here. By ana-lyzing their response to a field gradient in a magnetophore-sis experiment, we show that the ferrofluid they encapsu-late has a typical volume fraction ∼ 0.2% in magneticnanoparticles —approximately ten times less than that ofused ferrofluid. By analyzing their deformation under auniform magnetic field, we deduce the mechanical prop-erties of their membrane. Namely their bending modulusKb is found to be of the order of 2kBT on average andtheir pre-stress τ0 ∼ 10−6–10−5 erg/cm2. The low valuesof Kb found here are well explained in the framework ofA. Wurger’s model, taking in account the hydrophic tailscontribution and the unusually large polar head of thisamphiphile. The values of the pre-stress of the bilayersare consistent with the data in the literature for bilayersof different lipids.

Characterizations of bilayers and studies of auto-organization properties of CPA tested here may be im-portant in its application for delivery of plasmid DNA(pDNA) into target cell in vitro and, in future, in vivo.It is shown in this study that CPA may be used for thesynthesis of magnetic liposomes with a low bending mod-ulus close to kBT . Confirmation of this by other methodsof bending modulus measurements (for example by directregistration of membrane fluctuations) is pending for otherworks. The next step will be to synthesize smaller mag-netic liposomes, typically 50–100 nm in size, for a phar-macologically active transport molecule, with a predictedapplication for DNA transport by magnetofection.

This work was supported by OSMOSE program No 22497YE; the ESF projects No. 2009/0223/1DP/1.1.1.2.0/09/APIA/VIAA/008 at Latvian University (LU) and No. 2009/0197/1DP/1.1.1.2.0/09/APIA/VIAA/014 at Latvian Instituteof Organic Synthesis (OSI). The authors also are grateful toM.M. Maiorov from the Institute of Physics, LU for the mag-netic measurements, to S. Cribier from LBM–UPMC–Paris 6and V. Ose from the Latvian Biomedical Research and StudyCentre for image obtained on TEM. L.Q. Amaral from USP–Brazil and R. Danne from OSI for fruitful discussions.

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