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Jul 8, 2019 - To control the membrane charge density, we mixed lipids with negatively charged headgroups, DLPS and DOPS, with their zwitterionic ...
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Structure and Interactions between Charged Lipid Membranes in the Presence of Multivalent Ions Lea Fink, Ariel Steiner, Or Szekely, Pablo Szekely, and Uri Raviv*

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Institute of Chemistry and Center for Nanoscience and Nanotechnology, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 9190401, Israel ABSTRACT: When aqueous salt solutions contain multivalent ions (like Ca2+ or Mg2+), strong correlation effects may lead to ionbridging, net attraction, and tight-coupling between like-charged interfaces. To examine the effects of surface charge density, temperature, salt type, and salt concentration on the structures of tightly coupled charged interfaces, we have used mixed lipid membranes, containing either saturated or unsaturated tails in the presence of multivalent ions. We discovered that tightly coupled membrane lamellar phases, dominated by attractive interactions, coexisted with weakly coupled lamellar phases, dominated by repulsive interactions. To control the membrane charge density, we mixed lipids with negatively charged headgroups, DLPS and DOPS, with their zwitterionic analogue having the same tails, DLPC and DOPC, respectively. Using solution X-ray scattering we measured the lamellar repeat distance, D, at different ion concentrations, temperatures, and membrane charge densities. The multivalent ions tightly coupled the mixed lipid bilayers whose charged lipid molar fraction was between 0.1 and 1. The repeat distance of the tightly coupled phase was about 4 nm for the DLPS/DLPC mixtures and about 5 nm for the DOPS/DOPC mixtures. In this phase, the repeat distance slightly increased with increasing temperature and decreased with increasing charge density. When the molar fraction of charged lipid was 0.1 or 0.25, a less tightly coupled phase coexisted with the tightly coupled phase. The weakly coupled lamellar phase had significantly larger D values, although they were consistently shorter than the D values in monovalent salt solutions with similar screening lengths.

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that is fairly similar to a Wigner crystal.12 The correlated multivalent ions bridge opposite monovalent lipid molecules and lead to strong attraction between like-charged bilayers.14 Interface dielectric mismatch can also contribute to the attractive interaction.15 Like-charge attraction leads to a range of complex structures including bundling of DNA,16 filamentous proteins,17,18 virus crystals,19,20 and tight coupling between charged membranes.14,21−24 The factors that may determine the character of the interaction include the flexibility of the interface or chains, their charge-density, temperature, the type and chargedensity of the multivalent counterions, and the structure of the interfaces: spherical, cylindrical/rod-like, flat, or chain-like.25,6 It has been shown that the binding of calcium ions to zwitterionic and charged lipid bilayer membranes occurs spontaneously, but it is an endothermic process and is therefore entropy driven.24 The entropy gain is due to partial dehydration of the bilayer24,26 and release of water molecules from the hydration shells of the ions and the lipid headgroups, even though after the ions bind, the lipid molecules are more tightly packed, the membranes get stiffer, and their melting temperature increases.26,27 The binding to charged lipid

INTRODUCTION The associations of ions with charged lipids is involved in many interesting physiological processes.1−5 There have been some theoretical and experimental efforts to characterize and explain the interactions of multivalent ions with charged membranes.6 These interactions are essential for membrane structure, dynamics, stability, binding of proteins to or into membranes, membrane fusion, and transport of small molecules across membranes.7−9 Lipids with charged headgroups can form charged bilayers in water. The lipids have counterions that dissociate in aqueous solutions and induce a net repulsive interaction between two like-charged membranes.10,11 The Poisson−Boltzmann theory can explain the repulsive interactions when the counterions are monovalent but fails in the presence of multivalent ions.12 In this case, it is important to take into account the correlations between discrete ions next to charged surfaces. Strong electrostatic spatial correlations in the presence of multivalent counterions are expected when the coupling parameter, Ξ  2 π Z3lB3σ, exceeds unity.13 lB  e2(4πεε0kBT)−1 is the Bjerrum length (about 7 Å in water), and Z is the valence of the counterions. Therefore, when the membrane charge density, σ, exceeds 0.06 e/nm2 in solutions of divalent ions, such as calcium or magnesium, ion correlation effects may dominate. At a finite temperature, multivalent ions next to a charged membrane are expected to form a strongly correlated liquid © XXXX American Chemical Society

