ARTICLE pubs.acs.org/Langmuir
The Structure of Ions and Zwitterionic Lipids Regulates the Charge of Dipolar Membranes Or Szekely,† Ariel Steiner,† Pablo Szekely,†,‡ Einav Amit,† Roi Asor,† Carmen Tamburu,† and Uri Raviv*,† †
The Institute of Chemistry and ‡The Racah Institute of Physics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, 91904 Jerusalem, Israel
bS Supporting Information ABSTRACT: In pure water, zwitterionic lipids form lamellar phases with an equilibrium water gap on the order of 2 to 3 nm as a result of the dominating van der Waals attraction between dipolar bilayers. Monovalent ions can swell those neutral lamellae by a small amount. Divalent ions can adsorb onto dipolar membranes and charge them. Using solution X-ray scattering, we studied how the structure of ions and zwitterionic lipids regulates the charge of dipolar membranes. We found that unlike monovalent ions that weakly interact with all of the examined dipolar membranes, divalent and trivalent ions adsorb onto membranes containing lipids with saturated tails, with an association constant on the order of ∼10 M1. One double bond in the lipid tail is sufficient to prevent divalent ion adsorption. We suggest that this behavior is due to the relatively loose packing of lipids with unsaturated tails that increases the area per lipid headgroup, enabling their free rotation. Divalent ion adsorption links two lipids and limits their free rotation. The iondipole interaction gained by the adsorption of the ions onto unsaturated membranes is insufficient to compensate for the loss of headgroup free-rotational entropy. The iondipole interaction is stronger for cations with a higher valence. Nevertheless, polyamines behave as monovalent ions near dipolar interfaces in the sense that they interact weakly with the membrane surface, whereas in the bulk their behavior is similar to that of multivalent cations. Advanced data analysis and comparison with theory provide insight into the structure and interactions between ion-induced regulated charged interfaces. This study models biologically relevant interactions between cell membranes and various ions and the manner in which the lipid structure governs those interactions. The ability to monitor these interactions creates a tool for probing systems that are more complex and forms the basis for controlling the interactions between dipolar membranes and charged proteins or biopolymers for encapsulation and delivery applications.
’ INTRODUCTION þ
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Sodium (Na ), magnesium (Mg ), zinc (Zn ), and calcium (Ca ) ions are crucial to the regulation and function of many membraneassociated processes. Although these ions are expected to bind or remain close to charged interfaces,14 there is a great deal of curiosity about what these mobile ions that are widely found in nature do near or at dipolar (net neutral) interfaces. Therefore, we studied the manner in which ions interact with dipolar membranes composed of zwitterionic lipids with phosphatidylcholine (PC) headgroups. The adsorption of Ca2þ (or other divalent cations) onto zwitterionic membranes applies a charge to the otherwise neutral membrane surface.510 In pure water, the interbilayer (water) spacing, dW, in the multilamellar structure is determined by the balance between the attractive van der Waals (vdW) forces11,12 and the repulsive hydration1315 and undulation forces.1618 After Ca2þ ions adsorb, dW increases from a very short distance (ca. 2 to 3 nm) to a large distance, governed by the long-ranged electrostatic repulsion.1923 As the salt concentration increases, dW decreases because of the screening of the electrostatic repulsion.19,21,22,24 The interactions between ions (or charged molecules) and dipolar membranes can be used as a basis for protein or drug encapsulation and r 2011 American Chemical Society
delivery. This can be achieved by adsorbing charged macromolecules,25 such as proteins or peptides, to polar interfaces or using Ca2þ ions to adsorb DNA2628 or negatively charged dextran sulfate25 onto zwitterionic (PC) membranes. DNA binds to PC lipids2629 through “calcium bridges” and is “sandwiched” between the bilayers. Ca2þ binds and positively charges the bilayers. The DNA phosphate groups can then complex with them.26,29 Saturated-tail membranes such as 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) bind Ca2þ ions more strongly6,30 than do unsaturated-tail membranes such as 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), and gel-phase membranes (frozen acyl chains) bind more divalent cations than do liquiddisordered membranes (melted acyl chains).69,20,21,23,3133 The interaction of ions with the membrane surface is limited to the polar headgroup of the phospholipid,34,35 and the binding site of metal cations is limited to the phosphate moiety.3638 To accommodate cation binding, the headgroups realign26,34,3841 and the resulting lateral pressure compresses the lipid tails39,42 and creates a more ordered tail region.31,33,38,4248 Received: January 20, 2011 Revised: March 7, 2011 Published: May 20, 2011 7419
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Langmuir Therefore, Ca2þ binding favors the more ordered state of the membranes, namely, the gel phase, over the liquid-disordered phase and increases the gel-to-liquid phase transition temperature, Tm.8,31,39,42,43,4951 Other structural effects of Ca2þ binding include a decrease in the area per lipid headgroup41,48,52,53 and a slight increase in membrane thickness.41,53 The headgroup conformational changes, following calcium binding, decrease the number of water molecules that can bind to the lipid.41 Cation binding results in dehydration of the lipid headgroups24 and in entropy gain due to the release of water molecules into the solution.38,54,55 Salt reduces the vdW Hamaker coefficient,24 and divalent cation binding does not affect the short-range hydration repulsion but makes the repulsive double-layer forces longer-ranged.23 Several studies showed that the affinity of Ca2þ ions for the PC headgroup is relatively weak compared to that of anionic lipids.30,5560 Assuming that the binding constant is independent of lipid concentration and bilayer separation, different binding constants of Ca2þ and other ions to PC membranes with saturated tails were reported and are summarized in Tables S1S3 in the Supporting Information (SI). Other experiments were performed to examine the interaction of divalent and lanthanide (trivalent) cations with membranes containing unsaturated tails, such as natural lipid eggPC membrane, which is similar in composition (about 70%)61 to the synthetic “hybrid lipid” 1-palmitoyl-2oleoyl-sn-glycero-3-phosphocholine (POPC) containing a saturated and an unsaturated tail (Table S4 in the SI). Although the hybrid lipid POPC is considered to be an unsaturated lipid, earlier studies reported significant ion binding to the membrane, as summarized in Table S6 in the SI. The strength of the ionPC dipole interaction increases with the valence of the adsorbing cation.8,34,37,50,51,62,63 The effect of monovalent cations50 and some anions49,50 on lipid bilayers was also investigated. Some earlier reports indicated that there is a substantial binding of monovalent cations to membrane surfaces,64 but others24 observed that NaCl does not affect the lamellar interactions. The binding of monovalent ions has similar effects to that of divalent cations on the structural parameters of the bilayer,53,64 but these effects are generally much smaller. Monovalent ions do not affect the lipid headgroup orientation and hydration,64,65 in contrast to divalent cations. Most of the monovalent cations have little to no effect on the net force between the bilayers.66 The electrostatic repulsion, however, is progressively screened by increasing the added salt concentration, as is the vdW Hamaker coefficient. Hence, the swelling of the PC membranes monotonically increases with salt concentration.67 The binding of monovalent ions to zwitterionic membranes is significantly weaker than that of divalent or trivalent cations (Tables S1S3 and S5S6 in the SI). Some exceptions are large polarizable anions that interact with PC membranes and confer a negative charge to the lipid as a result of anion binding. This effect is apparent mainly for the interaction of lipids with SCN 50,68,69 or ClO4 70 or, according to the Hofmeister series,7174 with ions of increasing polarizability (Tables S2 and S6 in the SI). Zwitterionic PC membranes that adsorbed Ca2þ ions may differ from regular charged bilayers. The positive charge on the PC membrane surface results from ion adsorption. In membranes containing charged lipids with, for example, phosphatidylserine (PS) headgroups, the charges are covalently bound to the surface and are neutralized by counterions. In zwitterionic membranes, however, the surface charge comes from physically adsorbed ions, resulting in a regulated charged interface in which ions may adsorb or desorb from the surface when conditions vary. In earlier studies, for example, osmotic stress was applied to zwitterionic membranes in the presence of Ca2þ ions,21,22 causing adsorbed ions to detach from the surface. This effect is unachievable with charged membranes in which the effective surface charge density is regulated only by the counterion distribution next to the surfaces. Therefore, controlling the lipid concentration and the amount and type of ions next to dipolar membranes can regulate the interactions between bilayers. Because of the rather weak coupling interaction between the dipolar lipids and the ions, the thermodynamics of those interfaces is more involved than for charged interfaces.
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In this study, we investigated how the structure of lipid tails and the structure of the ions regulate the adsorption of those ions onto PC membranes and hence the membrane charge density. Using solution smalland wide-angle X-ray scattering (SAXS and WAXS, respectively), we studied the effects of ion valence and lipid tail saturation [using fully saturated lipids, hybrid lipids (containing a saturated and an unsaturated tail), and unsaturated lipids] on the interactions between dipolar membranes. We focused on the differences among divalent, polyvalent, and monovalent ions and on the balance between the iondipole interactions and the structural aspects of the membrane. We performed advanced data analysis and compared our findings with known theories. This work extends earlier studies and provides a more comprehensive and deeper understanding of those systems under a consistent framework.
