Direct Measurements of Effect of Counterion Concentration on

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Direct Measurements of Effect of Counterion Concentration on Mechanical Properties of Cationic Vesicles Mansi Seth,† Arun Ramachandran,‡ and L. Gary Leal*,† †

Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106-5080, United States Department of Chemical Engineering and Applied Chemistry, University of Toronto, Ontario, Canada M5S 3E5

‡

S Supporting Information *

ABSTRACT: Theoretical analyses of charged membranes in aqueous solutions have long predicted that the electric double layer surrounding them contributes significantly to their mechanical properties. Here we report the first, direct experimental measurements of the effect of counterion concentration on the bending and area expansion modulus of cationic surfactant vesicles. Using the classical technique of micropipet aspiration coupled with a modified experimental protocol that is better suited for cationic vesicles, we successfully measure the mechanical properties of a doubletailed cationic surfactant, diethylesterdimethyl ammonium chloride (diC18:1 DEEDMAC) in CaCl2 solutions. It is observed that the area expansion modulus of the charged membrane exhibits no measurable dependence on the counterion concentration, in accordance with existing models of bilayer elasticity. The measured bending modulus, however, is found to vary nonmonotonically and exhibits a minimum in its variation with counterion concentration. The experimental results are interpreted based on theoretical calculations of charged and bare membrane mechanics. It is determined that the initial decrease in bending modulus with increasing counterion concentration may be attributed to a decreasing double layer thickness, while the subsequent increase is likely due to an increasing membrane thickness. These mechanical moduli measurements qualitatively confirm, for the first time, theoretical predictions of a nonmonotonic behavior and the opposing effects of ionic strength on the bending rigidity of charged bilayers.

1. INTRODUCTION Charged surfactant membranes have received tremendous attention in the literature1,2 over the last three decades due their wide range of applicability and fundamental significance. Anionic lipids are constituents of many biological membranes,3 while cationic lipids are frequently used for DNA transfection in gene therapy.4,5 Charged vesicles are employed as drug carriers for transdermal delivery;6,7 in addition, charged surfactants form key ingredients of a wide range of personal and home care formulations.2,8 The processes for the development of such formulations are largely empirical; hence it is desirable to acquire an improved understanding of the relationships between their performance and membrane mechanical properties such as the area expansion (stretching) modulus KA, the bending rigidity kc, and the rupture tension among others. These mechanical properties play an important role in determining the size and shape of bilayer vesicles9,10 as well as permeability and deformability of membranes.11,12 Moreover, they can influence processes such as vesicle adhesion13−15 and vesicle fusion,16 which can impact the stability of vesicle based formulations.15 In aqueous solutions charged membranes develop an electric double layer, the presence of which can modify the existing balance of forces in the self-assembled bilayer and hence its mechanical properties.9,17 A sound understanding of such effects could allow for © XXXX American Chemical Society

better design of charged membrane systems with predictable mechanical behavior. The influence of electrostatics on mechanical properties of charged membranes has been extensively investigated theoretically.18−24 All these calculations show that the presence of an electric double layer leads to an increase in the bending modulus of a charged membrane, and a decrease of its area expansion modulus. Surprisingly, however, there are only few experimental studies or direct measurements of such effects in the literature.25 Song and Waugh26 measured the bending rigidity of mixed (anionic) 1-palmitoyl-2-oleoyl phosphatidyl serine (POPS) and (neutral) 1-stearoyl-2-oleoyl-phosphatidylcholine (SOPC) lipid vesicles and found no effect of membrane surface charge on the bending rigidity. Using vesicle fluctuation analysis, Rowat et al.27 measured an increase in the bending modulus of neutral dimyristoyl phosphatidylcholine (DMPC) lipid vesicles upon the incorporation of 5 mol % of an ionic surfactant, thereby proving that the presence of surface charges leads to stiffening of a membrane. Vitkova et al.28 studied the effect of varying surface charge density on the bending rigidity of mixed (anionic) L-α-phosphatidyl serine (bovine PS) and Received: August 30, 2013 Revised: October 14, 2013

A

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ments of the bending modulus. Furthermore, on interpreting our experimental measurements based on existing theoretical calculations of charged and bare membrane mechanics, we are able to confirm that the underlying mechanism for the observed nonmonotonicity in bending rigidity is likely the proposed38 opposing effects of increasing counterions on a charged bilayer. This paper is organized as follows. In section 2, we give details of our experimental setup, including the modified protocol for treatment of glass surfaces and its validation. In section 3, we present our experimental results and explain these based on theoretical models of the mechanics of charged bilayer membranes. We summarize our key findings in section 4.

