Role of Multivalent Cations in the Self-Assembly of Phospholipid−DNA

J. Phys. Chem. B 2007, 111, 14233-14238

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Role of Multivalent Cations in the Self-Assembly of Phospholipid-DNA Complexes Guillaume Tresset,*,† Wun Chet Davy Cheong,‡ and Yeng Ming Lam§ Institute of Bioengineering and Nanotechnology, 31 Biopolis Way, The Nanos 04-01, Singapore 138669, Institute of Materials Research and Engineering, 3 Research Link, Singapore 117602, and School of Materials Science and Engineering, Nanyang Technological UniVersity, Block N4.1, Nanyang AVenue, Singapore 639798 ReceiVed: August 6, 2007; In Final Form: October 2, 2007

In view of efficient and nontoxic delivery of genes to cells, complexes made of phospholipids (noncationic) and DNA are assembled through the mediation of multivalent cations. The association of lipids with DNA is explained through the charge reversal of lipid headgroups by specific adsorption of cations. The ion binding is quantified by the Gouy-Chapman-Stern theory which provides a good estimate for the minimal concentration of cations required to produce complexes. Coarse-grained Monte Carlo calculations support X-ray diffraction experiments in the sense that lipids form inverted micelles around hexagonally arranged DNA rods, with cations in between to maintain the cohesion. The complexes are more cohesive in terms of total free energy as the cation valence increases. The presented methodology may help develop predictive models for biomolecular self-assembled systems.

Introduction The compaction of DNAsand more generally, of nucleic acidssis a ubiquitous phenomenon in biological systems carrying genetic information. Because DNA is negatively charged under physiological conditions, a strong electrostatic barrier of repulsion must be overcome to accommodate it into the confined space of a cell nucleus or of a viral capsid.1,2 In the particular application of non-viral gene delivery, the tight packing of nucleic acid, indispensable for an efficient uptake by cells, is generally achieved by complexation with a positively charged entity such as polymers, peptides, lipids, or a combination thereof.3-5 Cationic lipid-DNA complexes consist of supramolecular assemblies of DNA strands which are either sandwiched between stacks of lipid bilayers or coated by lipid monolayers and arranged on a two-dimensional hexagonal lattice.6-10 Since their discovery by Felgner and co-workers in 1987,11 they have been intensively studied as promising nonviral gene delivery vectors.12-16 In spite of their ease of preparation, their absence of immunological response and the possibility to functionalize them for cell-specific targeting, cationic lipid-DNA complexes still suffer from a low efficiency of DNA transfer compared to their viral counterparts and more importantly, a high induced toxicity to cells.17 To cope with this issue, several groups have investigated the possibility of using zwitterionic or anionic lipidssespecially phospholipids, a natural compound of cell membranesinstead of cationic lipids which are believed to be increasingly toxic as their positive charge becomes high. The challenge is then to associate DNA and noncationic lipids in spite of unfavorable electrostatic interactions. It has been achieved mostly by the use of divalent cations. Investigations by small-angle X-ray scattering revealed that certain zwitterionic lipids could self-assemble with DNA through * To whom correspondence should be addressed. Phone: +65 6824 7176. Fax: +65 6478 9080. E-mail: [email protected]. † Institute of Bioengineering and Nanotechnology. ‡ Institute of Materials Research and Engineering. § Nanyang Technological University.