’ MATERIALS AND METHODS Materials. Highly purified water (Barnstead Nanopure Diamond) with a resistivity of 18.1 MΩ cm and total organic compounds (TOC) content of 1 ppb or less was used to prepare solutions. Salt solutions were prepared either by adding highly purified water to dry NaCl, CaCl2, ZnCl2, MgCl2, LaCl3, or spermine tetrahydrochloride (SPM) to obtain the concentrations used in the experiments or by diluting a 1 M standard NaCl or CaCl2 salt solution. Both dry salts and standard solutions were purchased from Sigma-Aldrich (St. Louis, MO, USA). The following lipids were used: 1,2-dilauroyl (C12:0)-sn-glycero-3phosphocholine, 1,2-dimyristoyl (C14:0)-sn-glycero-3-phosphocholine, 1,2-dipalmitoyl (C16:0)-sn-glycero-3-phosphocholine, 1-palmitoyl-2-oleoyl (C16:018:1)-sn-glycero-3-phosphocholine, and 1,2-dioleoyl (C18:1)-snglycero-3-phosphocholine corresponding to DLPC, DMPC, DPPC, POPC, and DOPC, respectively (Avanti Polar Lipids, Inc., Alabaster, AL, USA). Appropriate amounts of 25 mg/mL lipid solution in chloroform were extracted from a stock solution and placed into glass vials. The chloroform was evaporated in a fume hood overnight. The remaining chloroform was further evaporated in a vacuumed desiccator for about 2 h. As a result, a uniform lipid film formed. Alternatively, lyophilized (>99% pure, according to the manufacturer’s data) DOPC, POPC, DLPC, or DPPC was used without further purification, and the salt solution was added directly to obtain the desired concentrations of both lipid and salt. Sample Preparation. The following preparation methods were used. Volume Method. A phospholipid solution at a total lipid concentration of 30 mg/(mL of water) was prepared by adding the appropriate amount of highly purified water to the dried lipid film or to the lyophilized lipid. The concentrations, here and in all of the other solutions, correspond to the amount weighted (in mg) to which a mL of water (or salt solution) was added. The solution was vortex mixed for 2 h. Samples [15 mg/(mL of salt solution)] were prepared by mixing equal volumes of a 30 mg/ (mL of water) lipid solution and a salt solution at double the final required sample salt concentration. Mixing was performed in an Eppendorf tube or directly in a quartz capillary. The extruded POPC samples were prepared from a 30 mg/(mL of water) solution that was extruded through a 0.1 μm membrane filter using an Avanti mini-extruder. The lipid solution was transferred into quartz capillaries and salt solutions were added directly to the capillaries. Weight Method. Phospholipid solutions at a total lipid concentration of 15 mg/(mL of salt solution) were prepared by adding salt solutions at the final required salt concentrations to the dried lipid film or to the lyophilized lipid. Samples were prepared in an Eppendorf tube or directly in a quartz capillary. If samples were mixed with the salt solution in Eppendorf tubes (via either the volume or weight method), then they were vortex mixed for an additional 2 h before they were centrifuged at a relative centrifugal force (RCF) of 20 080g at 25 C for 100 min, using an Eppendorf 5810R centrifuge with an Eppendorf rotor. The samples were then transferred into quartz capillaries, centrifuged at RCF = 1780g for 5 min at ambient 7420
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Langmuir temperature using a Thermo IEC Centra CL2 centrifuge equipped with a 15 mL tube rotor, and flamed sealed. No vortex mixing was applied after salt was added to samples prepared directly in the quartz capillaries. The samples were centrifuged at RCF = 1780g for 5 min at ambient temperature using the CL2 centrifuge, flamed sealed, and centrifuged at RCF = 6000g at 25 C for 90 min using a Sigma 115PK centrifuge with a capillary rotor. In some cases after salt was added to the Eppendorf tube, the samples were vortex mixed above the lipid melting temperature and transferred into capillaries. The samples were then centrifuged in the CL2 centrifuge, flamed sealed, and centrifuged in the Sigma centrifuge. Lipid pellets were obtained, toward which the X-ray beam was aligned. Methods. Solution Small-Angle X-ray Scattering. The lamellar phases formed in the lipid solutions have been characterized by smallangle and wide-angle X-ray scattering (SAXS and WAXS). High-resolution SAXS measurements were taken primarily at the SWING beamline of the SOLEIL synchrotron (Saclay, France) and with our in-house state-of-the-art SAXS setup. In our in-house setup, the X-ray generator, MicroMax-007HF (Rigaku Corporation), is a rotating anode operating at 40 kV and 30 mA and has a copper target producing KR photons with an energy of 8 keV (wavelength of 1.54 Å). The rotating anode is water-chilled by a refrigerated air-cooled system (Haskris, R075). The focal spot size on the anode is 70 70 μm2. A focused monochromatic beam is obtained using Confocal Max-Flux optics consisting of a CMF-12-100Cu8 focusing unit (Osmic Inc., a Rigaku Company). The beam continues into a vacuum flight path (ca. 15 Torr), which is 1 in. in diameter and contains two slits. The slits are fully motorized, scatterless hybrid metalGe single-crystal slits (Forvis Technologies, Inc.). The performance is optimized when the first slit (after the optics) is set to 1 1 mm2 and the beam spot size is set by the second slit (close to the sample) at 0.7 0.7 mm2. Our motorized sample stage consists of a Huber goniometer (to control the rotational angle) combined with XYZ translation stages (Forvis Technologies, Inc.). The scattered beam enters a large He-filled flight path (ca. 36 cm in diameter). A MAR345 image-plate detector (Marresearch GmbH) is stationed at the end of this flight path on a motorized plate. For WAXS measurements, a motorized in-line insertion holder was added close to the detector on the left side of the He-filled flight path. A more detailed description of our setup was given elsewhere.75 For the SWING beamline, the beam size was 450 80 μm2 [horizontal (H) and vertical (V) full width at half-maximum (FWHM), respectively, at the sample position], and a PCCD170170 (AVIEX) area detector was used. Other measurements were obtained on the BM26B and ID02 beamlines at the ESRF synchrotron (Grenoble, France), the X33 beamline at the EMBL synchrotron (Hamburg, Germany), and the 5.2 L beamline at the ELETTRA synchrotron (Trieste, Italy). For the ID02 beamline, the beam size was 400 200 μm2 (H and V fwhm, respectively) at the sample position, and a fast-readout, low-noise (FReLoN) Kodak KAF-4320 image CCD-based sensor was used (area 100 100 mm2). For the BM26B beamline, the beam size was 400 350 μm2 (H and V fwhm, respectively) at the sample position, and a 2D multiwire gasfilled SAXS detector was used (area 133 133 mm2). In all of the above beamlines Si(111) was used as a monochromator. For the X33 beamline, Ge(111) was used as a monochromator, the beam size was 2000 600 mm2 (H and V fwhm, respectively) at the detector, and a 2D Mar345 image plate detector (Marresearch GmbH, Germany) was used. The X-ray photon energy was 10 keV in all of the above beamlines. For the 5.2 L beamline, the X-ray photon energy was 8 keV, Si(111) was used as a monochromator, the beam size was set to 1000 500 μm2 (H and V fwhm, respectively), and a MAR300 image plate detector (Marresearch GmbH, Germany) was used.
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Figure 1. Radially integrated scattering intensity profile of 15 mg/(mL of salt solution) DPPC membranes in a 10 mM CaCl2 solution prepared by the weight method either in a glass vial [open symbols (with vortex), below] or directly in the quartz capillary [solid symbols (without vortex), above]. The solid lines are the best fitted Gaussian structure-factor correlation peaks multiplied by form-factor models of three infinitely flat uniform slabs with an electron density profile along the z axis, which is normal to the bilayer surface, as shown at the inset and in the text. In all of the measurements, silver behenate was used as a standard to determine the sample-to-detector distance. All the 2D images obtained had concentric rings, resulting from the isotropic character of samples in solution. The images were radially integrated, using FIT2D,76 to obtain a 1D scattering curve of the scattering intensity as a function of the magnitude of the momentum transfer vector, q. Data analysis was conducted using the Xþ software developed in our laboratory.77 The data were fitted to a form factor model of a stack of infinitely flat uniform slabs with varying electron density to describe the electron density profile of the lamellar stack, where τhead is the headgroup layer thickness and τtail is the carbon chain region thickness (Figure 1, inset). Details about this model are given elsewhere.78 After an automatic baseline subtraction,77 an initial guess of the form factor parameters was given, and the structure factor peaks were fitted using Gaussian line shapes. At first, many Gaussians were added to the model in order to eliminate the impact of the structure factor parameters on the general fit. After a good fit to the form factor was achieved, the extra Gaussian peaks were removed, leaving only the relevant structure factor peaks corresponding to the lamellar phase. Then, a better fit of the remaining peaks’ center, width, and amplitude was found. Finally, a few back-and-forth iterations between the form factor and structure factor fitting routines were applied to find the best fitting parameters. The structure factor peaks correspond to the repeat distance, D, of the lamellar phase in the sample. D = (2π)/(qmin) or D = (2πh)/(qh), where qmin is the position of the first peak in the series and the other peak positions are qh = hqmin, where h is an integer. If there are two populations in the sample (e.g., two separate phases), then two repeat distances are observed by two sets of structure factor peaks and their harmonics (i.e., D1 = (2π)/(qmin,1) and D2 = (2π)/(qmin,2)). As described earlier,77 the bilayer repeat distance, D, can be divided into a bilayer thickness, δ, and a water layer thickness, dW. The bilayer thickness, δ, is fairly close to the head-to-head distance (dHH) in the electron density profile, as defined in our earlier study.77 The water layer thickness, dW, is given by dW = D δ. From our form-factor analysis, we found that the bilayer thickness remains constant for each lipid, even when the bilayers are far apart because of electrostatic repulsive interactions induced by the adsorption of Ca2þ. Ca2þ Concentration Measurements. Atomic absorption spectroscopy (AA) was used to determine the affinity of Ca2þ for the surface of the membrane. AA samples with known Ca2þ concentrations ([Ca2þ]0) were prepared by the weight method in Eppendorf tubes, vortex mixed 7421
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for 2 h, and left at 4 C for 1 week to reach equilibrium. The samples were then centrifuged at RCF = 20 080g at 25 C for 90 min using an Eppendorf 5810R centrifuge with an Eppendorf rotor. The clear supernatant was extracted and diluted by a known factor to reach a final Ca2þ concentration of between 1 and 5 ppm (1 ppm of Ca2þ = 25 μM Ca2þ) required for the AA measurements. The AA setup atomizes the molecules in the sample and transfers them to the gas phase using an acetylene flame combined with air. Then a monochromatic beam (λ = 423 nm) irradiates the sample and the Ca2þ ions absorb the photons according to Beer’s law, and their concentration in the supernatant ([Ca2þ]sup) is measured directly from the absorption measurements. To estimate the concentration of the adsorbed cations, we estimated the volume of the pellet using our SAXS data m D m = ANAV ð1Þ Vpellet ¼ Vper lipid in pellet NAV MW 2 MW
Table 1. Membrane Thicknesses Obtained from the Form Factor Analysis of the Lipids Used in This Study lipid
membrane thickness, δ (nm)
DLPC
2.89 ( 0.05
DMPC DPPC
3.61 ( 0.01 3.93 ( 0.01
DOPC
3.53 ( 0.03
POPC
3.58 ( 0.03
where D is the lamellar repeat distance, A is the lipid area per headgroup, m is the weighed lipid mass in the sample, Vper lipid in pellet is the volume per lipid in the pellet, MW is the lipid molar mass, and NAV is Avogadro’s number. The concentration of Ca2þ ions adsorbed to the membrane surface is then calculated using the equation ½Ca2þ adsorbed ¼
Vtotal ½Ca2þ 0 ðVtotal Vpellet Þ½Ca2þ sup Vpellet
ð2Þ
where Vtotal is the total solution volume. The membrane charge density (σ, the number of charges per unit area on the membrane surface) is then given by σ ¼
2Vlipid NAV ½Ca2þ adsorbed 2½Ca2þ adsorbed ¼ Aφ A½L0
ð3Þ
The factor of 2 is the cation valence, φ is the lipid volume fraction, Vlipid is the lipid volume, and [L]0 is the initial lipid concentration. The same procedure was applied in preparing the sample for inductively coupled plasmaoptical emission spectrometry (ICP-OES) measurements. The ICP-OES setup uses a plasma source in which energy is supplied by electrical currents produced by time-varying magnetic fields. The plasma produces excited atoms and ions that emit electromagnetic radiation at wavelengths characteristic of a particular element (Ca2þ in our case). The intensity of this emission is indicative of the ion concentration in the supernatant ([Ca2þ]sup). The ICP-OES measurements agreed with the atomic absorption measurements (Figure S1 in the SI). Osmotic Pressure Measurements. The osmotic stress applied by the ions on the membranes in select samples of DOPC with NaCl was measured directly using a vapor-pressure osmometer (VAPRO 5520, Wescor, Inc.) that determines the concentration of osmotically active particles (in mOs/kg = mmol/kg). Direct measurements of the osmotic pressure were performed either on the supernatant of the samples by measuring it after centrifugation at RCF = 20 080g at 25 C for 90 min using an Eppendorf 5810R centrifuge with an Eppendorf rotor or on an equilibrium dispersion by measuring samples directly after 2 h of vortex mixing (without centrifugation). No difference was detected between the two, suggesting that our samples reached equilibrium.
