Osmotic Stress Induced Desorption of Calcium Ions from Dipolar Lipid

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Osmotic Stress Induced Desorption of Calcium Ions from Dipolar Lipid Membranes Lea Fink,† Jehuda Feitelson,† Roy Noff,†,‡,§ Tom Dvir,†,‡ Carmen Tamburu,† and Uri Raviv*,† †

Institute of Chemistry and Center for Nanoscience and Nanotechnology and ‡Racah Institute of Physics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem, 9190401, Israel ABSTRACT: The interaction between multivalent ions and lipid membranes with saturated tails and dipolar (net neutral) headgroups can lead to adsorption of the ions onto the membrane. The ions charge the membranes and contribute to electrostatic repulsion between them, in a similar manner to membranes containing charged lipids. Using solution X-ray scattering and the osmotic stress method, we measured and modeled the pressure−distance curves between partially charged membranes containing mixtures of charged (1,2-dilauroyl-snglycero-3-phospho-L-serine, DLPS) and dipolar (1,2-dilauroyl-snglycero-3-phosphocholine, DLPC) lipids over a wide range of membrane charge densities. We then compared these pressure− distance curves with those of DLPC membranes in the presence of 10 mM CaCl2. Our data and modeling show that when low osmotic stress is applied to the DLPC bilayers, the membrane charge density is equivalent to that of a charged membrane containing ca. 4 mol % DLPS and 96 mol % DLPC. As the osmotic stress increased, the charge density of the DLPC membrane decreased and resembled that of a membrane containing ca. 1 mol % DLPS. These data are consistent with desorption of the calcium ions from the DLPC membrane with increasing osmotic stress.

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the multilamellar stack.14,10,16 The bound cations induce an electric field in the direction perpendicular to the membranes as well, prompting structural changes in the orientation of the zwitterionic headgroups.15,17−19 They also slightly change the area per headgroup, membrane thickness, and hydration coefficient20 and increase the main gel-to-liquid phase transition temperature, Tm.17,21 As long as the ions remain on the membrane surface, the bilayers interact in a similar way to charged membranes containing lipid molecules with charged headgroups. Nevertheless, as opposed to charged membranes, the ions that adsorb onto neutral membranes are physically rather than covalently bound to the membrane surface. In our earlier study, we already indicated that the adsorption of calcium ions to 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) membranes is reversible upon dilution of the DLPC/Ca2+ solution.14 The structure and concentration of the lipid and the type of ion (particularly its charge density) control the equilibrium partition of the ions among the surface of the membranes and the bulk solution, thereby controlling the charge density of the membrane. This versatile behavior complicates the analysis of the interactions between membranes charged by adsorbed ions, compared with covalently charged membranes. In the former case, both the surface charge density as well as the screening length are regulated by the conditions of the experiments.

INTRODUCTION Lipid chains with zwitterionic (dipolar, net neutral) headgroups, in water, form dipolar membranes, often resulting in closed multilamellar vesicles.1−3 The spacing between the lamella in the vesicles, controlled by the interaction between them, is known to be weakly affected by the presence of monovalent salts in the water volume between them.4−7 These distances and interactions, however, are strongly affected by the presence of salts with multivalent cations, particularly when the lipid tails are saturated.8−10 The interaction between multivalent ions and biological membranes that contain lipids with zwitterionic headgroups often occurs between the outer leaflets of cell membranes and the multivalent ions surrounding them. This interaction can initiate signaling in cells and membrane remodeling.11 Hence, there is a great deal of interest about the character of this interaction. Calcium (Ca2+), magnesium (Mg2+), and zinc (Zn2+) are examples of ions that are of interest in this regard. Lipids with phosphatidylcholine (PC) headgroups and saturated tails (and therefore sufficiently small area per lipid) can adsorb multivalent ions12,13 with an association constant on the order of ∼10 M−1. If, however, one or both tails are unsaturated, the area per lipid is larger and the rotational entropy of the tails competes with the ion−dipole adsorption energy, which is estimated at ∼4kBT (ca. 10 kJ/mol at room temperature), where kB is the Boltzmann constant and T is the absolute temperature.14,15 When multivalent ions adsorb to PC headgroups, they positively charge the membrane surface and induce swelling of © XXXX American Chemical Society

