Surface Electrostatics of Lipid Bilayers by EPR of a pH-Sensitive Spin-Labeled Lipid

Abstract

Many biophysical processes such as insertion of proteins into membranes and membrane fusion are governed by bilayer electrostatic potential. At the time of this writing, the arsenal of biophysical methods for such measurements is limited to a few techniques. Here we describe a, to our knowledge, new spin-probe electron paramagnetic resonance (EPR) approach for assessing the electrostatic surface potential of lipid bilayers that is based on a recently synthesized EPR probe (IMTSL-PTE) containing a reversibly ionizable nitroxide tag attached to the lipids’ polar headgroup. EPR spectra of the probe directly report on its ionization state and, therefore, on electrostatic potential through changes in nitroxide magnetic parameters and the degree of rotational averaging. Further, the lipid nature of the probe provides its full integration into lipid bilayers. Tethering the nitroxide moiety directly to the lipid polar headgroup defines the location of the measured potential with respect to the lipid bilayer interface. Electrostatic surface potentials measured by EPR of IMTSL-PTE show a remarkable (within ±2%) agreement with the Gouy-Chapman theory for anionic DMPG bilayers in fluid (48°C) phase at low electrolyte concentration (50 mM) and in gel (17°C) phase at 150-mM electrolyte concentration. This agreement begins to diminish for DMPG vesicles in gel phase (17°C) upon varying electrolyte concentration and fluid phase bilayers formed from DMPG/DMPC and POPG/POPC mixtures. Possible reasons for such deviations, as well as the proper choice of an electrostatically neutral reference interface, have been discussed. Described EPR method is expected to be fully applicable to more-complex models of cellular membranes.

Introduction

Anionic phospholipids play many roles in biophysical processes. These lipids cause the surface of cellular membranes to be negatively charged. Electrostatic potential of membrane surface affects the concentration of ions and other small molecules in the immediate vicinity (1) and facilitates interactions of charged residues of peripheral proteins with cellular membranes.

As of this writing, the arsenal of analytical methods for assessing electrostatic parameters of lipid bilayers is rather limited. It mainly consists of NMR (2–4), atomic force microscopy (5,6), interaction force measurements (7), fluorescent spectroscopy (8–10), and spin-probe electron-paramagnetic resonance (EPR) (11–18). Typically, EPR studies of bilayer electrostatics employ charged molecular probes that partition between the lipid and the aqueous phases of the membrane depending on the surface potential. The partition coefficient is determined from an analysis of EPR spectra and then the surface potential is derived through a calibration (19–23). Naturally, such a method is as accurate as the estimate of the relative populations of the probe bound to the charged bilayer and free in the bulk solution (19–23). One of the shortcomings of the method is an uncertainty of the exact location of the measured potential, with respect to the bilayer surface, because the locations of the partitioned EPR probe molecules are largely unknown.

A notable and generally applicable EPR approach for determination of electrostatic potentials at biological surfaces has been presented by Shin and Hubbell (15), who employed continuous-wave electron-electron double resonance to measure the collision frequency of a charged dissolved nitroxide with another nitroxide attached to the bilayer interface or a biomolecule such as DNA (15,24). Recently, results of the EPR collision exchange method for two small nitroxides were compared with Debye-Hückel calculations demonstrating a remarkable agreement (25). However, in applications to larger molecules and membrane systems, this method is expected to suffer from the same uncertainty in the local diffusion constant as analogous NMR methods based on measurements of the site-specific proton relaxation enhancement that occurs upon collisions of exposed residues with charged paramagnetic relaxers (2,26). Specifically, in relation to their detailed NMR study of electrostatically driven molecular collisions, Teng and Bryant have noted that “the three different combinations of the data sets do not yield internally consistent values for the electrostatic contribution to the intermolecular free energy” (27).