’ RESULTS Interactions between Ions and Zwitterionic Membrane Surfaces. We studied the interaction of ions with membranes
composed of either saturated tails (DLPC, DMPC, and DPPC) or unsaturated tails (DOPC) and a hybrid lipid containing a saturated and an unsaturated tail (POPC). In all cases, the lipids formed multilamellar phases in water. Using solution X-ray
Figure 2. Interlamellar spacing, dW, as a function of the CaCl2 concentration for lipid solutions containing saturated tails—DLPC, DMPC, or DPPC. In all of the samples, the final total lipid concentration was 15 mg/(mL of salt solution), equivalent to ∼1.5 wt % lipid. The corresponding molar concentration of each lipid is indicated. When two phases coexisted (denoted as P1 and P2), the phase shown with solid symbols was the dominat one and likewise in the other Figures.
scattering, we measured the repeat lamellar distance, D. We calculated the interlamellar water spacing, dW, for each lipid at different salt solutions by subtracting the corresponding membrane thickness, δ, extracted from the form factor analysis (Table 1) of each bilayer. Unlike charged membranes, in pure water (i.e., no added salt) the neutral (zwitterionic) membranes do not have electrostatic repulsive interactions. The balance of short-ranged hydration repulsion, undulation repulsion, and van der Waals (vdW) attraction determines the interaction between neutral membranes and sets dW to be smaller than ca. 3 nm (Figure 2). Saturated-Tail Membranes in CaCl2 Salt Solutions. Figure 2 shows the interbilayer separation of the saturated-tail membranes as a function of CaCl2 concentration. Each data set corresponds to the average of the two preparation methods (Figure 1), and the error bars correspond to the statistical errors of repeated measurements. The behavior of saturated-tail membranes in the presence of CaCl2 is intricate. At low CaCl2 concentrations, only one phase exists (indicated as P1 in Figure 2), with dW < 3 nm, as in pure water. At salt concentrations of 1 mM, a second phase appears in which the saturated-tail membranes swell into large interlamellar spacings (dW > 32 nm, P2 in Figure 2). This phase is the equilibrium phase26,79,80 that coexists 7422
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Figure 3. Illustration of cation adsorption onto saturated zwitterionic membranes. The interbilayer spacing, dW, of zwitterionic membranes in pure water is ca. 2 to 3 nm (middle panel). The adsorption of Ca2þ charges the membranes, and dW increases (right panel). The image is nearly to scale and corresponds to ca. 50 mM CaCl2. The addition of monovalent salt NaCl or polyamine salt SPM has little or no effect on dW (left panel). The ions are represented as colored spheres: green spheres, Cl; red spheres, Ca2þ; and yellow spheres, Naþ. The membrane thickness, δ, dw and the measured lamellar repeat distance, D, are indicated.
with phase P1 for samples prepared using the volume method and is the sole phase for samples prepared using the weight method. In the latter preparation method, salt solutions are added to dried lipid powder and the multilamellar structures are formed in the presence of calcium. In the volume method, multilamellar vesicles first form in water and then the CaCl2 solution is added. This system needs a longer time before the Ca2þ ions can affect its structure. After equilibrium is reached (generally about 2 months after preparation for the volume method samples and 1 week for the weight method samples), most of the lipids are in the primary (equilibrium) phase, indicated as P2 in Figure 2, and exhibit large interlamellar spacings when the Ca2þ concentration reaches ca. 1 mM. This spacing is similar to the spacing measured for charged membranes composed of 1,2-dilauroyl-sn-glycero-3-phospho-Lserine (DLPS) or 1,2-dioleoyl-sn-glycero-3-phospho-L-serine (DOPS) in a 3 mM NaCl salt solution that has a similar ionic strength81 to 1 mM CaCl2. We therefore attribute the observed large spacing to charging of the zwitterionic membrane, resulting from the adsorption of the divalent cation onto the PC headgroups, leading to electrostatic repulsion between the membranes. At higher salt concentrations, although more Ca2þ ions may adsorb onto the bilayers, the presence of more ions in the solution better screens the electrostatic repulsion and the interlamellar spacing decreases (Figures 2 and 3). The latter behavior is in accordance with the findings of Lis et al.22 on phosphatidylcholines at higher lipid concentrations (30 wt %). In the earlier study,22 however, the Ca2þ ions adsorbed onto the lipids, charged the membranes, and led to their ideal swelling according to D = δ/φ,82,83 where δ is the membrane thickness and φ is the lipid volume fraction. This behavior is typical of charged membranes at lipid concentrations above ca. 15 wt %. In our lipid volume fraction (ca. 0.015), we measured D values that are significantly shorter than the ideal swelling distance given by δ/φ. This behavior is consistent with our finding81 that selfassembled like-charged interfaces composed of charged lipids (DOPS or DLPS) deviate markedly from ideal swelling behavior
below a critical lipid concentration. Conversely, self-assembled charged interfaces condense into lamellar phases with repeat distances that increase with dilution but are much shorter than the bilayers were able to assume, if swelled ideally. This effect is reversible. We attribute this behavior to the negative Gaussian modulus84 of self-assembled charged interfaces. This modulus leads to structural rearrangements in the membranes and a microphase separation at which a disordered phase, composed of vesicles and closed tubes, coexists with the lamellar phase. The negative Gaussian modulus of self-assembled charged interfaces balances the elastic energy cost associated with the formation of the configurational entropically favorable disordered phase.8587 The disordered phase is depleted from the lamellar phase and applies an osmotic stress on it. The lamellar spacing, D, is determined by equating the water chemical potential and the pressures of the two phases. The results of the present study indicate that membranes composed of saturated zwitterionic lipids and adsorbed divalent ions follow a similar behavior to that of membranes composed of charged lipids. This suggests that the adsorbed ions induce a negative Gaussian modulus that leads to the formation of a disordered phase that coexists with the lamellar phase. Unsaturated-Tail Membranes in Multivalent Salt Solutions. To verify the role of the lipid tail structure on the ion adsorption capacity of the lipid headgroup, we checked if the same phenomenon occurs with membranes containing lipids with unsaturated tails (DOPC) or with the hybrid lipid (POPC), containing saturated and unsaturated tails (Figure 4). The unsaturated membranes have a much lower affinity for Ca2þ than do the saturated ones. The second phase, corresponding to membranes that adsorbed the cations, was observed only from 50 mM CaCl2 in the nonextruded samples and from 3 mM CaCl2 with extruded POPC. Even when two phases were observed the dominant phase was that in which the cations did not adsorb (Figure 5) and the membranes remained close together (with dW < 3 nm, as in pure water). The small fraction of unsaturated lipids that adsorbed the cations became charged. 7423
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Langmuir At these salt concentrations, the electrostatic repulsion was already highly screened and the membranes swelled to a relatively short interlamellar spacing (dW = 8 ( 2 nm for nonextruded membranes in 50 mM CaCl2 and dW = 15.2 ( 0.6 nm for extruded POPC in 3 mM CaCl2). To ascertain whether those observations are specific to Ca2þ ions, the behavior of different cations at the zwitterionic surfaces of the unsaturated-tail membranes was examined. Cl was the anion in all of the salts used. We measured dW for DOPC and for POPC in different multivalent salt solutions (Figures 6 and 7, respectively), and a similar phenomenon was observed for all of
Figure 4. Interlamellar spacing, dW, as a function of the CaCl2 concentration for lipid solutions containing unsaturated-tail DOPC or hybrid lipid POPC [prepared with or without extrusion (ext.)]. In all of the samples, the final total lipid concentration was 15 mg/(mL of salt solution), equivalent to ∼1.5 wt % lipid. The corresponding molar concentration of each lipid is indicated.