the mediation of divalent metal ions, and the resulting complexes exhibited a lamellar symmetry.18-22 Other type of zwitterionic lipids presenting a low bending modulus produced an inverted hexagonal structure instead,23 which is known to be more favorable for gene transfection in the case of cationic lipids.12,24 A complex polymorphism was observed with anionic lipids, where the lipid-DNA complexes underwent various phase transitions depending on the type and the concentration of divalent cations.25 Adsorption of DNA on a monolayer of zwitterionic lipids in the presence of Ca2+ or Mg2+ was investigated by a range of optical techniques; it was shown for example that the interaxial spacing of adsorbed DNA strands differs according to ions, demonstrating an ion specificity in the interactions between lipids and DNA.26 Phospholipids have shown a promising potential for gene delivery into cultured cells,27 especially when they are associated to DNA by trivalent or tetravalent cations.28 In the present work, we focus on the interactions between phospholipids and multivalent cations and their consequences on complexation with DNA. The ion adsorption is investigated by electrophoretic mobility and interpreted in terms of the Gouy-Chapman-Stern theory. We find by small-angle X-ray scattering that this adsorption theory can account for the onset of lipid-DNA complexation as the ion concentration increases. Monte Carlo simulations reproduce the three-dimensional structure of selfassembled complexes and provide us with quantitative information on cohesion. We anticipate that our methodology and findings will trigger further studies on phospholipid-DNA complexes and, to a larger extent, on the self-assembly of biomolecular systems. Experimental Methods Liposome Preparation. The lipids were purchased from Avanti Polar Lipids (Alabaster, AL), and stored at -20 °C in a mixture of chloroform and methanol 2:1 (v/v). Liposomes were prepared by drying the desired lipids with a vacuum rotary evaporator in a round-bottom flask dipping in a 42 °C water bath. To ensure a thorough evaporation of the organic solvent,

10.1021/jp0762830 CCC: $37.00 © 2007 American Chemical Society Published on Web 12/07/2007

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Figure 1. Surface potentials of DOPE liposomes with varying concentration of Ca2+. The solution comprises a 2:1 electrolyte (CaCl2) and 2 mM monovalent salt (Tris, pH 7.0). The experimental surface potentials (b) are computed from ζ potential measurements by solving the Poisson-Boltzmann equation within a Stern layer of thickness δ ) 1 Å. The solid lines are numerical solutions of eqs 1 and 2 by considering either no binding of Ca2+ to lipids or an adsorption with binding constant K ) 4.02 M-1 and density of binding sites N ) 0.627 nm-2. The intrinsic surface charge density is taken as σ0 ) -0.0025 C‚m-2, which corresponds to about one negative charge for a hundred lipid headgroups with an area of 70 Å.2 The dashed lines delimit a region in which the binding parameters vary by δK ) (1.1 M-1 and δN ) (0.148 nm-2 around the above-mentioned values. The inset shows the theoretical net surface charge density of liposomes versus Ca2+ concentration obtained from eqs 1 and 2 with adsorption of Ca2+.

Figure 2. Small-angle X-ray scattering pattern of DOPE-DNA complexes with 200 mM of Ca2+ and L/D ) 7. The solid lines are Lorentzian fitting functions. The integers in parentheses are Miller indices.

the flask was left overnight in a vacuum chamber. The dry lipids were hydrated for at least 2 h by either Millipore (Billerica, MA) sterilized water at 5 mg/mL for X-ray diffraction experiments or by 2 mM Tris, pH 7.0, at 0.5 mg/mL for electrophoretic mobility measurements. The size of the liposomes was subsequently reduced to ∼100 nm by 10 min tip sonication in ice, and the resulting solution was filtered through a 0.2 µm

Tresset et al.

Figure 3. Binding of La3+ on DOPE and complexation with λ-DNA. (A) Surface potential of DOPE liposomes in the presence of La3+. Experimental data (b) are computed from measured ζ potential by solving the Poisson-Boltzmann equation with a 1 Å thick Stern layer. The solid line is the theoretical prediction from eqs 1 and 2 with K ) 450 M-1, N ) 0.323 nm-2, and σ0 ) -0.0025 C‚m-2. (B) Electrophoretic mobility of λ-DNA versus [La3+]. (C) Small-angle X-ray scattering patterns of DOPE-DNA complexes with various concentrations of La3+. The experimental data are fitted with a sum of Lorentzian functions.