SOPC vesicles. Their results were in qualitative agreement with theoretical predictions of May.24 In a thorough investigation, Shoemaker and Vanderlick17 studied vesicles made from mixtures of anionic 1-palmitoyl-2-oleoyl-phosphatidylglycerol (POPG) and neutral 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) lipids and showed that the rupture tension of membranes decreased with increasing fractions of POPG. In addition, they found no measurable effect of surface charge density on the area expansion modulus, but were unable to measure the bending modulus of their highly charged vesicles owing to experimental difficulties.17 Delorme et al.25 used atomic force microscopy (AFM) to measure the bending rigidity of immobilized cat-anionic membrane polyhedrons and observed for the first time, its decrease with increasing ionic strength. More recently, Mitkova et al.29 measured a factor of 2 increase in the bending elasticity of SOPC vesicles on incorporation of 15 mol % (anionic) 1,2-dioleoyl-sn-glycero-3phospho-L-serine (DOPS). The literature on mechanical property measurements of charged surfactants is not only scarce,25 but also largely involves studies performed by incorporating up to 40% of charged surfactants into neutral lipids and varying the surface charge density of the resulting bilayer; very few measurements have been performed using 100% charged surfactant. One reason for the limited literature is perhaps the inherent difficulty in obtaining a functional yield of giant unilamellar vesicles (GUVs) from surfactant/lipid mixtures containing charged surfactants,30 particularly at higher mole fractions. Further, while neutral lipid GUVs have been prepared in high salt concentrations,31−34 the GUV yield for mixed anionic and neutral lipids at salt concentrations above 1 mM is often too low to allow experimentation, as noted by Shoemaker and Vanderlick17 who were unable to study the effects of salt concentration due to this limitation. Additionally, it is experimentally challenging to obtain reproducible and reliable mechanical data for highly charged vesicles,17 and this could be another source of the limited mechanical property measurements with such systems.17 In this study, we use the method of gentle hydration35 to successfully obtain a functional yield of GUVs made from 100% cationic double-tailed surfactant diethylesterdimethyl ammonium chloride (diC18:1 DEEDMAC, Figure 1a) in salt solutions having counterion concentrations up to 73 mM. It will be shown later that, under these solution conditions, the GUVs are highly charged. Using the classical technique of micropipet aspiration (MPA)11,12,36 in combination with a modified experimental protocol that involves deposition of small unilamellar vesicles (SUVs) for the treatment of glass surfaces, we measure key mechanical properties of the cationic surfactant GUVs and study the effect of counterion concentration on the same. To the best of our knowledge, our experiments are the first of this kind. It is observed that within the uncertainty of measurement, the area expansion modulus is invariant with the counterion concentration, but the bending modulus is observed to vary nonmonotonically. This nonmonotonic variation of the bending modulus has been previously predicted by self-consistent field calculations,37,38 but to our knowledge, has not yet been observed experimentally. While Claessens et al.38 additionally measured the variation of vesicle size with ionic strength to show that it correlates well with their self-consistent field theory (SCFT) predictions, our results are the first to experimentally verify predictions of this nonmonotonic behavior by direct measure-

2. EXPERIMENTAL SECTION 2.1. Materials. The double-tailed cationic surfactant diethylesterdimethyl ammonium chloride (diC18:1 DEEDMAC, mol wt = 697.5 g/mol, Figure 1a) is in the fluid state at room temperature and is a common component of commercial fabric softeners. It was provided to us by Procter and Gamble Co. (Cincinnati, OH) and was used without further purification. 2.2. Giant Unilamellar Vesicle Preparation. GUVs were prepared by the method of gentle hydration35 at a surfactant concentration of 0.2 mg/mL. The hydrating solution consisted of 200 mM sucrose and CaCl2 (commonly used salt in fabric softener dispersions) of desired concentration, ranging from 0.1 to 36 mM. Milli-Q water having a resistivity of 18.2 MΩ·cm was used to prepare all solutions. The pH of the solutions was adjusted to 3.0 (which minimizes hydrolysis of the ester linkage in the surfactant39) using concentrated HCl. The hydration period to obtain a good yield of GUVs was longer for higher salt concentrations and was optimized to 36−48 h, after which several 20−80 μm sized unilamellar vesicles were found in the suspending medium. (Figure S1 Supporting Information). This method of preparing the cationic GUVs was preferred over the alternate method of electroformation33 which resulted in a poor yield of GUVs that ruptured easily, making experimentation difficult. Note that unlike natural and synthetic phospholipids, the DEEDMAC surfactant is stable under aqueous conditions for several weeksmonths,40 enabling the use of gentle hydration for making GUVs. 2.3. Micropipet Aspiration Setup. In the technique of micropipet aspiration, a single GUV of 25−80 μm diameter is aspirated into a glass micropipet (3−8 μm diameter), by applying a known suction pressure ΔP (see Figure 1). The tension across the membrane (τ) is related to ΔP through a static pressure balance11,12

τ=

ΔP ⎛2 2 ⎞ ⎜ − R ⎟ ⎝ Rp v⎠

(1)

Here Rp and Rv are the pipet and vesicle radii, respectively. An increase in the suction pressure results in an increase in the projection length of the vesicle inside the pipet from its initial value L0 due to a relative area strain α

α=

(A − A 0) A0

(2)

where A0 is the projected membrane area of the vesicle measured at a low initial tension τ0 and A is the projected area at the increased suction pressure. Assuming constant volume conditions, α is calculated from the increase in projection length, ΔL, using the following geometric correlations12,41 Rp ⎤ ⎡ ⎛ 2πR L + 2πR 2 ⎞⎤ ⎢ 2πR p 1 − R v ΔL ⎥⎡ p 0 p ⎥ ⎢1 − ⎜ ⎟ α=⎢ ⎥ ⎜ ⎟⎥ 2 2 ⎢ 4πR v 4πR v ⎥⎣ ⎢ ⎝ ⎠⎦ ⎦ ⎣

(

)

(3)

Equation 3 differs from the equation typically used in the literature11,12,36 by a factor η, where η is given as B

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Figure 1. (a) Unsaturated double-tailed cationic surfactant diethylesterdimethyl ammonium chloride (diC18:1 DEEDMAC) used in experimental study. (b) Custom-built setup based on ref 12 used for micropipet aspiration (MPA) experiments. The major components of the setup include a water manometer, a differential pressure transducer, inverted phase contrast microscope, micropipets and aspiration chamber. The aspiration chamber cavity is designed to have a volume of ∼1 mL, with remaining dimensions optimized with respect to the working distance of the objective (2.7−4 mm) and available space in the setup. More details on the setup and MPA technique can be found in ref 12. (c) Images from an MPA experiment showing the length L inside the pipet at a certain pressure P and the increase ΔL corresponding to a ΔP increase in pressure.