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the divalent salts studied. In the presence of divalent cations, DOPC and POPC membranes maintain a short interlamellar spacing. Above ca. 13 mM salt concentration (depending on the ion), this spacing decreases further with salt concentration down to dW < 2 nm (when the salt concentration reaches 1 M). As we shall see later, this is partially due to the osmotic stress applied to the membranes by the ions excluded from the spacing between them and partially due to the effect that the ions have on the interactions between the bilayers. A comparison between the interactions of DOPC and POPC with Zn2þ ions is presented in Figure S6 in the SI. In the presence of SPM cations (that have 4 amine positive charges), the DOPC membranes exhibited two phases (P2 and P3 in Figure 6a) that swelled with increasing SPM concentration and coexisted with the main lamellar phase, with an interbilayer spacing that decreased with increasing SPM concentration (P1 in Figure 6). As we shall later see, in that sense SPM behaves as a monovalent cation rather than a multivalent one. The secondary phase, in which the membranes are far apart, formed at Zn2þ concentrations that were lower than the corresponding Ca2þ or Mg2þ concentrations (Figure 6a). It is also likely that more Ca2þ than Mg2þadsorbed because the spacing in the presence of the former was greater at each concentration. In the primary phase (Figure 6b) at a given salt concentration, dW followed the sequence Zn2þ > Ca2þ > Mg2 ≈ SPM. In this phase, a larger spacing suggests that fewer ions are free to apply osmotic stress on the bilayer. The findings in Figure 6 therefore suggest that the divalent ions bind to DOPC in the sequence Zn2þ > Ca2þ > Mg2þ, in agreement with earlier studies6,2022,42,45,51 that discussed the binding of Ca2þ and Mg2þ. This binding leads to small quantities of charged membranes (the secondary P2 phases in Figure 6), similar to that of membranes with saturated tail lipids. To adsorb onto the lipid headgroups, the ions need to penetrate between the bilayers in the multilamellar structure. This penetration may take time and may depend on the membrane morphology and the number of defects in the membranes through which ions can penetrate. To study the effect of ion penetration rate, we measured
Figure 5. Illustration of the behavior of ions near unsaturated zwitterionic membranes. The interbilayer spacing, dW, of zwitterionic membranes in pure water is ca. 2 to 3 nm (middle panel). The addition of the divalent salt CaCl2 (right panel), the monovalent salt (NaCl, left panel), or a polyamine salt (SPM, left panel) does not affect the membrane’s structural parameters. The ions are represented as colored spheres: green spheres, Cl; red spheres, Ca2þ; and yellow spheres, Naþ. 7424
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Figure 6. dW as a function of salt concentration for 15 mg/(mL of salt solution) DOPC membranes with different multivalent salts as indicated. (a) Solid symbols correspond to the predominant phases, and open symbols correspond to secondary phases that are significanly less prominent. (b) The main phase (P1) on an expanded scale.
Figure 7. dW as a function of salt concentration for 15 mg/(mL of salt solution). POPC membranes prepared with and without extrusion (ext.) in ZnCl2 and CaCl2 salt solutions, as indicated.
dW of POPC membranes in CaCl2 and ZnCl2 solutions, prepared with or without extrusion (Figure 7). Although the overall behavior is rather similar for the two preparation methods, the extruded membranes tend to absorb the divalent cations at lower salt concentrations. Those concentrations were still higher than the concentrations at which the saturated lipids (without extrusion) adsorbed the same ions. This indicates that the lower ion affinity to the unsaturated membranes cannot be attributed to a kinetic barrier. Ion Affinity to DLPC Membranes. DLPC Membranes in Multivalent Salt Solutions. To investigate the affinity of ions for membranes containing the saturated DLPC lipids, we compared the interactions of DLPC with Zn2þ and Ca2þ ions (Figure 8). For DLPC in ZnCl2 solutions, the same adsorption phenomenon was observed but the swelling of the membranes was maximized at shorter interlamellar gaps. For example, with a 1 mM CaCl2 solution, dW = 32 ( 10 nm, but with a 1 mM ZnCl2 solution, dW = 19.7 ( 0.8 nm. We also note that in the case of Zn2þ ions the slope of dW as a function of salt concentration is more moderate. This behavior is consistent with a lower affinity of Zn2þ ions for
Figure 8. dW as a function of salt concentration for 15 mg/(mL of salt solution) DLPC membranes with different salt solutions, as indicated.
DLPC, compared with that of Ca2þ ions. If fewer Zn2þ ions adsorb onto DLPC bilayers, then the bound counterion concentration in the gap will be lower and hence the repulsive forces between the bilayers will be weaker. In addition, more ions will remain unbound and screen the electrostatic repulsion to a greater extent. Figure 8 shows the interaction of trivalent ion La3þ with DLPC. La3þ ions readily adsorb onto the membrane surface at salt concentrations of as low as 0.05 mM and swell the membranes to dW = 54 ( 1 nm. This demonstrates that the affinity of La3þ ions for zwitterionic membranes is significantly higher than that of divalent ions, consistent with earlier studies with DPPC,34 eggPC37,40 or POPC.54 DLPC Membranes in Mixtures of CaCl2 and NaCl Solutions. As we saw above, the interaction between divalent cations and zwitterionic interfaces is consistent with the adsorption of the ions onto the membrane surface. We may therefore think about the membranes as charged surfaces that repel each other. To investigate the role of electrostatic forces in the overall interaction between the membranes, we performed screening experiments in which we added mixtures of NaCl and CaCl2 salt solutions to lyophilized DLPC. 7425
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Table 2. Screening Test Parameters for 15 mg/(mL of Salt Solution) DLPC Membranes with CaCl2 and NaCl (as Described in the Text) parameters of the salt mixture
parameters of the equivalent pure CaCl2 solution
initial CaCl2
added NaCl
concentration
concentration
free CaCl2 concentration
surface charge density,
(mM)
(mM)
dW (nm)
(mM) (λD (nm))
σ ( 102 e/nm2)
dW (nm)
2 3
3 6
22 ( 2 22 ( 3
1.59 ( 0.09 (3.4 ( 0.3) 2.4 ( 0.1 (2.6 ( 0.2)
5.3 ( 0.5 7.9 ( 0.8
30 ( 5 28 ( 6
2.4 ( 0.1 (3.6 ( 0.2) 4.0 ( 0.2 (2.8 ( 0.2)
5
1
23 ( 1
4.0 ( 0.2 (2.7 ( 0.2)
13 ( 1
28 ( 6 a
4.3 ( 0.2 (2.7 ( 0.1)
14 ( 1
3
21
18 ( 2
2.4 ( 0.1 (1.8 ( 0.1)
7.9 ( 0.8
20 ( 4
8.1 ( 0.4 (2.0 ( 0.1)
25 ( 2
5
15
17 ( 4
5
45
13.6 ( 0.4
free CaCl2 concentration
surface charge density,
(mM) (λD (nm))
σ ( 102 e/nm2) 7.9 ( 0.8 13 ( 1
4.0 ( 0.2 (1.8 ( 0.1)
13 ( 1
20 ( 4
8.1 ( 0.4 (2.0 ( 0.1)
25 ( 2
4.0 ( 0.2 (1.27 ( 0.08)
13 ( 1
19 ( 4
16.4 ( 0.8 (1.37 ( 0.06)
47 ( 5
a For a mixture of 5 mM CaCl2 and 1 mM NaCl, the equivalent solution should be 5.333 mM in CaCl2, for which the dW value is closest to that of the 5 mM CaCl2 sample.
Figure 9. dW for 15 mg/(mL of salt solution) DLPC membranes with different NaCl concentrations, as indicated, as a function of (a) added CaCl2 concentration and (b) the Debye screening length, λD, of the salt mixture and of the equivalent pure CaCl2 solution (data taken from Table 2). λD is calculated for the free ion concentration, taking the Ca2þ adsorption into account (see later).
According to the DebyeH€uckel theory, the electrostatic repulsion between two charged surfaces is screened by the presence of ions in the solution, according to their Debye screening length, λD, given by !1=2 8πF¥, i ðzi eÞ2 λD ¼ ð4Þ εw ε0 kB T i
∑
where F¥,i is the bulk salt concentration of the i-th ion and zi is its ionic valence. Therefore, the screening effect of a CaCl2 solution will equal that of a NaCl solution at three times the concentration. The screening experiments performed are summarized in Table 2 and in Figure 9. In Table 2, the interlamellar spacing of the salt mixtures is compared to the distance measured for DLPC membranes in the presence of the equivalent CaCl2 solution that has the same Debye screening length as the salt mixture (shown in Figures 2, 8, and 9; solid square symbols). This analysis assumes that the added NaCl contributes mainly to the Debye screening length. Assuming that only a negligible number
of Ca2þ or Naþ cations adsorb onto the membranes, we find that the concentration of the equivalent CaCl2 solution should be 1 ½CaCl2 equivalent ¼ ½CaCl2 initial þ ½NaCladded 3
ð5Þ
We find that the measured dW is larger in the CaCl2 solutions than in the equivalent salt mixtures (Figure 9a). We attribute this observation to the fact that the Naþ ions do not bind to the membranes and only screen the electrostatic interactions. Hence, the membrane charge density in the CaCl2 solutions is higher and the concentration of ions that are free to screen the electrostatic repulsion is lower than in the equivalent salt mixtures. As expected, at a given CaCl2 concentration, the electrostatic repulsion between the membranes is screened by the addition of NaCl and the interlamellar spacing decreases (Figure 9a; blue, green, and red open circles). These results support the assumption that the large dW in the presence of CaCl2 is due to repulsive electrostatic interactions that originate in the charging of the membranes by the adsorption 7426
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Table 3. Ion Concentrations in 15 mg/(mL of Salt Solution) DLPC with CaCl2 and NaCl Solutions, Measured by Atomic Absorption Spectroscopy
Figure 10. Level of calcium binding, determined by using atomic absorption spectroscopy, as a function of added CaCl2 concentration for 15 mg/(mL of salt solution) DLPC membranes (solid symbols). Solid line: calculated fit to the experimental data, using eq 6 with Ka = 10.8 ( 0.9 M1.
of Ca2þ ions. This conclusion is further emphasized in Figure 9b, where the measured dW of the membranes in the salt mixtures and in the equivalent pure CaCl2 solutions is plotted as a function of the Debye screening length (taking the Ca2þ adsorption into account, see later). The measured dW in the salt mixtures is smaller than that of the equivalent solution throughout all of the samples. Association Constant of CaCl2 to DLPC. To obtain the association constant of CaCl2 to DLPC, we used atomic absorption spectroscopy. Figure 10 shows the adsorption isotherm of Ca2þ ions to the DLPC membrane surface. As can be seen from Figure 10, the amount of Ca2þ adsorbed onto the DLPC membrane surface exceeds 12 mM for the high CaCl2 concentration, and the lipid concentration is 24.1 ( 0.3 mM. Therefore, a binding stoichiometry of 1:2 (bound Ca2þ/lipid) is unlikely, and the binding isotherm was fitted to a 1:1 binding stoichiometry model, as was assumed in most earlier studies.5,9,22,34,37,79,80 This observation was further supported by separate ICP-OES measurements (Figure S1 in the SI) in which the amount of bound Ca2þ reached a plateau at ca. 20 mM when the added salt concentrations were above 100 mM. The reaction we should consider is the following Ka
L þ Ca2þ T L2þ where L is the lipid and L2þ is the Ca2þlipid complex. At equilibrium, we get Ka ¼ ¼
½L2þ eq ½Leq ½Ca2þ eq ½L2þ eq ð½L0
½L2þ
eq Þð½Ca
2þ 0
½L2þ eq Þ
ð6Þ
where the index eq corresponds to the equilibrium concentration and the index 0 corresponds to the added concentration of each species. The quantity of complexes formed is equal to the quantity of bound calcium ions. Therefore, the data in Figure 10 were fitted using eq 6, and an association constant of Ka = 10.8 ( 0.9 M1 was extracted. This value is not too far removed from the binding constant of Ca2þ to DPPC at 5 C, 21 ( 9 M1, found in an earlier study80 or 19 M1, found at 59 C by Akustu and Seelig34 using 2H NMR. Using direct force
measured Ca2þ concentration
added NaCl
adsorbed Ca2þ
in the CaCl2 solution added
concentration
concentration
to the dry DLPC (mM)
(mM)
(mM)
0.9 ( 0.2
3
0.1 ( 0.4
2.0 ( 0.3
6
0.38 ( 0.07
1.7 ( 0.3 3.6 ( 0.4
21 1
0.4 ( 0.1 0.81 ( 0.06
3.0 ( 0.5
10
0.6 ( 0.2
3.1 ( 0.6
15
0.65 ( 0.05
3.2 ( 0.7
45
0.58 ( 0.06
Figure 11. Concentration of bound calcium ions, determined by atomic absorption spectroscopy, as a function of added CaCl2 concentration for 15 mg/(mL of salt solution) DLPC in mixtures of CaCl2 and NaCl solutions, as described in Table 3. The solid line is the adsorption isotherm from Figure 10, using Ka = 10.8 ( 0.9 M1.