polycarbonate membrane to remove any metal particle. The liposome solution could be stored at 4 °C for several months. Electrophoretic Mobility. Liposomes were diluted in 2 mM Tris, pH 7.0, with the desired cations to a final concentration of 0.1 mg/mL. After several hours for equilibration, the liposomes were introduced into a ZetaPALS system from Brookhaven Instruments (Holtsville, NY). The ζ potentials, or potentials at the hydrodynamic plane of shear, were deduced from the mobility measurements by the Smoluchowski model. X-ray Diffraction. Liposomes (5 mg/mL) and precipitated λ-DNA (Roche Applied Science, Singapore) were mixed thoroughly in a desired ratio prior to addition of cations in their chloride form (CaCl2 and LaCl3). The complexes were allowed from several hours to a couple of days to fully equilibrate. The small-angle X-ray scattering experiments were performed with the SAXSess instrument from Anton Paar GmbH (Graz, Austria) and the PW3830 laboratory X-ray generator (40 kV, 50 mA) with a long, fine-focus, sealed X-ray tube (Cu KR wavelength of λ ) 0.1542 nm) from PANalytical (Almelo, The Netherlands). The scattered image was scanned by the two-dimensional imaging-plate reader Cyclone from Perkin-Elmer (Wellesley, MA). The precipitate of phospholipid-DNA complexes was sandwiched in a Kapton cell after removing as much liquid in

Self-Assembly of Phospholipid-DNA Complexes excess as possible with filter paper. The X-ray exposure was carried out in the slit configuration with a solid sample holder during 20 min. Monte Carlo Simulations. The simulations were inspired by the studies of Farago and co-workers for fluid bilayer membranes29 and cationic lipid-DNA complexes.30,31 Lipids were simulated with a coarse-grained water-free model consisting of one hydrophilic and two hydrophobic spheres with shortrange pair interactions between them. The size of each lipid sphere was set to 6.3 Å. Unlike the work of Farago and coworkers, our lipid membranes needed a bending modulus much lower to be able to form a hexagonal structure. Therefore we modified the energy coefficients of the pair potentials between some lipid spheres in order to give more flexibility to the whole molecule, namely, 13 ) 2kBT and 23 ) 3.75kBT with kB the Boltzmann constant and T the temperature. The hydrophilic spheres carried one dipole moment of 5 e‚Å, oriented along the axis of lipid molecules with the positive charge pointing outward so as to mimic the 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE) lipids. The Lennard-Jones pair potentials of lipids are fully described elsewhere.29 Only one species of ion in solution was considered, and the ion diameter was fixed at Dion ) 2 Å. DNA was modeled as an infinitely long rigid rod with a uniform axial charge λDNA ) -0.59 e‚Å-1 and a diameter DDNA ) 20 Å. Its position was fixed in all simulations. It interacted with ions through the following pair potential:

[(

Uion-DNA(r) ) 50kBT

) ]

Dion + DDNA 2r

12

-1 -

zioneλDNA ln(r) 2π0

where Dion and zion stand for the diameter and the valence of the ion in consideration, r is the distance ion-DNA, and  and 0 are the dielectric constant and the permittivity of free space, respectively. The first term of the potential accounts for the hard core repulsion while the second term arises from the electrostatic interaction. For the interaction with hydrophobic lipid spheres, only the hard core repulsion term was considered, and for the interaction with zwitterionic lipid spheres, the second term was modified as -eλDNA/(2π0) ln(r+/r- ), with r+ and r- being the distances between the axis of DNA and the dipolar charges of lipids. The pair potential for the ion-ion interaction took a similar form:

( )

Dion Uion-ion(r) ) 4kBT r

12

zion2e2 + 4π0r

Similarly, only the hard core repulsion term was retained for the interaction between ions and hydrophobic lipid spheres, while the second term was taken as zione2/(4π0)(1/r+ - 1/r-) for the interaction with the dipolar charges of lipids. Each step in the canonical ensemble Monte Carlo simulation used to generate the self-assembly of the lipids and cations consisted of an attempt to translate and rotate each lipid molecule. The size of the simulation box with one DNA rod was 80 × 80 Å, and 216 lipids and cations were used in the simulation. The size of the simulation box with seven DNA rods was 250 × 250 Å, and 1500 lipids and cations were used in the simulation. The simulation cells were periodic in the axial direction of the DNA rods. Results and Discussion Theory of Ion Adsorption. The specific adsorption of cations on biological membranes contributes to many cellular processes such as insertion of proteins into membranes, membrane fusion,