Received: March 15, 2019 Revised: June 17, 2019 Published: July 8, 2019 A

DOI: 10.1021/acs.langmuir.9b00778 Langmuir XXXX, XXX, XXX−XXX

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Langmuir molecules is more endothermic and releases more water molecules than binding to the zwitterionic lipid molecules.24,28−31 The binding of divalent cations like calcium and magnesium to phosphatidylserine (PS) is deeper in the headgroup compared with monovalent cations like sodium.32 Calcium binding induces a conformational change in the P−O ester bonds from gauche-gauche to antiplanar-antiplanar. The carboxylate group remains hydrated in the PS-Ca2+ complexes, and a new hydrogen bond is formed between one of the ester C=O groups and water molecules.26 In this paper, we examined the effect of membrane surface charge density, temperature, and salt concentration on the structure of the forming lamellar phases by mixing the negatively charged saturated lipid 1,2-dilauroyl-sn-glycero-3phospho-L-serine (DLPS) with its zwitterionic (dipolar, net neutral) lipid analogue, 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC). In another set of experiments, we mixed the negatively charged unsaturated lipid dioleoyl(C18:1)-snglycero-3-phospho-L-serine (DOPS) with its zwitterionic lipid analogue 1,2- dioleoyl(C18:1)-sn-glycero-3-phosphocholine (DOPC) and investigated the effect of membrane surface charge density as well as salt concentration and type. On the basis of our observations, we determined the critical conditions for tight coupling between like-charged membranes and characterized the structural changes of those phases under the examined conditions.

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Figure 1. Lamellar repeat distance, D, of DLPS as a function of CaCl2 (solid symbols) and NaCl (open symbols) concentrations. Below 5 mM CaCl2, two lamellar phases coexisted: a tightly coupled phase (solid circles) and a second phase with much larger D values (solid squares). The concentration of the two salts are arranged so that concentrations with the same Debye screening length have the same position along the horizontal axis. The solid curve is the calculated D for the case of added NaCl, taken from reference 34. The measurements with CaCl2 were performed a few months after the CaCl2 was mixed with the lipids. Error bars are smaller than the size of the symbols when the lamellar repeat distances were 20 nm or less. At larger repeat distances, the error bars were ±1 nm.

RESULTS AND DISCUSSION Using solution X-ray scattering we have measured the lamellar repeat distance, D, of the saturated charged lipid DLPS as a function of CaCl2 concentration (Figure 1). At room temperature, all the CaCl2 concentrations (between 0.05 and 200 mM) tightly coupled the negatively charged DLPS membranes (solid gray circles in Figure 1). As the membrane charge density of DLPS bilayers was high (1.81 e/nm2), it is likely that strong local calcium ion correlation effects led to the observed strong attraction between the like-charged DLPS bilayers. The D value of the tightly coupled phase of DLPS was 38.9 ± 0.5 Å. At room temperature, the thickness of DLPS in water is about 32 Å.33 To examine the stability of the tightly coupled phase we incubated the tightly coupled phase at 60 °C for a month to allow the water molecules to evaporate. The D value, however, did not change (when measured at room temperature), suggesting that the water molecules between the lipid molecules were tightly bound to the bilayers and to the calcium ions between them. Similarly, application of osmotic stress (by 20 wt % of 20 kD polyethylene glycol) or dialysis against water for a month, freeze−thaw cycles, and bath sonication did not eliminate the tightly coupled phase or change its repeat distance. Figure 2 shows that in CaCl2 solutions, temperature only slightly increased D (by 1 Å or less). Similar temperature dependence was observed over a wide range of calcium concentrations (between 1 and 100 mM), suggesting that electrostatic screening effect had negligible contribution. Therefore, the scatter of the results reflects the measurement error. At 1 mM CaCl2, the tightly condensed phase coexisted with the weakly coupled phase (Figure 1, solid square symbol). The weak dependence of D on calcium concentration (Figure 2) suggests that at low calcium concentrations, the adsorption of calcium ions within the tightly coupled phase was higher than the lipid/calcium molar ratio in the solution.

Figure 2. Lamellar repeat distance, D, of DLPS as a function of temperature at different CaCl2 concentrations, as indicated. Error bars are below the size of the symbols.