⎛ 2πR L + 2πR 2 ⎞ p 0 p ⎟ η = 1 − ⎜⎜ ⎟ 4πR v 2 ⎝ ⎠

gravity on the vesicle shape may be present.42−44 Henriksen and Ipsen43 have treated this problem theoretically to determine criterion under which gravity effects may be significant. For the above density contrast, size of vesicles typically used (20 μm - 80 μm diameter) and the ranges of tension values accessible in MPA experiments (τ > 0.001 mN/m), we find that effects of gravity are negligible. A live feed of the MPA experiment is viewed on a monitor via a CCD camera (Sony, USA). Data collection is semiautomated via the use of a MATLAB routine that captures an image of aspirated vesicle and records the corresponding ΔP at every step. The images are postanalyzed using Image J software (National Institute of Health) to measure the vesicle and pipet diameter and the aspirated length of the vesicle L (uncertainty = ±0.29 μm); ΔL is calculated by subtracting the initial length L0 from L. 2.4. Micropipet Aspiration Experiments. Glass surfaces acquire a weak negative charge when in contact with aqueous solutions. An important aspect of MPA is appropriate pretreatment of the aspiration chamber and the glass pipet to ensure that vesicles do not adhere to any surface.12 For uncharged lipids, the common practice is to coat all surfaces with a layer of Surfasil and/or bovine serum albumin (BSA) thereby rendering them passive to interactions with the vesicles.12 However, it has been demonstrated by Shoemaker and Vanderlick17 that this traditional protocol is not suitable for the aspiration of charged vesicles and often leads to irreproducible mechanical data. Since our system consists of vesicles made from a cationic surfactant, we adopt a modified protocol while carrying out the MPA experiments. Instead of using BSA, we use a solution of cationic small unilamellar vesicles (SUVs) to coat the glass pipet and aspiration chamber surfaces. The SUVs are prepared from the same cationic surfactant and aqueous solution used to make the GUVs. A dried surfactant film is hydrated with the aqueous solution and subjected to eight to nine freeze−thaw cycles leading to the formation of SUVs, after which they are extruded (Lipex Biomembranes Inc. Vancouver, BC) though 100 nm pores (EMD Millipore, MA) to reduce their size. The solution is then placed in the aspiration chamber and a small suction pressure is applied, causing it to flow into the pipet. The SUVs being positively charged rupture on the negatively charged surfaces of the glass pipet and aspiration chamber, subsequently forming a bilayer on it.45 This prevents the cationic GUVs from adhering to the glass

(4)

This factor accounts for the fact that a vesicle may be deflated and hence nonspherical prior to aspiration. For a spherical vesicle η = 1. The above correction is identical to that derived by Henriksen and Ipsen41 who also showed that the measured elastic modulii are 10− 20% lower if the area strain is not corrected by the factor η. The MPA setup was custom-built in our laboratory following guidelines from the literature and similar existing setups.12 Briefly, the setup consists of a manometer made from two water reservoirs, one of which is movable thereby allowing us to control the suction pressure which is measured via a differential pressure transducer (Omega Instruments Inc., Stamford, CT). A custom aspiration chamber having a U-shaped cavity with a 5/8th inch opening at one end (resulting in a chamber volume of ∼1 mL) is fabricated from a single piece of acrylic (see Figure 1). The top of the chamber is sealed with a glass-slide using vacuum grease. Compared to traditional MPA chambers, this limits the number of assembled components to two and the number of openings to one, thereby minimizing evaporation from assembled and open portions of the chamber. The micropipets are fabricated by pulling glass capillaries (7740 glass, Friedrich & Dimmock, Inc., Millville, NJ) in a pipet-puller (P-87 Sutter Instrument, Novato, CA) and then cutting them to the desired tip diameter using a custom-built microforge. The aspiration chamber is filled with solution (pH = 3) containing 210 mM glucose and CaCl2 of desired concentration, ranging from 0.1 mM to 36 mM. A small quantity of the prepared GUVs is diluted with this solution and placed in the aspiration chamber. An inverted Nikon Diaphot 300 microscope (Nikon Inc., Melville, NY) equipped with a 40× (LWD 2.7−4 mM, 0.5 NA) Hoffman Modulation Contrast objective (Modulation Optics, Rochester, NY) is used to observe the GUVs. The mismatch in the glucose and sucrose concentration allows for a phase contrast between the vesicles and the surrounding medium. Furthermore, the use of slightly hyperosmotic glucose solution also serves to deflate the vesicle, thus aiding the process of aspiration. Due to the density difference between the glucose and sucrose solution (Δρ ∼ 12 kg/m3), the GUVs settle to the bottom of the chamber and can easily be picked up by a pipet. A disadvantage of the density contrast is that effects of C