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Figure 4. Monte Carlo simulations of lipid self-assembly. (A) Planar bilayer obtained with high interaction energies of lipids: 13 ) 200kBT and 23 ) 375kBT. (B) Micellar assembly resulting from low interaction energies of lipids: 13 ) 2kBT and 23 ) 3.75kBT. See Farago29 for a description of notations. The light-gray spheres represent the hydrophobic acyl chains, and the red spheres are the hydrophilic headgroups of lipids.

or neural signal transduction.32 The binding properties of various cations on phospholipid membranes have been investigated by electrophoretic mobility, NMR, titration calorimetry and molecular dynamics simulations.33-37 Multivalent cations possess the ability to reverse the charge of phospholipid membranes upon a sufficient concentration. The surface potentialsand, subsequently, the surface charge densitysof lipid membranes in the presence of cations can be described satisfactorily in terms of the Gouy-Chapman-Stern theory.34,38,39 The surface potential ψs of a membrane immersed in an electrolyte is related to its surface charge density σ through the equation,40

σ ) sgn(ψs)

x

20kBT

[ ( ) ]

∑k

nk(∞) exp -

zkeψs kBT

- 1 (1)

where  and 0 are the dielectric constant and the permittivity of free space, respectively, kB is the Boltzmann constant, T is the temperature, nk(∞) are the bulk ion concentrations, zk are the ion valences, and e is the elementary charge. The sum is performed over all ions in solution. In the absence of specific ion binding to the membrane, σ remains constant whatever the ion concentration is. Otherwise, the adsorption of ions induces variations of the surface charge density, which then depends upon the ion concentrations at the membrane surface. Following the logic of the Langmuir adsorption model, the membrane possesses a finite number of binding sites per unit area, and the ion binding can be understood as equilibrium between the free ions in solution at the membrane surface and the ions occupying a binding site. By denoting N+ and N- the densities of binding sites for cations and anions, respectively, Ki and Kj the binding constants of each of the cations and anions likely to get adsorbed onto the membrane, and setting σ0 as the intrinsic surface charge density of the lipid membrane under consideration, the net surface charge density σ is expressed by34

σ ) σ 0 + N +e

( ) ( )

∑i ziKini(∞) exp -

1+

zieψs kBT

∑i Kini(∞) exp -

+

zieψs kBT

( ) ( )

∑j zjKjnj(∞) exp -

N e 1+

zjeψs kBT

∑j Kjnj(∞) exp -

zjeψs kBT

(2)

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Figure 5. Self-assembly of a hexagonal lipid-DNA complex by Monte Carlo simulations. The DNA rods, represented in blue, are fixed on a hexagonal lattice during the simulation. Zwitterionic lipids and divalent cations (yellow spheres) are randomly distributed at the initial stage (inset).

K and N for Ca2+ were adjusted to fit the experimental data. The inset of Figure 1 shows the theoretical surface charge density starting from a negative σ0 at low Ca2+ concentrations and saturating to a highly positive charge density by an excess of cations. The ion concentration at which the inversion of surface charge density occurs can be estimated from eq 2 with the adsorption of one ion species:

ninv(∞) ) -

Figure 6. Total free energy of lipid-DNA complexes with varying cation valence. The total free energy is computed by simulating only one DNA rod surrounded by zwitterionic lipids and cations. The inset depicts the equilibrium states obtained with no cation and with divalent cations.

with the notations described previously and the indexes i and j pertaining to cations and anions, respectively. By solving simultaneously eqs 1 and 2 with the given binding parameters and bulk concentrations for all ions as well as the intrinsic surface charge density of the lipid membrane, we can compute the variations of the surface potential as a function of ion concentration and fit measurements inferred from electrophoretic mobility. Figure 1 depicts the surface potential of DOPE liposomes with a varying concentration of Ca2+; the rest of the ions in solution was assumed not to bind. As the cations were added to the liposome solution, the surface potential increased more steeply than that depicted theoretically with no binding mechanism, and peaked to a positive value. The binding parameters

σ0 1 σ0 + zeN K

(3)