We have shown that for DLPS in water, the area per headgroup increases with temperature, the bilayer thickness, δ, and membrane rigidity decrease with temperature.33 We therefore attribute the increase in D to the increasing water gap between the bilayers with increasing temperature. The B

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increases with NaCl concentration.51 Both at low salt concentrations and in the crystal, the screening lengths are very long, so a minimum screening length at a certain salt concentration is indeed expected. Our DLPS data (σ = 1.82 e/ nm2), however, showed that the lamellar repeat distance, D, monotonically decreased with increasing NaCl concentration all the way up to 5 M (Figure 1). The fact that D decreased with increasing NaCl concentration suggests that the results might depend on the exact conditions of the experiments, even though the screening length is a property of the bulk solution. The mica substrates used in the surface force measurements are rigid at all salt concentrations. In contrast, at high salt concentrations, lipid membranes have higher melting temperatures and stiffer bilayers52 and hence weaker repulsive undulation forces. The weaker repulsion could be consistent with the observed monotonically decreasing repeat distances in our experiments. We then repeated the measurements with the unsaturated charged lipid, DOPS, and by and large obtained similar behavior (Figure 3). A comparison of the behaviors of DOPS with DLPS (Figures 1 and 3) shows that below 5 mM CaCl2, both lipids had coexisting tightly coupled and weakly coupled phases. However, the D values of the weakly coupled phase of DOPS in CaCl2 were closer to the theoretical prediction and to the values of DOPS in NaCl, for the same screening length. Yet, in

increase in the water gap with temperature is therefore likely to be larger than the increase in D. The adsorption of calcium is endothermic and is hence expected to strengthen with temperature. Nevertheless, our data suggest that the water gap slightly increased with temperature. We hypothesize that the stronger ions adsorption had a negligible effect on the attractive interaction. Instead, we attribute the weaker attractive interactions to the increased undulations at higher temperatures that led to weaker ion correlations. Below 5 mM CaCl2, the tightly coupled DLPS phase (solid circles in Figure 1) coexisted with a second weakly coupled phase (solid squares in Figure 1), whose D values were much larger than those of the tightly coupled phase. We attribute the large D values to the repulsive electrostatic interaction between the negatively charged DLPS bilayers.35−40 The fraction of the tightly coupled phase (solid circles in Figure 1) was small at low CaCl2 concentration and increased with CaCl2 concentration. Above 5 mM, the tightly coupled phase was the only observed phase. The D values of the weakly coupled phase, however, were shorter than the D values found for DLPS in the equivalent NaCl solutions (open symbols and solid curve in Figure 1). Note that to attain the same Debye screening length, the equivalent NaCl concentration was three times higher than the concentration of CaCl2.41 The solid curve in Figure 1 corresponds to the calculated D values between DLPS bilayers as a function of NaCl concentration, taken from our earlier study.34 The calculation is based on theoretical free energy of charged liquid membranes. The model includes the van der Waals attractive interaction, hydration, undulations, and electrostatic repulsive forces. The electrostatic interactions were based on numerical solutions of the Poisson−Boltzmann (PB) theory,42 modified to account for surface charge regulation owing to nonelectrostatic interactions between the counterions and the surface, between the counterions themselves, and for the mixing entropy of the lipid molecules in the bilayer, which have dissociated counterions and nondissociated counterions, as explained.34,43,44 In the CaCl2 solutions, the D values of the weakly coupled phase are shorter than in the corresponding NaCl solutions (Figure 1, solid squares and open circles). This observation is surprising because some of the calcium ions were trapped in the tightly coupled phase. As a result, the screening lengths in the CaCl2 solutions should have been longer than in the corresponding NaCl solutions. The Poisson−Boltzmann theory, however, is not applicable to divalent ions, since ion correlation effects that dominated at the tightly coupled phase could contribute to the interactions and were not taken into account.45,46 We hypothesize that the Ca2+ ions induced a coexisting disordered phase (at a larger fraction than Na+ ions), which contributed an osmotic pressure and led to shorter D values.38,47−49 Another reason for the shorter D values, could be the fact that the adsorbed cations increased the stiffness of the bilayers and hence reduced the extent of the repulsive undulation forces between the membranes.50 Furthermore, the adsorbed divalent ions are bound deeper in the headgroup compared with monovalent ions,32 resulting in a more effective charge neutralization of the surface and weaker electrostatic repulsion. It is of interest to note that recent surface force measurements showed that when the NaCl concentration is above 1 M, the repulsion between atomically smooth mica surfaces, whose surface charge density is about 2 e/nm2,