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surfaces due to the electrostatic repulsion between the similarly charged bilayers. After ∼20 min, the flow direction is reversed to flush out the unadhered SUVs from the pipet. The aspiration chamber is also refilled with a fresh load of glucose and CaCl2 buffer solution prior to beginning the measurements. Although not demonstrated here, while working with anionic GUVs, one could adopt a similar protocol with an additional step of forming on top of the cationic bilayer, an anionic bilayer that will repel the GUVs. While the technique of coating surfaces with bilayers to prevent adhesion is certainly not new,46 it has been employed only recently in micropipet aspiration (e.g., the most recent comprehensive review12 does not cover it). It is crucial, particularly for highly charged vesicles, to ensure that the above procedure gives reproducible mechanical data and to ensure this, stress−strain hysteresis tests were performed. In these tests, a single GUV was aspirated into a pipet and the tension was increased in steps until it reached a value of ∼1 mN/m. This pulls out any attached tethers (hidden area) and excess area stored in the thermal undulations of the vesicle into the pipet. After this, the tension was lowered back to the initial (low) value (this procedure, known as prestressing, is performed on every examined vesicle in order to avoid undesirable effects of hidden area47,49). The tension is then increased once again to ∼1 mN/m and then lowered back to the initial value. This time, the corresponding area strain is measured at each step. Figure 2 shows the results from one such hysteresis test performed at a

Figure 3. Measured membrane tension versus area strain curves for three different diC18:1 DEEDMAC vesicles in 30 mM CaCl2. The values of critical area strain prior to rupture varied between 3.5% and 6% and the corresponding rupture tension values (τrup) varied from 1.5 to 3 mN/m. These values are 60−70% lower than the rupture tension values for uncharged surfactants, indicating that the charged membranes are weaker than uncharged ones.

presence of surface charges on a membrane lowers its mechanical strength. It has been well-established12,49 that the observed micromechanical response of the vesicle obeys the elastic compressibility relationship36,48,50 ⎛k T ⎞ ⎛ τ cτA ⎞ α = ⎜ B ⎟ ln⎜1 + ⎟+ kc ⎠ KA ⎝ 8πkc ⎠ ⎝

(5)

12

Here c is a constant of about 0.1. At low values of lateral tension (up to ∼0.5 mN/m), the observed logarithmic increase in projected area is a result of the smoothing out of thermal undulations from the membrane surface. Experimentally, plotting the natural log of the normalized tension (τ/τ0) versus the relative area strain in this “low-tension regime” (Figure 4a) allows one to measure the bending modulus kc from the slope as12,42,48,49

Figure 2. Hysteresis test on a diC18:1 DEEDMAC GUV in 18 mM CaCl2. The tension on a GUV is increased in steps to ∼1 mN/m and then lowered back to the initial value, and the corresponding area strain is measured at each step. (■) Increasing tension, (□) lowering tension. Overlay of data points from the increasing and decreasing tension runs confirms the mechanical reliability of the data, ensuring that vesicles are not adhering to the inner pipet wall.

α=

A − A 0 ⎛ kBT ⎞ ⎛ τ ⎞ =⎜ ⎟ ln⎜ ⎟ A0 ⎝ 8πkc ⎠ ⎝ τ0 ⎠

(6)

At higher values of membrane tension, direct stretching of the area per molecule of the membrane results in a linear increase of membrane area with tension. By convention, the slope of the tension versus relative area strain plot is measured to be the apparent area expansion modulus KA,app12,42,48,49 (Figure 4b). A − A0 τ = α= A0 KA,app (7)

CaCl2 concentration of 18 mM. The overlay of data points from the increasing and decreasing tension runs confirms that the vesicle is not adhering to the inner pipet wall and that the mechanical data is reliable.

This modulus is an apparent one since even at higher tensions, there is a small logarithmic contribution to the area strain due to the smoothing out of thermal undulations. The relative area strain at each step due to direct stretching only, α′(i) can be obtained by subtracting out the logarithmic contribution Δα(i) from the apparent, relative area strain α(i)

3. RESULTS AND DISCUSSION 3.1. Common Features of Tension−Strain Curves of DEEDMAC Vesicles. We begin by discussing common features of the measured membrane tension versus area strain graphs of diC18:1 DEEDMAC vesicles. For all salt concentrations studied, the area strain at which vesicle rupture occurred varied between 3.5% and 6% with an average rupture tension τrup of 2.5 ± 1 mN/m (within error, there was no measurable variation of τrup with counterion concentration). Figure 3 shows the tension−area strain graphs for three different DEEDMAC vesicles in 30 mM CaCl2 depicting this variability. The rupture tension values of charged diC18:1 DEEDMAC vesicles are 60−70% lower compared to uncharged surfactants, confirming previous observations17 that the

α′(i) = α(i) − Δα(i) where Δα(i) has been determined to be ⎛ k T ⎞ ⎛ τ (i ) ⎞ Δα(i) = ⎜ B ⎟ ln⎜ ⎟ ⎝ 8πkc ⎠ ⎝ τref ⎠

(8) 49

(9)

Here τref is the reference initial tension in the high tension regime, which we take to be 0.5 mN/m. The plot of tension D