Received: February 28, 2017 Revised: May 5, 2017 Published: May 17, 2017 A

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where ψ(z) is the electrostatic potential at distance z from the surface and ρ0 is the counterion concentration at the midplane between the membranes. If the membranes are in a liquid phase, we can use a more recent theory, the modified charge regulation theory (MCRT).30 This combines electrostatic (PB) and nonelectrostatic contributions to the free energy by taking into account the nonelectrostatic ion−surface interaction, the ion−ion interaction on the surface, and the mixing entropy of lipid molecules (uncharged and charged) with adsorbed or dissociated counterions:

In this paper, we addressed an aspect of this problem by investigating the interactions between a set of binary mixed lipid membranes, consisting of 1,2-dilauroyl-sn-glycero-3-phospho-Lserine (DLPS) and DLPC, covering a wide range of membrane charge densities. We found that replacement of as low as 1 mol % of DLPC (that has a zwitterionic headgroup) by DLPS (that has a negatively charged headgroup) significantly increased the repulsion between the bilayers and thus the gap between them. By adding long, neutral polyethylene glycol (PEG) chain molecules, which could not enter the interlayer gap, an osmotic stress was applied to the multilamellar vesicles. This pressure decreased the gap between bilayers, measured by solution X-ray scattering. Using the osmotic stress method, we measured the pressure−distance curve of each of the mixed DLPC/DLPS charged membranes. We also calculated the theoretical pressure−distance curves that fit the experimental data. We then measured the pressure−distance curve of the DLPC membranes that adsorbed calcium ions and compared them with the relevant charged membrane curves, as a function of the applied osmotic pressure. Our data and analysis show that osmotic stress induced desorption of Ca2+ ions from the DLPC bilayer.

a 2Fs 1 = eψη − αηs − χηs(1 − ηs) s s kBT 2 + ⎡⎣ηs ln ηs + (1 − ηsm) ln(1 − ηsm) + (ηsm − ηs) ln(ηsm − ηs)⎤⎦

Here Fs is the contribution of the surface to the free energy, ηsm is the molar fraction of charged lipid in the membrane, ηs = a2σ/e is the molar fraction of dissociated charged lipids out of the total charged lipid molecules (ηs varies between 0 and ηsm), ψs is the potential at the surface of the membrane, a is the square root of the area per lipid, σ is the membrane charge density (its maximum value is ηsm/a2), and α and χ are the nonelectrostatic ion−surface and ion−ion interaction parameters, respectively. The first term in the surface free energy expression is the interaction of the surface charge with the electric potential. The second term is the nonelectrostatic interaction between the absorbed ions and the surface, which favors absorption when the value of α is negative. The third term corresponds to the interaction between bound ions and allows for lateral phase separation between charged and uncharged lipids. The last term is the ideal mixing entropy between charged and uncharged lipid molecules on the surface. The contribution of the volume between the membranes, Fv, to the free energy is given by30

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INTERACTIONS BETWEEN CHARGED MEMBRANES The equilibrium distance between membranes in a multilamellar stack is determined by a balance between attractive and repulsive forces. Contributing to the interaction free energy per unit area, f, is on the one hand the vdW attractive interaction ( f vdW) balanced by hydration (f hyd) and undulation (fand) repulsive interactions on the other hand. When the membranes are charged, electrostatic interaction ( felec) should also be taken into account. The total free energy per unit area, as a function of the water spacing between membranes, dw, at temperature, T, can be approximated by1,11,22−26 f (dw ,T ) = fvdV + fhyd + fund + felec =−