Another group of methods for evaluating bilayer electrostatics is based on observing reversible ionization of fluorescent and EPR molecular probes upon pH titration. For many of such probes, their exact location, with respect to the lipid bilayer interface, is also unknown. For example, such a widely used membrane probe as 5-doxyl stearic acid yields different EPR spectra upon changes in pH, mainly due to the probe relocating with respect to the bilayer interface upon reversible ionization of the surface anchoring site (either COOH or COO- forms) (11,12,14). One of the most common fluorescent probes for membrane surface potentials, 4-alkyl-7-hydroxycoumarine, was found to be located approximately within the ester group region of the lipid bilayer with the ionizable OH-group being positioned below the lipid phosphate moiety (10). We also note that this probe is somewhat bulky and is likely to cause some local perturbations to the membrane structure in addition to bringing the OH-group deeper into the lipid bilayer.

Here we report on a new, to our knowledge, approach for assessing the surface electrostatics of model membranes—one which employs EPR of a phospholipid-based nitroxide electrostatic probe IMTSL-PTE (Fig. 1 A) that we have synthesized and characterized recently for micellar systems (28). Due to its lipidlike nature, this probe does not partition between the lipid and aqueous phases but instead becomes an integral part of the lipid bilayer. The chemical structure of IMTSL-PTE ensures that the nitroxide moiety is positioned at the lipid bilayer interface. Perturbations to the lipid bilayer, including the phosphate group region, are expected to be minimal because of the compact volume of the nitroxide reporter group. EPR spectra of IMTSL-PTE were shown to be pH-dependent allowing for determination of the interfacial pK_a of the reporter nitroxide group and the effective dielectric constant at the surface of micelles (28).

Figure 1.

Chemical structure of (A) phospholipid-based nitroxide electrostatic EPR probe (S)-2,3-bis(palmitoyloxy)propyl 2-(((1-oxyl-2,2,3,5,5-pentamethylimidazolidin-4-yl)methyl)disulfanyl)ethyl phosphate, IMTSL-PTE, and (B) nonionizable reference probe (S)-2,3-bis(palmitoyloxy)propyl 2-(((1-oxyl-2,2,5,5-tetramethyl-2,5-dihydro-1H-pyrrol-3-yl)methyl)disulfanyl)ethyl phosphate, MTSL-PTE.

Here we describe experiments using this new, to our knowledge, phospholipid-based nitroxide electrostatic EPR probe to evaluate surface electrostatics of lipid bilayers. Specifically, we have carried out the X-band (9.5 GHz) EPR titration experiments of multilamellar vesicles (MLVs) composed of either the anionic 1,2-dimyristoyl-sn-glycero-3-(phospho-rac-(1-glycerol)) (DMPG) or the zwitterionic 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) lipids. As examples of unsaturated lipids with longer acyl chains, MLVs composed of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) or 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-(1′-rac-glycerol) (POPG) lipids have been studied as well. We have chosen MLVs over extruded vesicles because the former are more widely used in biophysical experiments, offer better stability upon buffer exchange, and are essentially planar structures, thus simplifying comparison with the Gouy-Chapman (GC) theory.

Surface potential of cellular membranes is known to be regulated by both the fraction of anionic lipids in the bilayer and the bulk ion concentration. However, to the best of our knowledge, experimental measurements of the surface potential of bilayers composed of mixed lipids received little attention so far. Thus, we applied our method to MLVs composed of DMPC/DMPG and POPC/POPG mixed lipids and examined the effects of electrolyte. To reaffirm that the changes in EPR spectra of IMTSL-PTE are indeed arising from reversible protonation of this pH-sensitive nitroxides, we have carried out control experiments using a specially synthesized nonpH-sensitive analog MTSL-PTE (Fig. 1 B). Finally, electrostatic potentials of lipid bilayer surfaces obtained by EPR of IMTSL-PTE were compared with predictions from the GC theory.