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Table 1. Measured Values of the Area Expansion Modulus and Bending Modulus of diC18:1 DEEDMAC Surfactant at Different [Cl−] Concentrationsa [Cl−] (mM) 1.2 10 29 37 47.4 55 61 73

area expansion modulus KA (mN/m)

bending modulus kc (kBT)

± ± ± ± ± ± ± ±

9.6 ± 1.2 (24) 7. 2 ± 1.0 (22) 6.7 ± 0.6 (27) 6.2 ± 1.0 (25) 7.1 ± 1.2 (46) 7.9 ± 1.2 (27) 8.8 ± 1.1 (26) 8.7 ± 1.2 (30)

97 100 97 92 98 98 106 104

15 16 14 15 17 15 16 17

a

Values in parentheses indicate the number of vesicles on which measurements were made at each concentration. The average value of KA for cationic DEEDMAC bilayers is 99 ± 14 mN/m, which is about 50% lower than that of charged phospholipid (POPG/POPC) bilayers.17 Similarly, the measured bending moduli of cationic DEEDMAC bilayers are lower than those of charged phospholipid bilayers,27−29 but are comparable to some cat-anionic bilayers51 as well as to values determined from SCFT calculations for charged bilayers.38

Figure 4. Membrane tension versus measured, relative area strain α for a diC18:1 DEEDMAC GUV. (a) Low tension regime (τ < ∼0.5 mN/ m): Plot of natural logarithm of the normalized membrane tension ln(τ(i)/τ0), where τ0 is the initial (low) tension in the membrane, versus area strain is linear. The slope is equal to 8πkc/kBT from which the bending modulus kc is calculated (7.8 ± 1.1kBT). This bending modulus is underpredicted and needs to be corrected for stretching contributions41 (b) High tension regime (τ > ∼0.5 mN/m): before (solid) and after (open) subtracting the bending contribution eq 9. Slope of membrane tension versus apparent (actual), relative area strain gives the apparent (actual) area expansion modulus KA,app (KA) (78 ± 12 mN/m and 105 ± 15 mN/m, respectively). (c) Full tension regime: A fit of data to the full elastic compressibility relationship (eq 5) gives actual KA (105 ± 15 mN/m) and kc (9.6 ± 1.1kBT) directly, eliminating the need for additional corrections. Fitting is done using nonlinear least-squares regression.

3.2. Effect of Counterion Concentration on Area Expansion Modulus. The area expansion modulus KA of DEEDMAC vesicles is measured in CaCl2 concentrations ranging from 0.1 to 36 mM. Figure 5 shows a graph of these

versus the actual area strain in the high tension regime has a steeper slope and is the actual area expansion modulus KA, as seen in Figure 4b. Data over the entire tension range is shown in Figure 4c. Note that the choice of the initial reference tension only impacts the range of data utilized to obtain the slope (area expansion modulus) in the high tension regime but not its value. Henriksen and Ipsen41 have shown that the bending modulus determined from eq 6 is often under predicted since even at low values of tension, contributions from direct membrane stretching may not be negligible. Consequently, using this under predicted value of the bending modulus in eq 9 to correct KA,app may result in a slightly over predicted value of the area expansion modulus KA.41 An alternative approach is to obtain kc and KA directly by fitting the experimental data over the entire tension regime (Figure 4c) to the complete nonlinear elastic compressibility relationship (eq 5). Values of the mechanical moduli obtained in this manner are automatically corrected for the bending and stretching corrections,41 and are reported here in Table 1. Note that another method to correct the bending modulus for stretching contributions is to use a stretching correction factor proposed by Henriksen and Ipsen;41 applying this method to our data resulted in values that, within error, were similar to those obtained from the nonlinear fitting procedure and hence are not reported here. Furthermore, the qualitative nature of our results remains unchanged, irrespective of the method utilized to apply the corrections.

Figure 5. Actual area expansion modulus KA of cationic DEEDMAC vesicles as a function of counterion [Cl−] concentration. CaCl2 concentration ranges from 0.1 to 36 mM. The counterion concentration is calculated as [Cl−] = 2[CaCl2] + [HCl] where [HCl] is the 1 mM corresponding to pH = 3.0. Dashed line is a constant of 99 mN/m, the average of all the values.

values (given in Table 1) as a function of the chloride ion concentration [Cl−], where [Cl−] = 2[CaCl2] + [HCl]. As seen in the figure, within the uncertainty of measurement, there is no effect of the counterion concentration on the area expansion modulus. The average value of KA is found to be 99 ± 14 mN/ m. To understand this result, we consider a relatively simple model of bilayer elasticity. The free energy μ per surfactant molecule in a bilayer is given as52,53 γ μ = 2γa0 + (a − a0)2 (10) a where γ is the interfacial tension at the hydrocarbon−aqueous solution interface, a is the headgroup area of the surfactant molecule, and a0 is the optimal headgroup area at which the free energy is at its minimum value of 2γa0. When the bilayer is stretched from this minimum energy state, it expands elastically E

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and the free energy increases. As a first approximation, the area expansion modulus of the bilayer is related to the second derivative of its free energy, or the curvature about the minimum as KA = 2

d 2μ a0 = 4γ da 2

(11)

In another calculation of bilayer elasticity that is based on a polymer brush model, Rawicz et al. predict that the area expansion modulus of the bilayer is equal to 6γ.49 Thus, in general, the area expansion modulus of the bilayer is proportional to the interfacial energy at the hydrocarbon− water interface as KA = mγ, where m is numerical constant. Further, for a charged bilayer, it has been shown that the presence of surface charges leads to a reduction in the area expansion modulus, with the net area expansion modulus estimated to be17,19 KA = mγ − K Ael , K Ael