⎞ 2 1 H ⎛ 1 ⎜ 2 − ⎟ + 2 2 12π ⎝ d w (d w + δ ) (d w + 2δ) ⎠

2 a3Fv a3 ⎛ ψ ′[z] ⎞ = −ψ [z](ϕmi − ϕp) − ⎜ ⎟ kBT 8πlb ⎝ d w ⎠

⎛ k T ⎞2 1 + Phλh e−dw / λh + ⎜ B ⎟ A fl e−dw / λfl + felec ⎝ 2π ⎠ κ

+ ϕmi(log[ϕmi] − 1) + ϕp(log[ϕp] − 1) − log[ϕp](ϕp + ϕmi − 2ϕ0)

(1)

where H is the Hamaker coefficient, δ is the membrane thickness, Ph is the hydration pressure constant estimated to be ca. 0.01 kBT for phospholipids,27 λh is the hydration length (typically 2 Å), κ is the membrane bending rigidity, and Afl and λfl are related to membrane fluctuations. In the case of charged membranes, the electrostatic contribution (felec) to the free energy can be approximated by the mean-field Poission−Boltzman (PB) theory.25,28,29 This theory assumes that the free energy of ions in solution is determined by the balance of two forces. First, ion entropy tends to smear out the charge density, to allow the maximum number of states for the ions, and second, ion electrostatic energy drives oppositely charged counterions toward the membrane. At a finite temperature the nonlinear PB equation can be derived for two parallel flat charged surfaces, in a monovalent salt solution ⎛ eψ ⎞ 8πρ0 ∂ 2ψ sinh⎜ =− ⎟ 2 εw ∂z ⎝ kBT ⎠

(3)

(4)

where ϕmi(z) and ϕp(z) are concentration profiles for negative and positive ions, respectively, in the direction perpendicular to the bilayer, ϕ0 is the salt concentration at the midplane, and lb = e2/εkBT is the Bjerrum length (ca. 7 Å in water). Minimization of the total free energy with respect to ηs produces the following boundary condition for eq 2:30 ηs =

1 3 (−α − χηs + eψs / kBT )

1 + ρ0 a e

(5)

These equations require a solution that, for most configurations, must be computed numerically. Once a solution for the modified PB equation is attained, it is possible to extract the surface charge (σ), surface potential (ψ0), and the electrostatic pressure. In the case of lipid and monovalent salt:30 ⎛ eψ ⎞ Πelec(d w ) = kBT sinh⎜ 0 ⎟ ⎝ kBT ⎠

(2) B

(6) DOI: 10.1021/acs.langmuir.7b00596 Langmuir XXXX, XXX, XXX−XXX

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∂f (d w ,T ) ∂d w

(7)

At the equilibrium distance, a stack of membranes will show zero pressure. When applying external pressure, by exerting an osmotic stress using inert polymers, for example, PEG, that are excluded from the membrane stack, the membranes will be at a water spacing (dw) at which the pressure is equal to the external pressure.