measurements, Marra and Israelachvili23 found that the binding constant of Ca2þ to DLPC is ∼15 M1, which is also very close to the value reported here. Using an ICP-OES setup, we measured a binding constant of 15 ( 2 M1, in agreement with our atomic absorption results and with the data of Marra and Israelachvili.23 The fraction of bound Ca2þ cations is generally small (about 20%). The unbound Ca2þ ions are free to screen the electrostatic interaction between membranes containing bound Ca2þ ions. As more Ca2þ ions bind to the surface, the electrostatic repulsion increases as a result of the higher surface charge density and the lower concentration of free ions available for screening. To investigate the effect of added NaCl further, we checked its effect on the binding of Ca2þ to the DLPC membrane surface. Mixtures of NaCl and CaCl2 salt solutions were added to the DLPC lipid, as listed in Table 3. We measured the Ca2þ ion concentrations in the salt stock solutions (before adding them to the dry lipid) and in the supernatant of the centrifuged lipidsalt mixtures and estimated the adsorbed Ca2þ concentrations in the salt mixture solutions, using atomic absorption spectroscopy (Table 3). The results are shown in Figure 11 in which the adsorption isotherm is also incorporated, with the binding constant Ka = 10.8 ( 0.9 M1 obtained from the fit to the data in Figure 10. We can clearly see that under the conditions used in our experiments the addition of NaCl to the solution does not affect the binding of Ca2þ to the surface because the binding isotherm can still nicely fit the data. The added NaCl only screens the 7427
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Figure 12. dW as a function of NaCl concentration for 15 mg/(mL of salt solution) lipid solutions containing (a) saturated tails (DLPC, DMPC, and DPPC) and (b) unsaturated tails [DOPC and POPC, prepared with or without extrusion (ext.)]. When two phases coexist (denoted as P1 and P2), the solid symbols correspond to the predominant phase and the open symbols correspond to the secondary phase.
electrostatic repulsion, as seen in Figure 9. This is somewhat different from an earlier study5 that showed that with added NaCl the electrostatic repulsion between the adsorbed Ca2þ ions was screened and allowed the adsorption of more Ca2þ ions. The conditions of the earlier study, however, were slightly different from ours. In the earlier report, sonicated dispersions of unsaturated lipid eggPC or DOPC, for which the Ca2þ binding is already very weak, were used. Therefore, the addition of small amounts of NaCl was sufficient to allow more Ca2þ binding. In our study, lipids with saturated tails were used, where the amount of Ca2þ bound to the surface was higher and closer to saturation, hence the effect of added NaCl was significantly weaker. 2 H NMR experiments34 of the DPPCCa2þ binding isotherms at 59 C showed that the addition of NaCl enhanced Ca2þ binding. This finding differs from ours. It is possible that the atomic absorption method is not sensitive enough to detect very small changes in ion concentration. In general, the literature is somewhat inconsistent regarding the effect of NaCl addition on the binding affinity of divalent cations to PC membranes. Several papers claim that NaCl encourages divalent cation binding,5,21,34,37,40,62,63,88 and others suggest that it reduces the number of surface-bound cations.8,9,22,56 Our results are in the middle, considering that NaCl does not seem to affect cation binding. Monovalent Ions (Naþ) at the Membrane Surfaces. Recently, there were a few reports on the interactions of dipolar interfaces with monovalent ions.64,65,67,7274 Although the interaction between zwitterionic lipids and divalent ions is strongly dependent on the lipid saturation level and has a dramatic effect on dW, with monovalent salt NaCl we found significantly weaker effects. This difference must be due to the much weaker iondipole interaction between the lipid headgroups and the monovalent ions. We studied the interactions of NaCl with different saturated and unsaturated lipids. Figure 12 shows the measured dW for different membranous systems as a function of added NaCl concentration. The DPPC membranes did not swell throughout the entire concentration range whereas the DLPC and DMPC membranes swelled by up to 6 or 7 Å. The swelling of DLPC is in
agreement with an earlier study65 and was attributed to the weakening of the van der Waals attraction as a result of the added salt. The DOPC (unsaturated-tail) membranes behave in a similar way to DLPC and DMPC when NaCl is added; DOPC and POPC, however, have an additional coexisting phase in which the water gap decreases with NaCl concentration. The variation in dW is no more than 1 nm. Unlike the case of divalent ions, here there is very little dependence on tail structure and compact packing because each monovalent ion is likely to interact with one lipid (i.e., lateral interactions between lipids are unlikely). Because the interaction is weak, the added NaCl in the CaCl2 and NaCl mixture experiments, described in the earlier section, contributed mainly to the screening effect and most of the monovalent ions did not adsorb onto the surface (Figures 3 and 5, left panel).
’ DISCUSSION The saturated-tail membranes adsorb divalent and trivalent cations onto their surfaces, and the applied surface charge induces electrostatic repulsion between them. Therefore, they behave as charged membranes (such as DOPS or DLPS) in the sense that their intermembrane spacing is large. We shall try to determine whether these systems behave in a similar way to charged membranes also in the sense that a disordered phase coexists with the lamellar phase.81 We will also investigate how the membrane’s structural parameters are affected by the cation adsorption. Atomic absorption measurements indicated that the binding constant of Ca2þ to DLPC membranes is 10.8 ( 0.9 M1. We will use this binding affinity to study the interactions between these membranes and the reversibility of the adsorption. Even though the lipids have the same headgroup, the unsaturated-tail membranes (unlike saturated-tail membranes) have very little tendency to adsorb divalent cations (such as Ca2þ), and the intermembrane spacing of the main phase decreases with cation concentration. In the presence of monovalent ions, this phase coexists with another phase in which the membranes slightly swell with monovalent ion concentration. This behavior 7428
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Figure 13. Fitted lipid headgroup and tail thicknesses as a function of CaCl2 concentration using a form factor model of a stack of infinitely flat uniform slabs with varying electron density. Solution X-ray scattering curves were fitted to the parameters of the form factor using our Xþ analysis software.77 (a) 15 mg/(mL of salt solution) DLPC membranes and (b) 15 mg/(mL of salt solution) DPPC membranes.
is similar to that of saturated-tail membranes in the presence of monovalent ions. We shall try to clarify the differences between cation adsorption affinities of membranes with saturated tails as opposed to unsaturated tails and those between the effects of monovalent and divalent cations on the system. Interactions between Ions and Zwitterionic Membrane Surfaces. The dipole moment, μ, of the PC headgroup is ca. 19 D.89 If all of the headgroups are parallel to the membrane surface,90,91 then their contribution will vanish. A small inclination of the headgroups by 20 is sufficient to induce a dipole moment of about 6.5 D perpendicular to the membrane surface.92 The interaction, w, of the ions with the PC headgroup is given by93 wðr, θÞ ¼
ðzeÞu cos θ 4πεw ε0 r 2
ð7Þ
where e is the charge of an electron, z is the ionic valence, εw is the relative permittivity of water, ε0 is the permittivity of free space, r is the distance between the dipole center and the ion, and θ is the angle between the dipole to a line joining the ion and the dipole centers. Assuming r = 3 Å and θ = 0,94 this interaction is ca. 2kBT for the monovalent ions (z = 1), ca. 4kBT for the divalent ions (z = 2), and ca. 6kBT for the trivalent ions (z = 3), where kB is the Boltzmann constant and T is the absolute temperature. Any structural changes including the packing of the lipids in the membrane may compete with this relatively weak interaction. Saturated-Tail Membranes in CaCl2 Salt Solutions. When the membranes are far apart because of Ca2þ binding, both the form factor and the structure factor contribute significantly to the measured scattering intensity. We were therefore able to analyze both form and structure factors when Ca2þ adsorbed onto the membranes using a model of a stack of infinitely flat uniform slabs with varying electron density.77,78 In this model, the two tails were represented by one layer and each of the lipid headgroups was represented by two additional layers with a higher electron density surrounding the lipid tails (Figure 1,
Figure 14. Illustration of our suggested model for the difference in cation binding affinity between saturated (right) and unsaturated (left) zwitterionic membranes. The binding affinity is affected by the headgroup entropy associated with the free rotation of the headgroups goverened by the area per headgroup, which is smaller for the saturated membranes. Cation adsorption restricts the headgroup motion and is therefore feasible when the iondipole interaction overcomes the rotational entropy.