Figure 3. Lamellar repeat distance, D, of DOPS as a function of CaCl2 (solid symbols) and NaCl (open symbols) concentrations. The open triangles and open circles are two different sets of measurements. The concentrations are arranged so that concentrations with the same Debye screening length have the same position along the horizontal axis. The solid curve is the calculated D for the case of added NaCl, taken from reference 34. Error bars are smaller than the size of the symbols when the lamellar repeat distances were 20 nm or less. At larger repeat distances, the error bars were ±1 nm. The measurements with CaCl2 were perfomed a few months after the CaCl2 was mixed with the lipids. Figure 5A shows the measurements of the same samples after incubation of few days. C

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Figure 4. Azimuthally integrated X-ray scattering curves as a function of q, the magnitude of the scattering vector, from 15 mg/mL DOPS or DLPS in 10 mM CaCl2 solutions. (A) Small angle X-ray scattering (SAXS) curve of the tightly condensed lamellar phases of DLPS and DOPS. The lamellar repeat distances of DLPS and DOPS, obtained from the indexed correlation peaks, were 38.8 and 51.4 Å, respectively. (B) Wide-angle Xray scattering (WAXS) curve from DLPS. The series of high q peaks, indicated by arrows and pairs of indexes, correspond to a 2D gel phase with lattice parameters: a = 4.76 Å, b = 8.32 Å, γ = 78° (see reference 21 for more details about the analysis). The series of low q peaks indicated by arrows and a single index (corresponding to the direction normal to the membrane plane) are similar to those in the SAXS curve in A and correspond to the tightly condense lamellar phase. (C) WAXS scattering curves from DOPS. The series of high q peaks, indicated by arrows and pairs of indexes, correspond to a 2D gel phase with lattice parameters: a = 4.5 Å, b = 8.3 Å, γ = 89°. The series of low q peaks indicated by arrows and a single index are similar to those in the SAXS curve in part A and correspond to the tightly condensed lamellar phase. Measurements were performed in our in-house setup.

the CaCl2 solutions, the D values were consistently shorter than those in the corresponding NaCl solutions. This could be due to a lower fraction of a disordered phase, a weaker effect on membrane stiffness because the DOPS lipid tails were unsaturated, and/or a weaker electrostatic repulsion owing to deeper adsorption of the calcium ions.32 Figure 4A shows an example of the SAXS curves of DLPS and DOPS in 10 mM CaCl2 solutions. The domain size of the samples in Figure 4A was estimated according to the peaks’ full width at half-maximum, using Warren’s approximation.53,54 The domain size corresponds to the number of layers over which positional correlation is maintained. In DLPS and DOPS, positional correlations are maintained for about 11 ± 2 and 22 ± 2 layers, respectively. Figure 4B,C shows the wideangle X-ray scattering curves (WAXS) from which the lateral organization of the lipid molecules within the bilayer can be determined. Before CaCl2 was added, the lipids were in the fluid, Lα, phase37,55 with an area per headgroup of about 0.418 and 0.675 nm2 for DLPS and DOPS, respectively.21,26,55 In the presence of 10 mM CaCl2, we found that lipids were in gelphases and in tighter 2D lattices with an area per lipid of 0.383 nm2 for DLPS and 0.64 nm2 for DOPS, in agreement with the values of DLPS and DOPS in ZnCl2 solutions21 and with CaCl2 data, using other methods.31 Figure 5 shows the scattering curves from DOPS in the presence of increasing CaCl2 concentrations. The indices of selected correlation peaks, assigned to the weakly and tightly coupled lamellar phases, are indicated in the figure. The lamellar repeat distances of the two phases are shown in Figure 8A (open triangles show the weakly coupled phase and solid triangles show the tightly coupled phase). The correlation peaks of the tightly coupled phases dominated the scattering curves when the CaCl2 concentration was 3 mM or higher. Under these conditions, the mass fractions of the weakly coupled and disordered phases were very small. At lower CaCl2