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RESULTS AND DISCUSSION To investigate the effect induced by charge density changes owing to Ca2+ adsorption, we confirmed that Ca2+ adsorption does not affect the membranes structure. We then selected condition for the DLPC/DLPS/NaCl system in a similar range of charge densities and screening length. In Figure 1A, SAXS curves of DLPC membranes and DLPC in the presence of 10 mM CaCl2 are plotted. The plots are nearly identical, and formfactor analysis (Figure 1B) shows that the electron density profile did not change in the presence of the ions. This shows that the membrane thickness remained unchanged in the presence of Ca2+ ions. In our earlier study,14 we found that the association constant of Ca2+ to DLPC is 10.8 ± 0.9 M−1. This association constant suggests that when 10 mM CaCl2 was added to 20 mg/ mL (∼32 mM) DLPC, between 7 and 8 mol % of the lipid molecules adsorbed Ca2+ ions (and as a result the Cl− ions that were associated with them). The remaining added ions (between 7.4 and 7.8 mM) stayed in the bulk solution. The Ca2+ ions that adsorbed onto the DLPC membrane charged the membrane. The area per DLPC lipid, A, is 0.640 ± 0.002 nm2 and does not change significantly with Ca2+ adsorption;14 hence, the membrane charge density formed by the adsorbed ions was 0.08 e σ = 2e = 0.25 2 . This σ value is equivalent to a DLPS/ 0.64 nm 2 nm DLPC mixed lipid membrane containing about 16 mol % DLPS. The ions that remained in the bulk screened the electrostatic interaction between the membranes that were charged by the adsorbed ions. The screening length (λD) is given by31 ⎛ 8πρ (zie)2 ⎞−1/2 λD = ⎜∑i ε ∞ε ,ik T ⎟ where ρ∞,i is the bulk concentration ⎝ ⎠ 0 w B of the ith ion, zi is its ionic valence, e is the charge of an electron, εw is the relative permittivity of water, and ε0 is the permittivity of free space. The λD, created by the Ca2+ and Cl− ions that stayed in the bulk solution, was ca. 2 nm. This λD value is equivalent to an added ∼23 mM NaCl solution. Note that owing to the divalent character of Ca2+ ions, λD of a NaCl solution is 3 times longer than that of a CaCl2 solution at the same concentration. To obtain the screening length of 20 mg/mL DLPC in 10 mM CaCl2, we added 25 mM NaCl to all our DLPS/DLPC lipid mixtures. These mixtures included 1, 2.2, 3.3, 5, and 20 mol % DLPS, pure DLPC, and pure DLPS. In all the measurements, we observed a single set of peaks that correspond to a single lamellar phase, the repeat distance (D) of which is reported. Figure 2 shows that at low membrane charge densities σ (corresponding to 0−5 mol % DLPS) the pressure− distance curves are significantly different. We calculated theoretical pressure−distance curves (solid curves in Figure 2) using eq 1 and the MCRT modified PB theory for the

Figure 1. (A) Background-subtracted SAXS intensity curve (red and black) and a fitting to a model (blue). Data were measured from a solution of 20 mg/mL DLPC in water (extruded) or in 10 mM CaCl2. The model is a stack of infinite flat slabs that each has a Gaussian electron density (ED) profile along the direction normal to surface of the membrane (z). (B) ED profile of the model.

electrostatic interaction. We assumed that the fraction of DLPS was small enough that deviations from structural parameters of pure DLPC were negligible. The data are in good agreement with the theoretical prediction. The 5 mol % DLPS data displayed more experimental scatter; however, in general, it did follow a similar trend. Figure 3 shows that within our fairly large experimental scatter, in the presence of 25 mM NaCl, mixed DLPS/DLPC lipid membranes containing between 5 and 100 mol % DLPS had rather similar pressure−distance curves. The result confirms the fact that at this range the surface charge density has a much weaker effect on the interaction between membranes compared with the effect of screening, controlled by the bulk salt concentration.32 Figure 4 shows the pressure−distance curve of DLPC in the presence of 10 mM CaCl2. The experimental data are compared with the set of theoretically calculated pressure−distance curves C

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Figure 3. Measured (symbols) and computed (curves) osmotic stress as a function of the lamellar repeat distance (D) of mixed DLPS/DLPC membranes, in the presence of 25 mM NaCl: Pure DLPS (olive symbols and solid curve), 20% DLPS with 80% DLPC (black symbols and solid curve), and 5% DLPS with 95% DLPC (blue symbols and solid curve). Different symbols of the same color correspond to different experiments.

Figure 2. Measured (symbols) and calculated (solid curves) osmotic stress as a function of the lamellar repeat distance (D) of pure DLPC (red symbols and curve) and of mixed DLPS/DLPC membranes of low charge density, in the presence of 25 mM NaCl. The solid curves are the computed pressure−distance curves that best fit the data. Their membrane charge densities (DLPS percentage) are indicated in the figure. In the mixed membranes, the DLPS mole percents of the experimental data were 1, 2.2, 3.3, and 5 (±0.1). The color of the symbols match the color of the curves that best fit the data. Different symbols of the same color correspond to different experiments. The solid curves are replotted in Figure 4.

attributed to condensation of the counterions back into the membranes rather than ion desorption as in the present case.