Materials and Methods

Materials and chemicals

All lipids were purchased from Avanti Polar Lipids (Alabaster, AL) as chloroform solutions and stored at −80°C before use. IMTSL-PTE was synthesized as we described in Voinov et al. (28). Methanethiosulfonate spin label S-(1-oxyl-2,2,5,5-tetramethyl-2,5-dihydro-1H-pyrrol-3-ylmethyl) ester (MTSL) was synthesized by modifying the original procedure (29). A nonpH-sensitive analog MTSL-PTE was synthesized from dipalmitoyl-sn-glycero-3-phosphothioethanol and MTSL similar to our published procedure (28). Crude product was purified on a preparative TLC plate (Kieselgel 60 F254; Merck, Whitehouse, NJ) with a mixture of CHCl₃ (80 mL), CH₃OH (30 mL), and H₂O (1 mL) as eluent. The fraction with R_f = 0.55 was collected. Time-of-flight high-resolution mass spectrometry [M + H]⁺, calculated for C₄₆H₈₆NNaO₉PS₂, was 915.5458; the number actually found was 915.5452. All other chemicals were purchased from Sigma-Aldrich (St. Louis, MO) or Acros Organics (Morris Plains, NJ) unless otherwise indicated.

Preparation of spin-labeled lipid vesicles

Spin-labeled MLVs were prepared by mixing chloroform solutions of the desired lipids with IMTSL-PTE or MTSL-PTE at 1 or 2 mol %. Organic solvents were removed with a nitrogen stream yielding a thin lipid film on the surface of a conical glass vial. Residual solvent was removed by evacuating the vial in a vacuum desiccator overnight. Dried lipid films were hydrated by adding 50 mM phosphate buffer at pH = 7.0 and then subjected to 10 consecutive freeze-thaw cycles between liquid nitrogen and a water bath at 305 K. The total lipid concentration was ∼20 w/w %.

pH adjustment

Method 1

Approximately 50 μL of a lipid dispersion was placed into a 1.5-mL Eppendorf tube and pH of the solution was adjusted by titration with a 0.3 or 0.05 M HCl solution or a 0.1 M NaOH solution. To ensure uniform pH in the sample after adjusting pH, the dispersion was then subjected to at least three consecutive freeze-thaw cycles between liquid nitrogen and a water bath at 305 K while vortexing occasionally. The pH was measured by an Orion pH electrode 98 series (Thermo Scientific, Beverly, MA) at the temperature of the EPR experiment.

Method 2

Approximately 50 μL of the lipid dispersion was placed into a 1.5-mL Eppendorf tube and 1 mL of 50 mM buffer solution with the required pH was added. The resulting mixture was vortexed thoroughly, subjected to a few freeze-thaw cycles, and then the lipids were spun down using a Beckman Coulter (Indianapolis, IN) Microfuge 22R centrifuge at 12,000 rpm for 13 min. The centrifugation temperature was set to that of the EPR experiment in which the sample will be used. The clear supernatant solution was removed by a pipette, the remaining lipid dispersion was topped up with a fresh buffer of the same pH, and the procedure was repeated twice. This method was also used to change electrolyte concentration in the sample.

EPR measurements

Continuous-wave X-band EPR spectra from aqueous samples in polytetrafluoroethylene tubes (0.81 × 1.12 mm, Jaguar Industries, Stony Point, NY) were recorded at 17 or 48°C with either a Bruker BioSpin E500 (Billerica, MA) or a Varian E-109 (Palo Alto, CA) spectrometer interfaced to a PC and digitized to 2048 data points. When using the Varian spectrometer, the sample temperature was maintained by a digital variable temperature accessory with a stability better than ±0.02°C and a gradient below 0.07°C/cm over the sample region (30).