inset). The capabilities and limitations of this simple model were extensively discussed.78 Although the extracted headgroup size may be an upper limit, a qualitative trend can be depicted. Figure 13 shows the tail and headgroup thicknesses in the form factors that best fit the data, as obtained using program Xþ developed in our laboratory.77 The values in Figure 13 are the average values of different preparation methods. The error bars correspond to statistical errors in repeated measurements. The adsorption of the Ca2þ cation has little to no effect on the headgroup thickness of DLPC membranes. The headgroup thickness of DPPC increases slightly with salt concentration. We attribute this observation to the increased electron density of the outer layer when the Ca2þ ions adsorb onto the bilayer. If all of the ions adsorb onto the bilayers and each cation binds to two lipid headgroups, then saturation is expected above ca. 10 mM CaCl2. If, however, the binding stoichiometry is 1:1 (i.e., one Ca2þ ion per lipid headgroup), 7429
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Figure 15. Calculated interaction free energy per unit area, f, as a function of dW for 15 mg/(mL of salt solution) DLPC membranes at different salt concentrations. The calculation was made using eq 8, taking the Ca2þ adsorption into account. Solid lines are theoretical calculations, and solid symbols represent the measured equilibrium interbilayer gaps for which we calculated the free energy of interaction. (a) DLPC with CaCl2. The dW values (solid symbols) are taken from Figures 2 and 8. (b) Screening tests: DLPC with CaCl2 and NaCl. The measured dW values (solid symbols) are from Figure 9 and Table 2. The salt concentration of each curve is indicated. (c) Measured (solid symbols) and theoretical (open symbols) dW as a function of the Debye screening length, λD, for DLPC with CaCl2 (circles) and for the screening tests (triangles). The expected values are taken from the minima of the free-energy curves in plots a and b. (d) Measured dW as a function of the membrane charge density, σ, for DLPC in pure CaCl2 solutions (open symbols) and in CaCl2 and NaCl mixtures (solid symbols). The data are taken from Table 2.
then saturation is expected at ca. 20 mM CaCl2. For DLPC, our electron density profiles cannot distinguish between the two options. The 1:1 stoichiometry, however, is consistent with the DPPC headgroup thickness that saturates above 20 mM (Figure 13b). Although we cannot account for the absolute values of the headgroup layer thickness, we can see that the layer of DPPC is thicker than that of DLPC. For DPPC in the gel phase, the area per lipid headgroup, A, is 47.9 Å2 95 and that for DLPC (which is in the liquid phase) is A = 63.2 ( 0.5 Å2.96 Our WAXS measurements (Figures S2S4 and Table S7 in the SI) gave A = 39.7 ( 0.2 Å2 (or A = 41.5 ( 0.1 Å2 if we assume that the tails form a hexagonal lattice) for DPPC and A = 64.5 ( 0.2 Å2 for DLPC. Thus, the headgroup volume remains the same, and the difference in the headgroup thicknesses is plausible. The smaller area per PC headgroup in DPPC results in a more extended conformation of the headgroup toward the water and
hence a larger headgroup layer thickness, as we found. The DLPC headgroup has a larger area, and on average, we can assume a lower tilt angle with respect to the bilayer surface, hence a model with a headgroup layer that is thinner in the z direction (the axis perpendicular to the bilayer surface) fits the scattering curves better. The slight increase in DPPC headgroup thickness with Ca2þ concentration is therefore consistent with the decrease in the lipid area per headgroup associated with cation binding.41,48,52,53,64 This decrease in the DPPC area per headgroup, however, is very small and hence immeasurable in our WAXS setup with Ca2þ (Figure S3 in the SI) or Naþ (Figure S4 in the SI). This result contrasts with earlier studies of DPPC with Ca2þ 41,48 or Naþ.64 Furthermore, the DLPC area per headgroup does not change at all, as evident from Figures 13a and S2 (in the SI). There is no effect whatsoever on the tail thickness because the Ca2þ ions are unlikely to penetrate and interact with the 7430
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carbon chains of the phospholipids, in accordance with earlier findings.35 The low penetration is due to the large change in the Born free energy upon transferring ions from a medium with a high dielectric constant (water with ε = 78) to a low dielectric medium (the carbon tails, with ε ≈ 2). This barrier is on the order of 100kBT per ion.93 The molar fraction of ions in the tail domain, given by the Boltzmann factor, is therefore extremely low (∼1044). Ca2þ Adsorption onto Saturated- and Unsaturated-Tail Membranes. It is apparent that unsaturated lipids DOPC and POPC do not adsorb divalent cations as strongly as do saturated lipids DLPC, DMPC, and DPPC. One double bond in the lipid tail is sufficient to reduce ion adsorption considerably. Divalent cations interact with the phosphate moiety in the PC headgroup,3438 which is identical for all of these lipids, so the difference in cation binding affinity is not due to different interaction energies. The reason must lie in the different tail properties of the different membranes. The saturation level of the lipid tails strongly influences the packing of the lipid molecules in the membrane. Saturated tails can pack efficiently whereas unsaturated tails cannot. This limitation lowers their gel-phase melting temperature. Saturated carbon chains adopt an all-trans conformation and create a tightly packed membrane in which the headgroups have little configurational and rotational entropy. Lipids with unsaturated tails, however, create membranes with relatively loose packing because of the “kink” in their tail, formed by the cis configuration of their double bond. This relatively loose packing enables free rotation of the headgroups (Figure 14). Although the binding experiments here and in earlier studies indicate a binding stoichiometry of 1:1, divalent cation adsorption can still link laterally between adjacent lipid molecules, limit their rotation and lower the headgroup entropy. In the case of membranes with unsaturated carbon chains, the iondipole interaction gained by the adsorption of the ions is insufficient to compensate for the entropy loss associated with headgroup rotation. In the case of saturated tails, however, the packing is tight
felec
8 ! > πk T 1 1 > B > 1 þ > > > πlσdW ðπlσdW Þ2 > > 4ldW > > > 8kB T dW =λD > > e < πlλD ¼ kB T > > > lnðdW Þ > > πlb > > > > kB T dW > > > > : πlb2 λD coth 2λD 1
and the entropic loss is lower, thus cation binding is energetically favorable. Ion Affinity for DLPC Membranes. Interactions between DLPC Membranes in the Presence of Ca2þ Ions. Knowing the number of free ions and the association constant Ka (Figures 10 and 11), we estimated the Debye screening length, λD, in each of the screening experiments (summarized in Table 2). We then calculated the surface charge density, σ, using eq 3 with an area per headgroup, A, of 63.2 ( 0.5 Å2(taken from ref 96) and a [L]0 of 24.1 ( 0.3 mM. Larger values of σ lead to stronger electrostatic repulsive interactions. Considering the screening effect, we estimated the interaction free energy per unit area, f, for each salt concentration (Figure 15a,b, solid lines) using the well-established65 expression ! H 1 2 1 f ðdW , TÞ ¼ 2 2þ 12π dW ðdW þ δÞ ðdW þ 2δÞ2 þ P h λh e
dW =λh
kB T þ 2π
2
1 Af l edW =λf l þ felec ð8Þ KC
where H is the Hamaker coefficient, δ is the membrane thickness, Ph is the hydration pressure constant, λh is the hydration length, Kc is the membrane bending rigidity, and Afl and λfl are the parameters related to the fluctuations of the membrane. For all of the curves in Figure 15a,b, the interaction parameters were taken from the earlier study:65 H = (9.2 ( 0.5) 1014 erg, Ph = (1.6 ( 0.2) 109 dyn/cm2, λh = 2.1 ( 0.1 Å, Kc = (5.8 ( 0.2) 1013 erg, Afl = (1.06 ( 0.10) Å2, and λfl = 6.0 ( 0.2 Å. Note that the interaction curves were calculated with fixed parameters, measured in earlier studies, and with parameters measured in this study. Although no free parameters were used, the parameters from the earlier study65 fit the interactions between DLPC membranes in pure water, whereas in our experiments salts were added. felec is the electrostatic interaction between membranes, resulting from ion adsorption, and is given by the solution to the nonlinear PoissonBoltzmann equation17,97
λD > d W > b
Gouy Chapman ðGCÞ region
d W > λD > b
intermediate region
b > dW , λD 2 > ðbdW Þ
ideal gas ðIGÞ region
λD > dW , λD 2 < ðbdW Þ or λD < b, λD < dW
Debye H€uckel ðDHÞ region
where l is the Bjerrum length, given by l = (e2)/(4πε0εwkBT), and is equal to 7 Å for water at room temperature, and b is the GouyChapman length, given by b = e/(2π|σ|l). The free-energy curves result from a few effects. Unlike membranes of charged lipids (such as DLPS), for which the surface charge density, σ, is constant at all salt concentrations, here σ strongly depends on the number of ions and lipids in the solution. At a given lipid concentration, the amount of Ca2þ binding and hence σ and λD depend on the salt concentration. Therefore, the electrostatic interactions of this system differ from those of charged membranes. This difference is apparent, for example, in Figure 15a, where at dW < 35.2 nm the free-energy
ð9Þ
curve of DLPC in a 1 mM CaCl2 solution is less repulsive than the 2 mM curve. In the case of 1 mM, σ = (2.7 ( 0.3) 102 e/nm2 and λD = 6.2 ( 0.3 nm, whereas in the 2 mM case σ = (5.3 ( 0.5) 102 e/nm2 and λD = 4.4 ( 0.2 nm so the electrostatic repulsion in the first case is lower at low dW because of the short surface charge density. In Figure 15a, the measured dW is substituted into eq 8 (solid symbols), and we can see that this equation well describes the equilibrium force for CaCl2 concentrations between 5 and 20 mM and for very high concentrations (500 and 750 mM). For intermediate concentrations, however, the interaction parameters may differ from those of Petrache et al.65 because we used 7431
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Langmuir the parameters of DLPC in pure water. The earlier study65 showed that the Hamaker coefficient decreases and the hydration pressure constant increases with increasing monovalent salt concentration. For intermediate CaCl2 concentrations in Figure 15a, the measured interbilayer gaps are smaller than expected from the free-energy curves, suggesting that under our conditions there are weaker repulsive interactions or stronger attractive interactions. At very low concentrations, the free energy is repulsive and ideal swelling behavior is expected, as in charged membranes.82,83 At the low lipid concentrations used in the present study, charged membranes phase separate to lamellar and disordered phases.81 The disordered phase applies an osmotic stress on the lamellar phase and leads to the observed dW values. We attribute the deviation in Figure 15a to the coexistence of the lamellar phase with a similar stress-applying entropically-stabilized disordered phase. In Figure 15c, the measured intermembrane distances (solid symbols) are plotted versus the solution Debye screening length. For comparison, we also plot the expected gaps based on the minima in the free-energy curves in Figure 15a,b (open symbols). For high salt concentrations (small λD), the measured dW values well fit the expected gaps, but when the screening length is above ca. 2 nm, the measurements deviate markedly from the expected values. The deviation increases with λD and resembles the deviation from ideal swelling behavior of charged membranes in pure water.81 In the latter case, this anomaly was attributed to the existence of a disordered phase that applies pressure on the ordered lamellar phase and prevents it from swelling ideally. Here too, a coexisting disordered phase may prevent the membranes from reaching the spacing that fulfills the force balance of eq 8. From Table 2 and Figure 9b we can see that the screening lengths are consistent with the measured values of dW within the experimental scatter. This strongly suggests that pure electrostatic interactions dominate the interactions between dipolar interfaces that are able to adsorb divalent ions. Figure 15d shows the measured dW as a function of the membrane charge density, σ, for DLPC in pure CaCl2 solutions or in NaCl and CaCl2 mixtures. At a given membrane charge density, dW is larger in the pure CaCl2 solutions than in any of the salt mixtures because in the pure CaCl2 solutions, fewer ions are available to screen the electrostatic interactions. Reversibility of Ca2þ Adsorption to DLPC Membranes. To determine whether the adsorption of Ca2þ cations to the membrane surface is reversible, we prepared a sample of 60 mg/(mL of salt solution) DLPC [φ = (58.8 ( 0.9) 103] in 4 mM CaCl2 and diluted it by a factor of 4 to compare it with a sample of 15 mg/(mL of salt solution) DLPC [φ = (15.4 ( 0.2) 103] in 1 mM CaCl2. Figure 16 shows the results of this experiment. For the control sample, 15 mg/(mL of salt solution) DLPC with 1 mM CaCl2 (data the same as in Figures 2 and 8), the intermembrane spacing of the swelling phase (P2) is 32 ( 10 nm. The DLPC sample with φ = (58.8 ( 0.9) 103 and 4 mM CaCl2 adsorbed the Ca2þ ions, and the membranes swelled to dW = 7.4 ( 0.3 nm. The equilibrium gap at the higher φ (ca. 7 nm) is lower than the spacing of 15 mg/mL DLPC with 4 mM CaCl2 (29 ( 7 nm), interpolated using the data of 15 mg/mL DLPC with 3 and 5 mM CaCl2 from Figures 2 and 8. On the basis of the DLPCCa2þ association constant Ka, at the higher volume fraction 2 mM Ca2þ ions adsorb onto the membrane and 2 mM Ca2þ ions are free in the solution. At the lower volume fraction (with the same CaCl2 concentration), the concentration of bound cations is ca. 0.8 mM and the concentration of free ions is ca. 3.2 mM. In
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Figure 16. dW as a function of the volume fraction of DLPC, for the reversibility test (see text). The control datum (open symbol) is taken from Figure 8.