With the binding parameters of Ca2+ obtained from experimental data, it yields ninv(∞) ≈ 3.1 mM. Phospholipid-DNA Complexation. Since phospholipids can be turned cationic by adsorption of multivalent cations, they present the potential to be complexed with negatively charged nucleic acids. Figure 2 shows the small-angle X-ray pattern of DOPE complexed with λ-DNA in the presence of 200 mM Ca2+. The lipid-to-DNA mass ratio (L/D) was 7. At [Ca2+] ) 200 mM, the surface charge density of DOPE reconstructed from eqs 1 and 2 is ∼+0.03 C‚m-2 (Figure 1 inset), and indeed the X-ray data revealed an ordered liquid-crystalline structure associating lipids, DNA, and cations. Two different phases were distinguishable, one denoted HII and corresponding to a phase of pure DOPE 41 and a second one labeled HIIC referring to the DOPE-DNA complex phase. The Bragg peaks of both phases were positioned according to the ratios 1:x3:2 characteristic of a hexagonal arrangement.42 The unit cell size a, deduced from the wavenumbers of Bragg peaks qhk ) 4πxh2+kh+k2/x3a, where h and k are Miller indices, were 78 and 69 Å for the HII and HIIC phases, respectively. For the latter phase, the unit cell size corresponded well to the thickness of one DOPE membrane bilayer (∼45 Å) plus the diameter of one DNA chain (∼20 Å) and two layers of ∼2 Å each to accommodate the bridging

Self-Assembly of Phospholipid-DNA Complexes cations. The structure of the complexes will be depicted in the section devoted to Monte Carlo simulations. Below the charge inversion concentration given in eq 3, we expect no complexation to take place. As an example, we considered the case of zwitterionic DOPE with trivalent La3+. It must be noted that unlike monovalent and divalent cations,1,43,44 trivalent cations may also reverse the charge of DNA either by specific adsorption and/or by correlation-induced charge inversion.45-47 Figure 3A depicts the variations of surface potential of DOPE liposomes in the presence of La3+. The charge inversion concentration was estimated at ∼36 µM. Figure 3B shows that with 100 µM La3+ the electrophoretic mobility of DNA was still negative and the charge inversion of DNA occurred for a higher concentration (∼300 µM). Yet a complexed phase of lipid and DNA was observed for [La3+] ) 100 µM (Figure 3C). At [La3+] ) 10 µM, below the charge inversion concentration of lipids, no pattern was detected and no precipitate was even formed. Two additional features can be noted on the X-ray diffraction patterns: (i) even though both HII and HIIC were observed at 200 mM La3+, only the complexed HIIC remained at 1 mM and 100 µM; (ii) the cell unit size of HIIC increased slightly from 68 Å at 200 mM to 71 Å at 100 µM, possibly because of a weaker interaction between lipids and DNA. We also tried to use monovalent K+ ions for DOPE-DNA complexation. However, no ordered structure was detected by X-ray diffraction. This is because monovalent cations do not recognize enough binding sites to counterbalance and to override the intrinsic surface charge density of either phospholipids or DNA. Structure of Phospholipid-DNA Complexes by Monte Carlo Simulations. To get a better insight into the detailed structure of the complexes and their thermodynamical stability, we performed Monte Carlo simulations with a coarse-grained water-free model of lipids. The procedure allowed us to calculate the equilibrium state of such large supramolecular assemblies at a reasonable computational cost. Figure 4 illustrates the assemblies obtained with two models of lipid. By setting high interaction energies between lipid spheres, the simulations yielded a planar lipid bilayer consistently with a bending modulus of ∼54kBT as estimated by Farago.29 Reducing the interaction energies resulted in a lower bending modulus, and a micellar assembly of lipids was formed with the hydrophilic parts pointing toward the aqueous environment and the hydrophobic parts protected from the implicit water. This model was more consistent with DOPE, which has a typical bending modulus of less than 1kBT. We aimed at reproducing the hexagonal liquid-crystalline structure revealed by X-ray diffraction. To do so, we fixed DNA rods on a hexagonal lattice, and we distributed randomly zwitterionic lipid molecules and divalent cations throughout the simulation box. Then we let the lipids and cations evolve until equilibrium was reached. Figure 5 depicts the equilibrium and initial states of the simulation. The lipids formed inverted micelles around the DNA rods with cations in between screening the electrostatic repulsion. The DNA rods were initially positioned at a minimal distance from each other sufficient to accommodate two lipid molecules; however, we can see that all the inter-DNA space was filled although it implied that some hydrophilic lipid heads were dissociated from DNA. The stability of complexes is illustrated in Figure 6, where only one DNA rod was introduced into the simulations. In the absence of cation, the lipid-DNA complexes possessed a high total free energy arising from an unstable and disordered state.