Figure 6. Nonmonotonic variation of the bending modulus kc of cationic diC18:1 DEEDMAC vesicles as a function of counterion [Cl−] concentration. The modulus levels off beyond [Cl−] = 60 mM. Plotted values are averages of measurements on 20 or more vesicles with bars indicating one standard deviation. Differences in values of kc at varying [Cl−] were statistically significant (P < 0.05) as evaluated by Student’s t test (α = 0.05) (see Table S1 in the Supporting Information). CaCl2 concentration ranges from 0.1 to 36 mM. The counterion concentration is calculated as [Cl−] = 2[CaCl2] + [HCl] where [HCl] is the 1 mM corresponding to pH = 3.0.

with

⎛ ⎞−1 ⎞2 λe 2 2e 2λ 2 ⎜ ⎛ = 2 ⎜ ⎜ ⎟ + 1 ⎟⎟ κa εε0 ⎝ 2κaεε0kBT ⎠ ⎝ ⎠

(12)

Here, κ is the inverse Debye length that depends on the counterion concentration and e, ε, and ε0 are the elementary charge of an electron, dielectric constant of the medium, and permittivity of free space, respectively. λ is the average charge per headgroup (which depends upon the level of dissociation of the charged bilayer). The surfactant diC18:1 DEEDMAC has 1 charge per headgroup, and from zeta potential measurements it is estimated to be around 10−13% dissociated at pH = 3.0, corresponding to a surface charge density σ of about 0.037 C/ m2 (σ is found to not vary significantly with counterion concentration; see Figure S2 in the Supporting Information). This gives λ = 0.10−0.13. For counterion concentrations ranging from 1 to 80 mM, γ is a constant and the magnitude of the predicted variation in values of KelA lie within the uncertainty of the measurements (Table S1 in the Supporting Information). As a consequence, no measurable variation in KA with counterion concentration is expected, which is consistent with our experimental result. 3.3. Effect of Counterion Concentration on Bending Modulus. The measured bending modulus of cationic DEEDMAC vesicles varies nonmonotonically with the counterion concentration and shows a minimum, as seen in Figure 6 (values in Table 1). Between counterion concentrations of 1.2 and 37 mM, the bending modulus steadily decreases from 9.6 ± 1.2 to 6.2 ± 1.0kBT. However, on further increasing the counterion concentration, the value of the bending modulus begins to rise once again and then levels off beyond [Cl−] = 60 mM. Note that differences in values of the bending modulus at different [Cl−] were statistically significant (P < 0.05), as evaluated by Student’s t test (α < 0.05) as seen in Table S2 in the Supporting Information. Such a nonmonotonic variation of the bending modulus for charged bilayers was predicted by Claessens et al. using SCFT calculations.38 For a charged membrane, the bending modulus kc is a sum of two contributions,38

kc = kc,bare + kc,el

modulus due to the presence of an electric double layer. Claessens et al.38 proposed that while the electrical contribution to the bending modulus decreases on increasing counterion concentration, the bare membrane contribution increases, and these two effects compete with one another resulting in a nonmonotonic variation of the total bending modulus. We proceed here to determine whether such an explanation is qualitatively consistent with our experimental findings. We begin by interpreting our results based on existing theoretical calculations of charged and bare membrane mechanics and seek to obtain a microscopic picture of the various changes that occur in the charged bilayer on increasing the counterion concentration. For a charged membrane kc,el has been calculated to be1,18−20 ⎤ ⎛ εε k T ⎞ ⎡ 8 8 ⎥ = ⎜ 0 2B ⎟κ −1⎢1 − 2 + 2 ⎝ πe ⎠ ⎣ kBT s s (1 + s 2 /4)1/2 ⎦ kc,el

(14)

where s = 4πeσ/εε0kBTκ. For systems with a high surface charge density at low salt concentrations, s is large (s ≫ 1) and the above equation reduces to kc,el kBT

=

⎛ 1 ⎞ −1 ⎜ ⎟κ ⎝ πl ⎠

(15)

Here l is the Bjerrum length = 4πεε0/kBT which has a constant value of 0.7 nm in aqueous solutions at room temperature. Our system falls well within this regime for all studied salt concentrations (see the Supporting Information for s values), indicating that our GUVs are highly charged. Equation 15 predicts that kc,el is proportional to the Debye length. If the observed decrease in the bending modulus is primarily due to a reduction in kc,el, then the plot of kc with the Debye length should be linear. In Figure 7, we plot the measured (total) bending modulus kc (in the decreasing regime) as a function of the Debye length along with the predicted kc,el from eq 15 (solid line in Figure 7). It can be seen that the reduction in the bending modulus agrees well with the linear prediction, suggesting the observed initial decrease in kc is indeed due to the electrical contribution kc,el

(13)

Here kc,bare is the bending modulus of the bare membrane and kc,el is an additional, electrical contribution to the bending F