the lower volume fraction, the screening is stronger but the membrane charge density is higher. By substituting those values into the expression for the free energy per unit area (eq 8), we find that the expected interaction between the membranes in the higher-volume-fraction solution is more repulsive than in the lower-volume-fraction solution. The disordered phase of the higher lipid concentration may apply more pressure to the lamellar phase, which may affect the water spacing as well (see later). After a 4-fold dilution, at equilibrium, we expect the bound cation concentration to be 0.2 mM and the free cation concentration to be 0.8 mM (as in the control sample). After dilution, the membranes swell to ca. 40 nm (triangle in Figure 16), which is beyond the control solution of DLPC (φ = (15.4 ( 0.2) 103) with 1 mM CaCl2, suggesting that the pressure between the surfaces was stronger than in the control sample. By the 4-fold dilution of the DLPC in 4 mM CaCl2, the concentration of adsorbed cations is expected to be 0.5 mM. However, to obtain the theoretical free-energy curve that has a minimum at the measured spacing of the diluted sample (ca. 40 nm), the adsorbed cation concentration should be only ca. 0.266 ( 0.001 mM. This discrepancy indicates a large degree of reversibility in the adsorption phenomenon. Effect of DLPC Concentration on Ion Affinity. We investigated Ca2þ adsorption to DLPC membranes at different lipid volume fractions in 5 or 10 mM CaCl2 solutions (Figure 17). In the 5 mM CaCl2 solution, a slight decrease in dW with increasing DLPC content, up to φ = (58.8 ( 0.8) 103, was observed. At high DLPC concentrations, dW increased. For the 10 mM CaCl2 solution, the intermembrane spacing remained constant until φ = (72.5 ( 0.7) 103. At the highest lipid concentration, two lamellar phases coexisted. In charged membranes, a disordered phase coexists with a single lamellar phase.81 Because we have a three-component system (salt, lipid, and water), the maximum number of phases, according to Gibbs’ phase rule, is three (rather than two in the case of charged membranes in pure water). This is why in addition to the disordered phase, observed in charged membranes in water, here two lamellar phases may coexist (Figure 17b) with the disordered phase. 7432
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Figure 17. dW as a function of the DLPC volume fraction, φ, in (a) 5 and (b) 10 mM CaCl2 solutions.
Figure 18. Calculated interaction free energy per unit area, f, as a function of dW for DLPC membranes at different volume fractions in (a) 5 and (b) 10 mM CaCl2 solutions. In the inset of b, the scale is enlarged.
In charged membranes in pure water at low lipid concentrations, the disordered phase prevents the system from ideal swelling and dW decreases with lipid concentration. Here, dW is determined by a competition between the effect of the lipid volume fraction on the swelling behavior and the higher electrostatic repulsion due to further Ca2þ adsorption at higher DLPC concentrations and weaker screening. The data in Figure 17 result from these counter effects. Using eq 8, we have calculated the free energy per unit area for the samples with different DLPC volume fractions in either 5 or 10 mM CaCl2 solutions (Figure 18, solid lines), taking the Ca2þ adsorption into account (using the binding constant Ka). The measured intermembrane distances were also substituted into eq 8 and were added to Figure 18 (solid symbols). As the lipid concentration increases, the free-energy curve becomes more repulsive because of the higher level of Ca2þ binding and
weaker screening, so we expected an increase in the intermembrane gaps. Nevertheless, the measured dW decreased (Figure 18a) or remained constant (Figure 18b) with the DLPC concentration. This behavior is consistent with the existence of a disordered phase that exerts pressure on the ordered lamellar phase, leading to dW values that are smaller than expected, as in charged membranes.81 Interactions of Monovalent and Polyvalent Ions with Zwitterionic Membranes: The Dual Behavior of Polyvalent Ions. We studied the interaction of DLPC with the monovalent salt NaCl and the tetravalent salt spermine (SPM). Figure 19 shows that when the measured dW is plotted as a function of the Debye screening length, λD, both salts behave similarly. These results suggest that from the lipid’s point of view (i.e., on a small scale or close to the SPM ions), SPM behaves as a monovalent salt in the sense that it does not charge the membrane. 7433
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Figure 19. dW as a function of the Debye screening length, λD, for 15 mg/(mL of salt solution) DLPC in NaCl (squares) or SPM (triangles) solutions. The λD of SPM was calculated as a (a) a tetravalent salt (i.e., z = 4) or (b) a monovalent salt (i.e., z = 1) at 4 times the SPM concentration.
Figure 20. dW as a function of the Debye screening length, λD, for the swelling phases of 15 mg/(mL of salt solution) DOPC in NaCl or SPM solution. The λD of SPM was calculated as (a) a tetravalent salt or (b) a monovalent salt at 4 times the SPM concentration.
The charges of the polyamine are sufficiently separated from each other so that the lipid headgroups experience them as four monovalent ions (per SPM molecule). Therefore, their iondipole interaction is too weak for membrane adsorption. Figure 19, however, demonstrates better agreement between the two salts when the polyamine is treated as a tetravalent salt (Figure 19a), when calculating λD. This result indicates that although on the microscopic level the polyvalent ions are experienced by the dipolar interface as if their charges are separated, on the macroscopic level (i.e., the bulk solution) the proximity of the amine groups is sufficient to treat the SPM as a tetravelent salt. In other words, in the bulk the details of the exact locations of the polyvalent charged groups become indistinguishable. The phase in which the DOPC membranes swell with the NaCl concnetration (Figure 12b) is shown in Figure 20 and
compared with the swelling induced by SPM (taken from Figure 6a). As in the case of DLPC, the addition of SPM to DOPC produced a swelling behavior similar to that of monovalent salts but still on the macroscopic level, SPM should be regarded as a tetravalent salt (Figure 20a). Effect of Nonadsorbing Ions on the Interactions between the Membranes. The other phase appearing in the unsaturated system, in which dW decreases with NaCl concentration, is similar to the nonasorbing CaCl2 phases of the unsaturated lipids (Figures 4 and 6b). Therefore, those phases correspond to the exclusion of the Cl and Naþ (or Ca2þ) ions from the gap (i.e., salting out of those ions). The ions outside the gap apply osmotic stress to the membranes and suck water from the interbilayer gap. Figure 21 shows the osmotic stress exerted by the excluded ions 7434
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Figure 21. Logarithm of the osmotic pressure, Π, as a function of dW caculated using van’t Hoff’s law (see text) for DOPC with NaCl (solid circles) or with CaCl2 (solid diamonds) and POPC with NaCl (open circles) or with CaCl2 (open diamonds). The solid line is the experimental DOPC pressuredistance curve obtained from the osmotic stress measurements of Tristram-Nagle et al.98 The dashed line is a calculated pressure distance curve of POPC using parameters from Stallmach et al.99 and Bouvrais et al.100 The black open squares and open triangles are our direct measurements of the osmotic pressure of DOPC with 10, 100, 500, and 1000 mM NaCl . Open squares correspond to osmotic stress measurements from the supernatant, and open triangles corresponds to osmotic stress measurements of the whole mixture, as described in the text.