concentration, the fraction of the weakly coupled phases increased and the bilayer form-factor dominated the scattering curves. The reversibility of the weakly and tightly coupled phases upon dilution of the CaCl2 solution was examined in Figure 6. The data show that the tightly coupled phase remained even after the CaCl2 concentration was reduced from 5 to 0.1 mM. The repeat distance of the weakly coupled phase, however, reversibly increased after decreasing the CaCl2 concentration. We attribute the apparent irreversibility of the tightly coupled phase to the highly cooperative bridging of the lipid membranes by the calcium ions. To decouple the membranes, many calcium ions had to simultaneously desorb. The number of layers over which positional correlation is maintained (the domain size) within the lamellar phases in Figures 5 and 6 was estimated using Warren’s approximation.53,54 In the weakly coupled phases, 4 ± 2 layers were in positional correlations, whereas in the tightly coupled phases, 18 ± 2 layers were in positional correlations. These numbers serve as a lower limit to the actual numbers (because we ignored the contribution of the instrument resolution function to the peak width). We then examined the behavior of mixed DLPS/DLPC bilayers with varying membrane charge density (between 0 and 1.82 e/nm2, corresponding to neutral and one charge per lipid). Figure 7 shows the measured D values as a function of temperature for different DLPS/DLPC mixtures in 100 mM CaCl2 (about five times the lipid concentration). At high membrane charge density (σ ≥ 0.99 e/nm2, corresponding to half a charge per lipid), the only observed phase was the tightly coupled phase (solid star and square symbols in Figure 7) with D values of about 3.9 nm. The D values of the tightly coupled lamellar phase decreased with increasing the membrane charge density. At σ = 0.21 or 0.52 e/nm2 (corresponding to one tenth or a quarter of a charge per lipid, respectively) the tightly D

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Figure 5. Azimuthally integrated X-ray scattering curves as a function of q, from 15 mg/mL DOPS in CaCl2 solutions, whose concentrations are indicated in the figure in mM units. The tightly coupled phase is indexed in red, and selected peaks of the weakly coupled phase are indexed in blue. The broken red lines serve as a guide for the eye and show that the repeat distance of the tightly coupled phase did not change with increasing CaCl2 concentration. The values of the lamellar repeat distances are shown in Figure 8A (open triangles show the weakly coupled phase and solid triangles show the tightly coupled phase). Measurements were performed at the X33 beamline (Desy synchrotron at Hamburg).

coupled lamellar phase (solid triangle and circle symbols in Figure 7) coexisted with a second less tightly coupled lamellar phase (open triangle and circle symbols in Figure 7) whose D values were about 5.5 nm. This value was still much shorter than the D value of DLPS (about 12 nm) in the equivalent 300 mM NaCl solution (Figure 1, open circle symbol). The D values of the second less tightly coupled phase at σ = 0.21 or 0.52 e/nm2 (open triangle and circle symbols in Figure 7) were very different from that of 100% DLPC in 100 mM CaCl2 (Figure 7, solid orange diamonds) studied in our earlier papers.56,57 The temperature dependence of the second less tightly coupled phase (open triangle and circle symbols in Figure 7), however, was similar to DLPC in water (Figure 7, open diamonds). The comparison with pure DLPC suggests that at charge densities with phase coexistence, the mixed lipid bilayers did not phase separate to pure DLPC and pure DLPS. A coexistence of DLPC-rich and DLPS-rich phases or a liquid−liquid phase separation within the same bilayer are both consistent with our data and earlier studies.14,58 The D values of the DLPC-rich membranes (the less tightly coupled phases; open triangle and circle symbols in Figure 7) were about 5.5 nm owing to weaker ion correlations at the lower membrane charge density.

Figure 6. Reversibility measurements. (A) Azimuthally integrated Xray scattering curves as a function of q, from 15 mg/mL DOPS in CaCl2 solutions, whose concentrations are indicated in the figure in mM units. The tightly coupled phase is indexed in red, and selected peaks of the weakly coupled phase are indexed in blue. The broken red lines serve as a guide for the eye and show that the repeat distance of the tightly coupled phase did not change with increasing CaCl2 concentration. (B) Scattering curves after incubation in 5 mM CaCl2 and dilution to the indicated CaCl2 concentration. Measurements were performed at the BM26B beamline, ESRF (Grenoble).