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CONCLUSION We used solution X-ray scattering and osmotic stress to determine the interactions between DLPC lipid membranes in the presence of calcium ions. The calcium ions adsorbed onto the bilayers and charged the membranes. When osmotic stress was applied to the membranes, we found that above a critical pressure, calcium ions desorbed from the lipid bilayers in order to regulate the membrane charge density. This behavior is similar to that of membranes containing charged lipids, the charge group of which is covalently attached to the lipid headgroup and can be modeled by a modified PB equation.33 The calcium desorption regulation mechanism is different from that of charged membranes that regulate their charge, when pressure is applied, by condensation of their counterions back onto the membrane surface.

that were experimentally confirmed in Figure 2. The theoretical curves were computed at the relevant screening length with 20 mg/mL DLPC in 10 mM CaCl2 and covered the range of membrane charge densities that included all the experimental data of DLPC in 10 mM CaCl2. By comparing the data with the calculated curves in Figure 4, we estimated the membrane charge density (σ) of DLPC in 10 mM CaCl2 as a function of applied osmotic stress. This comparison assumes that no significant ion correlation effects took place under the relatively low charge densities and salt concentrations used in our experiments, enabling us to compare the results to the calculated curves that were verified experimentally in the monovalent case (Figure 2). Figure 5 shows the reduction in σ with applied osmotic stress resulting, most likely, from desorption of Ca2+ ions as the pressure increased. The mechanism of surface charge density regulation that we found in this study is different from that of charged membranes like DLPS, the charged groups of which are covalently attached and cannot easily detach from the bilayer. Charge regulation in DLPS was observed in our earlier paper at much higher osmotic pressures.33 The mechanism of this charge regulation was

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EXPERIMENTAL SECTION

Lipids [2-didodecanoyl-sn-glycero-3-phosphocholine (DLPC) and its charged analogue 1,2-dilauroyl-sn-glycero-3-phospho-L-serine (DLPS)] were purchased from Avanti Polar Lipids, Inc. (Alabaster, AL) and used as received. The lipids were purchased as lyophilized powders (>99% pure, according to the data of the manufacturer). Highly purified water (Barnstead Nanopure Diamond) with resistivity of 18.1 MΩ · cm and total organic compounds of 1 ppb or less was used. Polyethylene glycol (PEG) with average MW of 20 000 D

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Figure 5. Estimated membrane charge density, σ, of DLPC in the presence of 10 mM CaCl2 as a function of applied osmotic stress. σ was estimated by comparing the osmotic stress data from Figure 4 (solid symbols) and the membrane charge density of the computed pressure− distance curves in Figure 4. The point at osmotic stress of 10 Pa on the logarithmic scale corresponds to no applied pressure. The solid curve is a guide to the eye. The open star symbol corresponds to the membrane charge density computed using the calcium binding equilibrium constant K = 10.8 ± 0.9 M−1, obtained in our earlier study.14 When no pressure was applied, the value of σ in this study corresponds to K = 16 ± 6 M−1, assuming each calcium ion bound a single DLPC molecule. The total lipid and calcium concentrations were 32 and 10 mM, respectively. At room temperature, the K value corresponds to a calcium binding free-energy change, ΔG, of 6.9 ± 0.8 kJ/mol (this study) and 5.9 ± 0.3 kJ/mol (in our earlier study).