for DOPC and POPC samples with NaCl or CaCl2. The osmotic stress was calculated using van’t Hoff’s law: Π = RT(Φic), where c is the molarity of the solution, i is the number of moieties into which the solute dissociates (i = 2 for NaCl and 3 for CaCl2), Φ is the osmotic coefficient (0.93 for NaCl and 0.86 for CaCl2), R is the universal ideal gas constant, and T is the absolute temperature. The validity of this calculation was verified by our own osmotic stress measurements on a few points along the pressuredistance curve. Furthermore, the equilibrium of those phases was confirmed by obtaining identical osmotic pressures from measurements of the mixed dispersion and after centrifuging the dispersion and sampling the supernatant. The interbilayer spacing, dW, was taken from Figures 4 and 12b (using the phases in which dW decreases below its pure water value with salt concentration). The solid line in Figure 21 corresponds to measurements of the osmotic stress [applied via polyvinylpyrrolidone (PVP)] on DOPC membranes performed by Tristram-Nagle et al.98 The applied osmotic pressure is equal to the pressure between the membranes resulting from the van der Waals, hydration, and undulation interactions65 ! H 1 2 1 PðdW , TÞ ¼ þ 6π dW 3 ðdW þ δÞ3 ðdW þ 2δÞ3 kB T 2 1 Af l dW =λf l dW =λh þ e ð10Þ þ Ph e 2π KC λf l where the parameters are the same as described in eq 8 and P(dW,T) = ∂f(dW,T)/(∂dW). The interaction parameters are those that gave the best fit to data in the earlier study:98 H = 4.7 1014 erg, Ph = 5.5 108 dyn/cm2, λh = 2.22 Å, Kc = 7 1013 erg, λfl = 5.8 Å, and Afl = 1.06 Å2. The last two parameters were measured for DLPC and they should be similar in the case of DOPC.65
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The resulting pressuredistance curve exhibits a trend similar to that of the osmotic pressure exerted by the salts. The osmotic pressure applied by the ions, however, is systematically higher than the theoretical curve at each dW. The two phases in Figure 12b may be accounted for if the membranes exclude some of the Naþ and Cl ions and other ions adsorb on the DOPC membrane surface. However, the CaCl2 data (that applies a similar osmotic pressure) disproves this explaination. If Ca2þ ions were to adsorb onto the membranes, a distinct rise in dW should have been observed in Figure 4. This was not observed; therefore, most of the Ca2þ ions did not adsorb onto DOPC. If Naþ or Cl were adsorbing onto DOPC membranes, the osmotic pressure curve exerted by them would have been weaker than that of CaCl2. Because those two pressures are similar (Figure 21, solid symbols), we conclude that most of the monovalent ions are unlikely to adsorb onto DOPC membranes. Furthermore, the results of our own osmotic stress measurements (Figure 21, open squares and open triangles) fall exactly on the calculated pressures. This strongly suggests that there is indeed little or no ion adsorption on the surface of the membranes and all of the ions are free to apply osmotic pressure. A similar conclusion can be reached for the POPC membranes in Figure 21 (open symbols), where the interaction parameters were taken from Stallmach et al.:99 Ph = (7 ( 1) 108 dyn/cm2 and λh = (2.4 ( 0.1) Å, from Bouvrais et al.100 Kc = (9.9 ( 0.1) 1013 erg with H = (8 ( 2) 1014 erg (as in eggPC14) and the undulation pressure parameters are Afl and λfl as in DOPC. It is possible that the presence of ions changes the interaction parameters, such as the Hamaker coefficient H.65 The osmotic stress that the Naþ and Cl ions need to apply in order to bring the DOPC and POPC membranes to a certain dW is much higher than that applied by the PVP (for the same dW). This suggests that the interactions between the membranes in the presence of salt become more repulsive (or less attractive). This is in agreement with the findings of Marra and Israelachvili23 in which the addition of monovalent salts screens the vdW attraction between bilayers and the Hamaker coefficient is smaller in the presence of these salts.65,67 The general conclusion is that Naþ and Cl ions adsorb weakly, if at all, onto zwitterionic interfaces and most of the ions do not adsorb onto any of the membranes’ surfaces, in agreement with earlier suggestions.9,24,56,67,88,101 This membrane ion exclusion is due to the weak iondipole interaction between the monovalent ions and the zwitterionic headgroup. It has been suggested62 that divalent and trivalent ions can overcome an energy barrier to approach the membrane surface associated with the extended conformation of the PC headgroup. This barrier may be attributed to the headgroup configurational entropy loss associated with ion binding. The monovalent ionPC interaction (ca. 2kBT as opposed to 4kBT and 6 kBT for di- and trivalent ions, respectively) is insufficient to overcome this entropic barrier. Cl is also the counterion of Ca2þ, suggesting that the Ca2þ rather than the Cl ions drive the affinity of the CaCl2 to the membrane with saturated lipids.
’ CONCLUSIONS We demonstrated that divalent and trivalent cations may charge dipolar (neutral) membranes. As opposed to charged membranes, the charges in this system are not covalently bound to the surface. Therefore, the structure and concentration of the lipids and the salt ions govern the equilibrium partition of the 7435
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Langmuir ions among the surface of the membranes and the bulk solution. This behavior complicates the interaction analysis of the system compared with charged membranes because both the surface charge density and the screening length depend on the above parameters. The complexity of the system allows it to form up to three different phases rather than two in the case of charged membranes in pure water. Our results indicate that by analogy to charged membranes81 a disordered phase may coexist with the lamellar (ordered) phase (and in some cases with two different lamellar phases, see Figure 17b). The disordered phase applies osmotic pressure to the lamellar phase and therefore prevents it from swelling ideally because of the positive charge of the membranes. This effect modifies the force balance that determines the gap, dW, between the membranes and leads to its marked deviation (Figure 15c) from the expected behavior on the basis of eq 8. The binding affinity of cations to PC membranes depends on several parameters. The degree of saturation of the hydrocarbon chains has a significant effect on cation binding. Multivalent cations predominantly bind saturated membranes. We may attribute this observation to competition between iondipole interactions and the configurational entropy of the headgroups. The headgroup entropy is significantly lower when the lipids have saturated tails. Therefore, the binding of divalent cations is stronger to membranes with fully saturated tails because the system gains iondipole enthalpy and loses little headgroup entropy. The valence of the cation determines the strength of the iondipole interaction and therefore plays a significant role in the binding affinity of the ions to PC membranes. The strength of cation binding to DLPC membranes follows the order La3þ > Ca2þ > Zn2þ > Naþ ≈ SPM. This order results from the higher iondipole energy associated with the binding of cations with higher valence. Naþ ions do not bind to DLPC membranes because the iondipole interaction energy is insufficient to compensate for the headgroup entropy loss. The PC headgroups perceive the SPM ion as four separate monovalent ions, and hence SPM does not adsorb onto the membrane. From the bulk or the electrostatic screening point of view, however, the SPM ion behaves as a tetravalent ion (Figures 19a and 20a). The charging of the zwitterionic membranes by cations is expected to affect biological processes because cell membranes, mainly composed of zwitterionic lipids, often bind those ions. This study suggests that the complexity of the system and the binding properties of cations can delicately regulate the charge density and hence the interactions between zwitterionic membranes in biologycal systems.
’ ASSOCIATED CONTENT
bS
Supporting Information. Binding constants of several ions to PC membranes, ICP-OES measurements of the Ca2þ binding to DLPC, WAXS measurements, and the interaction of ZnCl2 with DOPC and POPC. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Tel: þ972-2-6586030. Fax: þ972-2-5618033.
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’ ACKNOWLEDGMENT The SOLEIL synchrotron, SWING beamline, EMBL Hamburg, beamline X33, Elettra, 5.2 L SAXS beamline, and ESRF, beamlines BM26B and ID02 are acknowledged because some of the data were acquired there. We acknowledge helpful discussions with D. Harries, S. A. Safram, and P. A. Pincus. This project was supported by the Israel Science Foundation (grant number 351/ 08), The Human Frontiers Science Program Organization (Career Development Award, CDA 0059/2006), the US-Israel Binational Science Foundation (grant numbers 2005-234 and 2009-271) and the James Frank program. P.S. and O.S. acknowledge support from the Samuel and Lottie Rudin Foundation fellowships. U.R. acknowledges support from the Alon Fellowship for Young Investigators. We also thank the Safra, Wolfson, and Rudin Foundations for supporting our laboratory. ’ REFERENCES (1) Sundler, R.; Papahadjopoulos, D. Control of membrane fusion by phospholid head groups I. Phosphatidate/phosphatidylinositol specificity. Biochim. Biophys. Acta, Biomembr. 1981, 649, 743–750. (2) Wilschut, J.; Duezguenes, N.; Papahadjopoulos, D. Calcium/ magnesium specificity in membrane fusion: kinetics of aggregation and fusion of phosphatidylserine vesicles and the role of bilayer curvature. Biochemistry 1981, 20, 3126–3133. (3) Hauser, H.; Shipley, G. G. Interactions of divalent cations with phosphatidylserine bilayer membranes. Biochemistry 1984, 23, 34–41. (4) Philipson, K. D. Interaction of charged amphiphiles with Naþ-Ca2þ exchange in cardiac sarcolemmal vesicles. J. Biol. Chem. 1984, 259, 13999–14002. (5) McLaughlin, A.; Grathwohl, C.; McLaughlin, S. The adsorption of divalent cations to phosphatidylcholine bilayer membranes. Biochim. Biophy. Acta, Biomembr. 1978, 513, 338–357. (6) Lau, A. L. Y.; McLaughlin, A. C.; MacDonald, R. C.; McLaughlin, S. G. A. The Adsorption of Alkaline Earth Cations to Phosphatidyl Choline Bilayer Membranes: A Unique Effect of Calcium. Bioelectrochemistry: Ions, Surfaces, Membranes; American Chemical Society: Washington, DC, 1980; pp 4956. (7) Klein, J. W.; Ware, B. R.; Barclay, G.; Petty, H. R. Phospholipid dependence of calcium ion effects on electrophoretic mobilities of liposomes. Chem. Phys. Lipids 1987, 43, 13–23. (8) Tatulian, S. A. Binding of alkaline-earth metal cations and some anions to phosphatidylcholine liposomes. Eur. J. Biochem. 1987, 170, 413–420. (9) Satoh, K. Determination of binding constants of Ca2þ, Naþ, and Cl ions to liposomal membranes of dipalmitoylphosphatidylcholine at gel phase by particle electrophoresis. Biochim. Biophys. Acta, Biomembr. 1995, 1239, 239–248. (10) Sabín, J.; Prieto, G.; Ruso, J.; Sarmiento, F. Fractal aggregates induced by liposome-liposome interaction in the presence of Ca2þ. Eur. Phys. J. E: Soft Matter Biol. Phys. 2007, 24, 201–210. (11) Ninham, B. W.; Parsegian, V. A. van der Waals interactions in multilayer systems. J. Chem. Phys. 1970, 53, 3398–3402. (12) Parsegian, V. A.; Ninham, B. W. Van der Waals forces in manylayered structures: Generalizations of the Lifshitz result for two semiinfinite media. J. Theor. Biol. 1973, 38, 101–109. (13) Leneveu, D. M.; Rand, R. P.; Parsegian, V. A. Measurement of forces between lecithin bilayers. Nature 1976, 259, 601–603. (14) Lis, L. J.; McAlister, M.; Fuller, N.; Rand, R. P.; Parsegian, V. A. Interactions between neutral phospholipid bilayer membranes. Biophys. J. 1982, 37, 657–665. (15) Rand, R. P.; Parsegian, V. A. Hydration forces between phospholipid bilayers. Biochim. Biophys. Acta, Rev. Biomembr. 1989, 988, 351–376. (16) Helfrich, W. Steric interaction of fluid membranes in multilayer systems. Z. Naturforsch., A: Phys. Sci. 1978, 33, 305–315. 7436
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