J. Phys. Chem. B, Vol. 111, No. 51, 2007 14237 As the valence of cations increased, the total free energy dropped progressively indicating a better cohesion between lipids, cations, and DNA. The inset of Figure 6 shows the neat arrangement of a lipid bilayer wrapping up a single DNA rod in the presence of divalent cations, which must be compared to the disordered arrangement obtained without cations. The simulations also suggested that no significant gain in cohesion was obtained beyond valence +4. Conclusions In spite of unfavorable electrostatic interactions, DNA and noncationic lipids such as phospholipids can be complexed into an ordered liquid-crystalline structure upon the mediation of multivalent cations. The affinity of DNA for yet zwitterionic lipids like DOPE is explained in terms of ion adsorption: the lipid headgroups become positively charged upon the binding of multivalent cations. As DNA and lipids approach each other, the ions in excess are released and the complexation takes place accompanied by a loss of translational entropy. The process is identical to the like-charge attraction responsible for the condensation of charged polymers.48,49 Coarse-grained Monte Carlo simulations support the hexagonal arrangement inferred from X-ray diffraction experiments and show that lipids self-assemble to form inverted micelles around DNA rods with multivalent cations acting as “molecular glue”. The theories and models presented herein, although in good accord with experiments, are not accurate enough to give a fine understanding of the molecular interactions accounting for the self-assembly of phospholipid-DNA complexes. A consistent theory of the like-charge attraction, whether based on local density fluctuations of counterions or correlations between condensed counterions, and including ion size effects, has yet to be worked out. With the rapidly growing performances of computers, we can envision molecular dynamics simulations of self-assembling systems taking into account explicitly the solvent and the atomic structure of molecules, thus allowing the development of predictive models. Such knowledge might help design promising supramolecular assemblies or machineries like phospholipid-DNA complexes for gene delivery. Acknowledgment. The X-ray diffraction experiments were carried out with the support of Nanyang Technological University. This work was funded by the Agency for Science, Technology and Research (A*STAR) in Singapore. References and Notes (1) Bloomfield, V. A. Biopolymers 1997, 44, 269-282. (2) Gelbart, W. M.; Bruinsma, R. F.; Pincus, P. A.; Parsegian, V. A. Phys. Today 2000, 53, 38-44. (3) Allen, T. M.; Cullis, P. R. Science 2004, 303, 1818-1822. (4) Luo, D.; Saltzman, M. W. Science 2000, 18, 33-37. (5) Mastrobattista, E.; van der Aa, M. A. E. M.; Hennink, W. E.; Crommelin, D. J. A. Nat. ReV. Drug DiscoVery 2006, 5, 115-121. (6) Safinya, C. R. Curr. Opin. Struct. Biol. 2001, 11, 440-448. (7) Lasic, D. D.; Strey, H.; Stuart, M. C. A.; Podgornik, R.; Frederik, P. M. J. Am. Chem. Soc. 1997, 119, 832-833. (8) Ra¨dler, J. O.; Koltover, I.; Salditt, T.; Safinya, C. R. Science 1997, 275, 810-814. (9) Koltover, I.; Salditt, T.; Ra¨dler, J. O.; Safinya, C. R. Science 1998, 281, 78-81. (10) Koltover, I.; Wagner, K.; Safinya, C. R. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 14046-14051. (11) 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, 7413-7417. (12) Ahmad, A.; Evans, H. M.; Ewert, K.; George, C. X.; Samuel, C. E.; Safinya, C. R. J. Gene Med. 2005, 7, 739-748.

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