Between σ = 0.02 and 0.1 e/nm2 (corresponding to one hundredth and one twentieth of a charge per lipid, respectively), no tight coupling was observed and D was 9.1 E

DOI: 10.1021/acs.langmuir.9b00778 Langmuir XXXX, XXX, XXX−XXX

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star symbol), suggesting that the contribution of calcium ion correlations to the attractive interactions was negligible. An earlier study showed that the association of calcium ions with negatively charged lipids has an intrinsic 1:1 association constant, KI. Hence, KI is equal to the reciprocal of the calcium concentration at which the charged membrane reverses sign. The negatively charged membrane made of pure phosphatidylserine (PS) has a KI of about 12 M−1 (in other words, the membrane charge is reversed when the calcium concentration is 0.08 M). For magnesium ions, KI = 8 M−1. KI slightly decreases with temperature. KI decreases with increasing membrane charge density.59 These findings are consistent with weaker ion correlations and hence larger repeat distances at lower membrane charge densities, as observed in this study. In the tightly condensed phase, increased temperature led to larger D values (Figure 7; solid square, solid star, solid circle, and solid triangle symbols). These observations are consistent with the data in Figure 2 and are attributed to the enhanced thermal fluctuations as discussed earlier. The temperature dependence of pure DLPC in the presence of CaCl2 is similar to the behavior of other charged lipid bilayers.47 In the presence of CaCl2, the calcium ions adsorbed onto the DLPC that became charged.33,56,57,60 Although the electrostatic repulsion between charged membranes increases with temperature, the spacing between like-charged membranes decreases with increasing temperature.47 The negative Gaussian modulus of charged membranes softens the bilayers and reduces the elastic energy cost associated with partial melting of the lamellar phase into a disordered phase, containing vesicles and tubular structures.47,61 The disordered phase coexists with a lamellar phase and is entropically favorable. Hence, the fraction of the disordered phase increases with temperature. The disordered phase applies an osmotic stress to the lamellar phase, which increases with temperature. As a result, the D values of 100% DLPC in CaCl2 decreased with temperature (Figure 7, orange diamonds). This effect was examined and explained in our earlier publication.47 We have also investigated the effect of membrane charge density on the phase behavior of the unsaturated DOPS membrane by mixing DOPS with DOPC. The molar fraction of DOPS was varied between 0.1 and 1 (charge density between 0.14 and 1.41 e/nm2). Figure 8 presents the measured lamellar repeat distances of the tightly and weakly coupled phases in the presence of different multivalent ions (Ca2+, Mg2+, Zn2+, and spermine4+). At high membrane charge density, the weakly coupled phase was observed when the salt concentration was below 5 mM, as in the case of DLPS (Figure 1). Interestingly, at lower membrane charge densities (0.70 e/ nm2 or less), the weakly coupled phase was detectable even when the salt concentration was 200 mM. Figure 8 shows that by and large for all the cations at low charge densities (10 and 25 mol % DOPS = 0.14 and 0.35 e/nm2 or one tenth and onequarter of a charge per lipid), the D values of the weakly coupled phase were consistently smaller than the D values at higher charge densities. In the presence of all the added salts, the tightly coupled phases were already detected at salt concentrations much below the lipid concertation (Figure 8). The results of the tightly coupled phase with a large molar excess of calcium (Figure 8A) have already been observed14 and were in good agreement with our data. Under large molar excess of calcium, the adhesion energy between the tightly coupled DOPS bilayers was estimated to be 65 erg/cm2.14 For comparison, the

Figure 7. Lamellar repeat distance, D, as a function of temperature of mixed DLPS/DLPC lipid bilayers in 100 mM CaCl2. The membrane charge densities, σ, in units of e/nm2, are indicated in the figure and correspond to 100 mol % DLPS (1.81 e/nm2 or one charge per lipid), 50 mol % DLPS (0.99 e/nm2 or half a charge per lipid), 25 mol % DLPS (0.52 e/nm2 or a quarter of a charge per lipid), 10 mol % DLPS (0.21 e/nm2 or one tenth of a charge per lipid), and 0, which corresponds to 100% DLPC. The open black diamonds correspond to 100% DLPC in water, as a reference. The solid diamonds correspond to 100% DLPC in 100 mM CaCl2. The crossed open star symbol indicates the D value obtained with 1 mol % DLPS (0.02 e/nm2 or one hundredth of a charge per lipid), 2 mol % DLPS (0.04 e/nm2 or one fiftieth of a charge per lipid), 3 mol % DLPS (0.06 e/nm2 or three hundredth of a charge per lipid), and 5 mol % DLPS (0.1 e/nm2 or one twentieth of a charge per lipid) at ambient room temperature. Open circles are lamellar phases that coexisted with the lamellar phases indicated by the solid circles, obtained with 25 mol % DLPS (0.52 e/nm2 or a quarter of a charge per lipid). Open triangles are lamellar phases that coexisted with the lamellar phases indicated by the solid triangles, obtained with 10 mol % DLPS (0.21 e/nm2 or one tenth of a charge per lipid). Error bars are below the size of the symbols.