Figure 4. Measured (symbols) osmotic stress as a function of the lamellar repeat distance (D) of DLPC membranes, in the presence of 10 mM CaCl2. Different symbols correspond to different experiments. The solid curves are the calculated osmotic stress profiles of mixed DLPS/ DLPC membranes in the presence of 25 mM NaCl, assuming the mol % of DLPS was as indicated in the figure. The solid curves are taken from Figure 2. Da, analytical grade chloroform, standard 1 M NaCl, and standard 1 M CaCl2 solutions were purchased from Sigma (Rehovot, Israel) and used as received. DLPC and DLPS powders were mixed in glass vials using chloroform, at a range of DLPS mol %: 1, 2.2, 3.3, 5, and 20. Samples were uniformly vortex mixed for 10 min. The chloroform was then allowed to evaporate overnight in a fume hood and then ca. 3 h at 50 °C in an oven. Highly purified water, salt solution, or salt solution with the required PEG concentration (between 0.5 and 10 wt %) were added to the dry lipid mixture to get a final total lipid concentration of 20 mg/mL. To avoid effects that are related to lipid concentration,32 this lipid concentration was kept fixed in all the experiments. Under our conditions, the lipid formed multilamellar vesicles, whose diameter vary and can reach several tens of micrometers. Each lipid solution was vortex mixed at ambient room temperature (above the melting temperatures of DLPC and DLPS, ca. −2 and 17 °C, respectively) for ca. 1 h in an Eppendorf tube. After equilibration for about 7 days, samples were transferred into quartz capillaries that were then flame-sealed and centrifuged at a relative centrifugal force of 6000g, using a Sigma 1-15PK centrifuge equipped with rotor No. 11024, suitable for capillaries. Samples were kept refrigerated for another day or two before X-ray measurements were performed. Our in-house high-resolution solution small-angle X-ray scattering (SAXS) setup was used as described elsewhere,34−36 and the resulting 2D scattering patterns were radially integrated.37 The scattering intensity (I) as a function of the magnitude of the momentum transfer vector (q) was then analyzed to determine the repeat distance (D) of the lamellar phase. The analysis was done using X+ software developed in our laboratory35,36 as explained also in refs 14, 32, 34, and 38.

PEG (MW = 20 000 Da) was used as received to apply osmotic stress to the bilayers. The osmotic pressure, Π, of our PEG solution was measured using a vapor pressure osmometer (Vapro 5520, Wescor, Inc.) and verified against a well-established expression.39 Using SAXS, we measured the lamellar spacing (D) at each pressure (Π).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +972 2 658-6030. Fax: +972 2 566-0425. ORCID

Uri Raviv: 0000-0001-5992-9437 Present Address §

R.N.: Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot, 7610001, Israel. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to Daniel Harries for helpful discussions. We thank Lavi Bigman and Niv Drucker for experimental help. This E