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Figure 8b suggests the hydrocarbon core thickness increases over examined range of salt concentration. This elongation of the hydrocarbon core region on increasing counterion concentration is a result of its incompressible nature; on increasing the counterion concentration, there will be a decrease in the headgroup area of the cationic surfactant molecules (verified by surface pressure isotherm measurements; see the Supporting Information), allowing the bilayer to accommodate a greater number of molecules in a given area. As a result, the bilayer becomes more compact and the thickness of the hydrocarbon core increases to preserve its volume. Indeed, as predicted by Claessens et al.,38 the increase in h (and hence kc,bare) begins to overwhelm the effect of decreasing doublelayer thickness (as the electrical contribution kc,el reaches a plateau value), resulting in a net increase of the bending modulus kc and the nonmonotonic variation that we capture experimentally. Further, at a particular counterion concentration, the hydrocarbon core will reach a critical thickness (corresponding to a minimum value of the charged surfactant headgroup area a0). As a result, the bending modulus should also reach a limiting value. This is conceivably why we observe that the measured bending modulus ceases to increase and levels off beyond a certain counterion concentration, a result that is not obtained in the self-consistent field simulations.38

Figure 7. Total bending modulus kc plotted as a function of the Debye length κ−1 (only points in the decreasing regime are shown). Dashed line is the linear best-fit to the experimental data and solid line is the theoretical prediction of kc,el (eq 15). which predicts kc,el is proportional to the Debye length κ−1 .The observed decrease in the bending modulus agrees reasonably well with the linear prediction of eq 15 and is attributed primarily to the decreasing double layer thickness on increasing counterion concentration.

The difference between the measured bending modulus kc and the electrical contribution kc,el is the contribution arising from the bare membrane, kc,bare, which is shown Figure 8a. The bare bending modulus of a membrane kc,bare is related to its area expansion modulus KA via its thickness,49 and for fluid bilayers this well-established mechanical relationship is given as49 kc,bare =

KAh2 24

4. CONCLUSIONS We have demonstrated that use of a modified experimental protocol for treatment of glass surfaces along with the technique of micropipet aspiration allows for reliable mechanical measurements of highly charged cationic surfactant vesicles. Our measurements show that there is no measurable effect of counterion concentration on the area expansion modulus of a charged membrane. The area compressibility of cationic diC18:1 DEEDMAC membrane is measured to be 99 ± 14 mN/m over the range of salt concentrations studied. On the other hand, values of the bending modulus are found to vary nonmonotonically between 9.6 ± 1.2 and 6.2 ± 1.0kBT, initially decreasing and then increasing with counterion concentration. These are the first experiments to directly confirm, via measurements of the bending modulus, theoretical predictions of a nonmonotonic behavior, and the opposing effects of counterion concentration on the electrical and bare membrane contribution to the bending modulus.37,38 On increasing the counterion concentration, the bending modulus

(16)

Here h is the thickness of the hydrocarbon core of the bilayer. Since KA is known at all counterion concentrations, we can determine h as a function of counterion concentration using the relationship h = (24kc,bare/KA)1/2; the result is shown in Figure 8b. The h values that we obtain range from 2.4 to 2.8 nm. These values are in good agreement with measurements of Rawicz et al.,49 who employed X-ray diffraction and measured an h value of 2.69 ± 0.04 nm for a diC18:1 phospholipid bilayer (having eighteen carbon atoms with one unsaturation on each tail), similar to the tails of diC18:1 DEEDMAC surfactant studied here. This serves as an independent verification of the self-consistency of our mechanical modulii measurements and the analysis done thus far.

Figure 8. (a) Bare membrane bending modulus kc,bare as a function of counterion-concentration. kc,bare is obtained by subtracting the electrical contribution kc,el from the (total) measured bending modulus kc. kc,el is calculated from the theoretical prediction eq 15 (dashed line). (b) Hydrocarbon core thickness of diC18:1 DEEDMAC surfactant calculated using the relationship h = (24kc,bare/KA)1/2 . The values of h are consistent with those obtained by Rawicz et al.49 by X-ray diffraction measurements on a phospholipid with similar (diC18:1) tails as the surfactant used here. The hydrocarbon core thickness increases over the examined range of counterion concentration. G