nm, similar to 100% DLPC in 100 mM CaCl2 (Figure 7, crossed open star symbol) yet shorter than the D value of DLPS (about 12 nm) in the equivalent 300 mM NaCl solution (Figure 1, open circle symbol). As a reference, Figure 7 (open diamonds) shows the D values of DLPC in pure water as a function of temperature. In the absence of calcium ions, the decrease and then increase of D with increasing temperature was, most likely, owing to the balance between attractive van der Waals (vdW) interactions that dominated at lower temperatures and repulsive undulation forces that dominated at higher temperatures.47 Close to the melting temperature of DLPC (−1 °C), an anomalous pretransition may take place and account for the increase in D at low temperatures.57 In the presence of calcium ions, the larger D values at low membrane charge density (solid triangle and circle symbols in Figure 7) are consistent with weaker divalent ion correlations, which reduced the attractive interactions between the bilayers in the tightly coupled lamellar phase. Between σ = 0.02 and 0.1 e/nm2, the repeat distance was 9.1 nm (Figure 7, crossed open F

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Figure 8. Lamellar repeat distance, D, of mixed DOPS/DOPC lipid bilayers as a function of salt concentration. The total lipid concentration was 15 mg/mL (about 20 mM). Measurements were performed a few days after salts were mixed with the lipids. Solid symbols correspond to the tightly coupled lamellar phases. Open symbols correspond to the (long-ranged) weakly coupled coexisting lamellar phases. The membrane charge densities are indicated in part A and correspond to 100, 75, 50, 25, and 10 mol % DOPS (corresponding to 1, 3/4, 1/2, 1/4, and 0.1 charge per lipid, respectively). CaCl2 was added in part A. MgCl2 was added in part B. ZnCl2 was added in part C. Spermine4+ was added in part D. The solid curve is the calculated D for the case of added monovalent salt, taken from reference 34. The solid curve is plotted so that monovalent and multivalent ion concentrations with the same Debye screening length have the same position along the horizontal axis. Error bars are smaller than the size of the symbols when the lamellar repeat distances were 20 nm or less. At larger repeat distances, the error bars were ±1 nm.

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CONCLUSIONS Membranes of negatively charged lipids, DLPS or DOPS, were mixed with calcium ions. The ions bound themselves to the charged lipid headgroups and induced coexisting multilamellar phases. Owing to ion correlation effects, which generated likecharged attractive interactions, tightly coupled lamellar phases formed with repeat distance, D, of 38.9 ± 0.5 Å in DLPS and 51.0 ± 0.5 Å in DOPS. At low calcium concentrations, the tightly coupled lamellar phase coexisted with a weakly coupled lamellar phase, dominated by repulsive electrostatic interactions. The repulsive interactions were slightly weaker than those in the corresponding NaCl solutions with similar screening lengths, possibly owing to divalent ion correlation effects or stiffer lipid bilayer and weaker repulsive undulation interactions. The effect of temperature and membrane charge density on the tightly coupled phase was examined. D increased with increasing temperature or with decreasing membrane charge density. At low DLPS membrane charge density, another phase coexisted with the tightly coupled phase with a D value of about 55 Å. Further decrease of membrane charge density lead to D of 91 Å; both repeat distances were still lower than the repeat distance in the equivalent NaCl solution, with similar ionic strength. We attribute both effects to the weakening of the ion correlation effects at lower membrane charge densities or at higher temperatures, owing to higher ion solution entropy. We also found that adsorption of calcium ions decreased the area per lipid and induced a rectangular gel phase. The number of layers that maintained