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(20) Uhrikova, D.; Kucerka, N.; Teixeira, J.; Gordeliy, V.; Balgavy, P. Structural changes in dipalmitoylphosphatidylcholine bilayer promoted by Ca(2+) ions: a small-angle neutron scattering study. Chem. Phys. Lipids 2008, 155 (2), 80−89. (21) Helfrich, W. Steric Interaction of Fluis Membranes. Berichte Der Bunsen-Gesellschaft-Physical Chemistry Chemical Physics 1978, 82 (9), 927−927. (22) Andelman, D. In Structure and Dynamics of Membranes; Handbook of Biological Physics; Lipowsky, R., Sackmann, E., Eds.; North-Holland, 1995; Vol. 1, pp 603−642.10.1016/S1383-8121(06) 80005-9 (23) Roux, D.; Safinya, C. R. A Synchrotron X-Ray Study of Competing Undulation and Electrostatic Interlayer Interactions in Fluis MultimembranelYotropic Phases. J. Phys. 1988, 49 (2), 307−318. (24) Leneveu, D. M.; Rand, R. P.; Parsegian, V. A. Measurements of Forces Between Lecithin Bilayers. Nature 1976, 259 (5544), 601−603. (25) Parsegian, V. A.; Rand, R. P.; Fuller, N. L.; Rau, D. C. Osmotic stress for the direct measurement of intermolecular forces. Methods Enzymol. 1986, 127, 400−416. (26) Rand, R. P.; Parsegian, V. A. Hydration Forces Between Phospholipid-Bilayers. Biochim. Biophys. Acta, Rev. Biomembr. 1989, 988 (3), 351−376. (27) Petrache, H. I.; Gouliaev, N.; Tristram-Nagle, S.; Zhang, R. T.; Suter, R. M.; Nagle, J. F. Interbilayer interactions from high-resolution xray scattering. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1998, 57 (6), 7014−7024. (28) Harries, D.; Raviv, U. Soft matter physics of lipid membranes based assemblies. In Liposomes, Lipid Bilayers and Model Membranes: From Basic Research to Technology; Kucerka, N., Katsaras, J., Mu-Ping, N.; Pabst, G., Eds.; Francis and Taylor, 2014. (29) Leneveu, D. M.; Rand, R. P.; Parsegian, V. A.; Gingell, D. Direct Measurement and Theory of Electrostatic Repulsion Between Phosphlipid Membranes. J. Electrochem. Soc. 1975, 122 (3), C106− C106. (30) Harries, D.; Podgornik, R.; Parsegian, V. A.; Mar-Or, E.; Andelman, D. Ion induced lamellar−lamellar phase transition in charged surfactant systems. J. Chem. Phys. 2006, 124 (22), 224702. (31) Israelachvili, J. N. Intermolecular and Surface Forces, revised 3rd ed.; Elsevier Science, 2011. (32) Steiner, A.; Szekely, P.; Szekely, O.; Dvir, T.; Asor, R.; YuvalNaeh, N.; Keren, N.; Kesselman, E.; Danino, D.; Resh, R.; Ginsburg, A.; Guralnik, V.; Feldblum, E.; Tamburu, C.; Peres, M.; Raviv, U. Entropic Attraction Condenses Like-Charged Interfaces Composed of SelfAssembled Molecules. Langmuir 2012, 28 (5), 2604−2613. (33) Dvir, T.; Fink, L.; Asor, R.; Schilt, Y.; Steinar, A.; Raviv, U. Charged membranes under confinement induced by polymer-, salt-, or ionic liquid solutions. Soft Matter 2013, 9 (44), 10640−10649. (34) Nadler, M.; Steiner, A.; Dvir, T.; Szekely, O.; Szekely, P.; Ginsburg, A.; Asor, R.; Resh, R.; Tamburu, C.; Peres, M.; Raviv, U. Following the structural changes during zinc-induced crystallization of charged membranes using time-resolved solution X-ray scattering. Soft Matter 2011, 7 (4), 1512−1523. (35) Ben-Nun, T.; Ginsburg, A.; Szekely, P.; Raviv, U. X+: a comprehensive computationally accelerated structure analysis tool for solution X-ray scattering from supramolecular self-assemblies. J. Appl. Crystallogr. 2010, 43, 1522−1531. (36) Szekely, P.; Ginsburg, A.; Ben-Nun, T.; Raviv, U. Solution X-ray Scattering Form Factors of Supramolecular Self-Assembled Structures. Langmuir 2010, 26 (16), 13110−13129. (37) Hammersley, A. P.; Svensson, S. O.; Hanfland, M.; Fitch, A. N.; Hausermann, D. Two-dimensional detector software: From real detector to idealised image or two-theta scan. High Pressure Res. 1996, 14 (4−6), 235−248. (38) Szekely, O.; Schilt, Y.; Steiner, A.; Raviv, U. Regulating the Size and Stabilization of Lipid Raft-like Domains and Using Calcium Ions as Their Probe. Langmuir 2011, 27 (24), 14767−14775. (39) Rand, R. P. Osmotic Stress Data. https://www.brocku.ca/ researchers/peter_rand/osmotic/data/peg20000.

project was supported by the Israel Science Foundation (1372/ 13) and by the Nanocenter of the Faculty of Mathematics and Sciences at the Hebrew University through the FTA-Hybrid Nanomaterials program and the Planning and Budgeting Committee of the Israel Council of Higher Education and a fellowship support to L.F. We thank the Safra, Wolfson, and Rudin Foundations for supporting our laboratory. Finally, we wish J.F. a happy 95th birthday.

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DOI: 10.1021/acs.langmuir.7b00596 Langmuir XXXX, XXX, XXX−XXX