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(8) Laughlin, R. G.; Munyon, R. L.; Fu, Y. C.; Fehl, A. J. Physical Science of the Dioctadecyldimethylammonium Chloride-water System. 1. Equilibrium Phase Behavior. J. Phys. Chem. 1990, 94 (6), 2546− 2552. (9) Israelachvili, J. N. Intermolecular and Surface Forces, 3rd ed.; Academic Press: San Diego: 2011. (10) Seifert, U. Configurations of Fluid Membranes and Vesicles. Adv. Phys. 1997, 46 (1), 13−137. (11) Needham, D.; Zhelev, D. V. The Mechanochemistry of Lipid Vesicles Examined by Micropipet Manipulation Techniques. In Vesicles; Rossof, M., Ed.; Dekker: New York, 1996; Chapter 9: pp 373−444. (12) Longo, M. L.; Ly, H. V. Micropipet Aspiration for Measuring Elastic Properties of Lipid Bilayers. Methods Mol. Biol. 2007, 421−437. (13) Evans, E. Entropy-Driven Tension in Vesicle Membranes and Unbinding of Adherent Vesicles. Langmuir 1991, 7 (9), 1900−1908. (14) Seifert, U.; Lipowsky, R. Adhesion of Vesicles. Phys. Rev. A 1990, 42 (8), 4768−4771. (15) Ramachandran, A.; Anderson, T. H.; Leal, L. G.; Israelachvili, J. N. Adhesive Interactions between Vesicles in the Strong Adhesion Limit. Langmuir 2011, 27 (1), 59−73. (16) Chernomordik, L. V.; Kozlov, M. M. Mechanics of Membrane Fusion. Nat. Struct. Mol. Biol. 2008, 15 (7), 675−83. (17) Shoemaker, S. D.; Vanderlick, K. T. Intramembrane Electrostatic Interactions Destabilize Lipid Vesicles. Biophys. J. 2002, 83 (4), 2007−2014. (18) Mitchell, D. J.; Ninham, B. W. Curvature Elasticity of Charged Membranes. Langmuir 1989, 5 (4), 1121−1123. (19) Lekkerkerker, H. N. W. Contribution of the Electric Double Layer to the Curvature Elasticity of Charged Amphiphilic Monolayers. Phys. A 1989, 159, 319−328. (20) Winterhalter, M.; Helfrich, W. Bending Elasticity of Electrically Charged Bilayers: Coupled Monolayers, Neutral Surfaces, And Balancing Stresses. J. Phys. Chem. 1992, 96 (1), 327−330. (21) Fogden, A.; Ninham, B. W. Electrostatics of Curved Fluid Membranes: The Interplay of Direct Interactions and Fluctuations in Charged Lamellar Phases. Adv. Colloid Interface Sci. 1999, 83 (1−3), 85−110. (22) Pincus, P.; Joanny, J. F.; Andelman, D. Electrostatic Interactions, Curvature Elasticity, and Steric Repulsion in Multimembrane Systems. Europhys. Lett. 1990, 11, 763. (23) Higgs, P.; Joanny, J. F. Enhanced Membrane Rigidity in Charged Lamellar Phases. J. Phys. (Paris) 1990, 51, 2307. (24) May, S. Curvature Elasticity and Thermodynamic Stability of Electrically Charged Membranes. J. Chem. Phys. 1996, 105 (18), 8314−8323. (25) Delorme, N.; Bardeau, J.-F.; Carrière, D.; Dubois, M.; Gourbil, A.; Mohwald, H.; Zemb, T.; Fery, A. Experimental Evidence of the Electrostatic Contribution to the Bending Rigidity of Charged Membranes. J. Phys. Chem. B 2007, 111 (10), 2503−2505. (26) Song, J.; Waugh, R. E. Bilayer Membrane Bending Stiffness by Tether Formation From Mixed PC-PS Lipid Vesicles. J. Biomech. Eng. 1990, 112 (3), 235−240. (27) Rowat, A. C.; Hansen, P. L.; Ipsen, J. H. Experimental Evidence of the Electrostatic Contribution to Membrane Bending Rigidity. Europhys. Lett. 2004, 67 (1), 144−149. (28) Vitkova, V.; Cenova, J.; Finogenova, O.; Mitov, M. D.; Ermakov, Y.; Bivas, I. Surface Charge Effect on the Bending Elasticity of Lipid Bilayers. C. R. Acad. Bulg. Sci. 2004, 57 (11), 25−30. (29) Mitkova, D.; Stoyanova-Ivanova, A.; Ermakov, Yu. A.; Vitkova, V. Experimental Study of the Bending Elasticity of Charged Lipid Bilayers in Aqueous Solutions with pH5. J. Phys.: Conf. Ser. 2012, 398, 012028. (30) Herold, C.; Chwastek, G.; Schwille, P.; Petrov, E. P. Efficient Electroformation of Supergiant Unilamellar Vesicles Containing Cationic Lipids on ITO-Coated Electrodes. Langmuir 2012, 28 (13), 5518−5521. (31) Akashi, K.-I.; Miyata, H.; Itoh, H.; Kinosita, K., Jr. Preparation of Giant Liposomes in Physiological Conditions and Their Character-

initially decreases due to the decreasing double layer thickness, and then increases as a result of increased membrane thickness. However, the latter effect saturates when the chargedheadgroup reduces to a minimum value, and as a result the bending modulus reaches a limiting value. Finally, we also observe that the presence of surface charges lowers the mechanical strength of a charged membrane, confirming previous results of Shoemaker and Vanderlick.17

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ASSOCIATED CONTENT

S Supporting Information *

Images of giant unilamellar vesicles (GUVs); surface pressure isotherms of surfactant in varying levels of [Cl−] and estimation of headgroup area; table of t test values between measured bending moduli; measured zeta potentials and the corresponding calculated values of surface charge density at varying levels of [Cl−]; table of values of KelA calculated from eq 12. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by a research grant from Procter and Gamble, via a collaboration led by Dr. Bruce Murch, and by a National Science Foundation grant (NSF-GOALI Grant # CBET-0968105). The authors would like to thank Dr. Bruce Murch, Dr. Pierre Verstraete, and Dr. Pieter Saveyn from Procter and Gamble Co. and Prof. Cyrus Safinya at the University of California, Santa Barbara, for their valuable input during the course of this research. We thank Prof. Marjorie Longo for an educational visit to her laboratory and several useful tips on micropipet aspiration, Prof. Deborah Fygenson and Kim Weirich for microscopy training, Prof. Carol Vandenberg for access to the pipet-puller, and Dr. John Frostad for assistance with the fabrication of the aspiration chamber. We also thank Dr. Johann Walter for several useful discussions and critical reading of the manuscript.

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