adhesion energy between PC membranes in water is lower by an order of magnitude.62 In the presence of all the added salts at charged lipid molar fraction of 0.1, (10 mol % DOPS = 0.14 e/nm2 or one tenth of a charge per lipid) the less tightly coupled phase was observed and its D values were significantly longer than the tightly coupled phase, observed at higher membrane charge densities. In the case of Ca2+, the D spacing of the tightly condensed phase only slightly decreased with membrane charge density (above 10 mol % DOPS = 0.14 e/nm2 or one tenth of a charge per lipid) or calcium concentrations (Figure 8A). In the case of the other ions (Figure 8B−D) the D spacing of the tightly coupled phase was larger as the charge density decreased. With Zn2+ ions (Figure 8C), two tightly coupled phases coexisted with D values of 4.95 and 5.56 nm, and as shown earlier, at equilibrium, the two phases collapsed into a single phase with a repeat distance of 5.24 nm.21 The solid curves in Figure 8 are the calculated D values for the case of added monovalent salt, taken from reference 34. As observed in Figure 3 for the case of pure DOPS and in Figure 1 for the case of pure DLPS, the D values of the weakly coupled phase were slightly shorter than the calculated curve. This deviation was larger in the cases of Ca2+ and SPM4+ (Figure 8A,D). We explained this phenomenon (see above) by the limited applicability of the Poisson−Boltzmann theory to multivalent ions and by the effect of multivalent ions on the physical properties of the membranes. The data in Figure 8 also suggests that ion specific effects may play a role. G

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synchrotron at Hamburg, beamline X33 (D. Svergun and his team) and ESRF, beamline BM26B (W. Brass and his team), and beamline ID02 (T. Narayanan and his team). This project was supported by the Israel Science Foundation (656/17). L.F. thanks the Lev Tzion foundation for a fellowship support and Teacher-Scholars Program of the Hebrew University, supported by the Jerusalem Municipality, JDA, and the Trump Foundation. We thank the Safra, Wolfson, and Rudin Foundations for supporting our laboratory.

positional correlations in the multilamellar phase was between 10 and 20 in the tightly coupled phases and only few layers in the weakly coupled phase. In the case of DOPS, four different multivalent ions were examined and showed some weak ionspecific effects. In the weakly coupled lamellar phases, the repeat distance was shorter at low membrane charge density. Biological membranes may have a wide range of local membrane charge densities and interact with multivalent ions. Our study therefore provides insights into the possible interactions and structures that biomembranes may adopt.

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EXPERIMENTAL SECTION

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AUTHOR INFORMATION

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REFERENCES

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1,2-didodecanoyl-sn-glycero-3-phosphocholine (DLPC), 1,2-dilauroyl-sn-glycero-3-phospho-L-serine (DLPS), dioleoyl(C18:1)-sn-glycero3-phospho-L-serine (DOPS), and 1,2- dioleoyl(C18:1)-sn-glycero-3phosphocholine (DOPC) were purchased from Avanti Polar Lipids, Inc.,(Alabaster, AL, U.S.A.) and used as received. The lipid was purchased as lyophilized powder (>99% pure, according to the data of the manufacturer). We have used highly purified water (Barnstead Nanopure Diamond) with resistivity of 18.1 MΩ and total organic compounds of 1 ppb or less. ZnCl2, spermine, and standard 1 M CaCl2 and 1 M MgCl2 solutions were purchased from Sigma (Rehovot, Israel) and used as received. DLPC, DLPS, DOPC, and DOPS lyophilized powders were mixed in glass vials using chloroform at a range of different mole percent values. Samples were uniformly vortex mixed for 10 min. The chloroform was then allowed to evaporate overnight in the fume hood, and the mixture was lyophilized. Highly purified water or saltsolution was added to the lyophilized lipid mixture to get a final total lipid concentration of 15 mg/mL. After equilibration at the required temperature and salt concentration, samples were transferred into quartz capillaries that were then flame-sealed and centrifuged at a relative centrifugal force of 6000 g, using a SIGMA 1−15PK centrifuge equipped with rotor No. 11024, suitable for capillaries. Samples were kept at the equilibration temperature until and during X-ray measurements. Dialysis of DLPS solution was performed using 8 kDa membranes against water. Freeze−thaw cycles were between freezing in liquid nitrogen and 40°C. Our in-house high-resolution solution small- and wide-angle X-ray scattering (SAXS and WAXS) setup was used as described elsewhere,21,47,54,63 and the resulting 2D scattering patterns were radially integrated.64 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 (https://scholars.huji.ac.il/uriraviv/ software/x) developed in our laboratory54,65,66 as explained.21,34,47,63 WAXS data analysis was done as explained.21 SAXS measurements were also performed at the X33 beamline (Desy synchrotron, Hamburg) and at beamlines BM26B and ID02 of the European Synchrotron Radiation Facility (ESRF) in Grenoble, described elsewhere.21

Corresponding Author

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

Uri Raviv: 0000-0001-5992-9437 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to Daniel Harries, Monica Olvera de la Cruz, and Phil Pincus for helpful discussions. We acknowledge Desy H

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