Results, Data Analysis, and Discussion

Interfacial pK_a and electrically neutral reference interface

The pK_aⁱ of an ionizable group of a molecule located at a charged interface differs from pK_a⁰ in pure water by terms corresponding to the Gibbs free energy, ΔG_pol, required to transfer the probe from the bulk water onto a location with a different local electric permittivity, ε_i, and ΔG_el attributed to the local electric potential, Ψ, affecting the equilibrium between charged and uncharged species,

$$\text{p}{K}_a^i=\text{p}{K}_a^0+\Delta \text{p}{K}_a^{el}+\Delta \text{p}{K}_a^{pol},$$ (1)

where ΔpK_a^pol and ΔpK_a^el are polarity and electrostatic contributions, respectively (8,10,31). The surface electrostatic potential Ψ relates toΔpK_a^el as

$$\Delta \text{p}{K}_a^{el}=\frac{-e\psi }{\ln \left(10\right)kT},$$ (2)

where e is the elementary charge, k is the Boltzmann constant, and T is the absolute temperature.

Electrostatic pK_a shift, ΔpK_a^el, can be derived from Eq. 1 if other contributions to pK_aⁱ are determined. Whereas pK_a⁰ can be obtained from the experimental EPR titration of a model compound (28), the value of ΔpK_a^pol could be affected by the position of the probe with respect to the interface, as well as by specific chemical moieties in its immediate vicinity. This could be resolved by measuring pK_aⁱ for a probe incorporated into a model system with a chemically similar but uncharged interface, so that Ψ = 0 and ΔpK_a^el = 0. As further articulated in the Supporting Material, we have chosen the Triton X-100 micelles as the reference interface. According to our preceding report (28), the pK_aⁱ of IMTSL-PTE in Triton X-100 micelles was only slightly temperature-dependent: pK_aⁱ = 2.52 ± 0.01 and 2.39 ± 0.03 units of pH at 23.0 and 48.0°C, respectively. Using the intrinsic pK_a⁰ = 3.33 ± 0.03 of IMTSL-PTE, the ΔpK_a^pol values were determined to be −0.81 ± 0.03 (23.0°C) and −0.94 ± 0.04 (48.0°C) (28). These values of ΔpK_a^pol demonstrate that the pH-sensitive nitroxide of IMTSL-PTE experiences a significantly less-polar environment at the interface of the Triton X-100 micelles versus that of pure water.

Surface electrostatic potential of DMPG bilayers

To avoid any ambiguity regarding the bilayer phase during titration, EPR experiments were carried out at temperatures below (17°C) and above (48°C) the main phase transition temperature of DMPG (T_m ≈ 23°C). Titration was carried out using Method 2. The left panel of Fig. 2 shows that X-band EPR spectra of DMPG MLVs doped with 1 mol % of the nonionizable MTSL-PTE reference probe are essentially identical from pH = 7.0 to pH as low as ≈2.0 units. Changes in EPR spectra at pH = 2.0 and below, albeit very minor, are likely caused by a bilayer reorganization upon protonation of the lipid phosphatidyl groups (pK_a of this group was reported to be from 2 to 3 units of pH depending on the ionic strength of the solution (32,33). Such protonation is expected to affect the bilayer packing and, thus, the nitroxide tumbling. Excluding these minor effects, the EPR spectra of MTSL-PTE—a lipid labeled with a nonionizable nitroxide—appear to be essentially insensitive to pH-changes even in the range of protonation of the phosphatidyl moiety. This also indicates that the immediate environment (i.e., microviscosity and polarity) of this nitroxide tethered to the lipid polar head is not affected by pH (at least to a degree noticeable from EPR spectra).

Figure 2.

Representative X-band EPR spectra from pH titration experiments of DMPG MLVs doped with 1 mol % of either pH-sensitive IMTSL-PTE (right) or control MTSL-PTE (left). Spectra were acquired at T = 17°C when the bilayer is in a gel phase.

In contrast, EPR spectra of DMPG MLVs doped with 1 mol % of ionizable IMTSL-PTE display significant reversible changes over a broad pH range from 6.0 to ≈1.0 units (Fig. 2, right panel). Because the nonionizable probe MTSL-PTE reveals no changes in local microviscosity (Fig. 2, left), the observed changes in rotational dynamics of IMTSL-PTE must be attributable to the appearance of an ionized fraction of the nitroxide and electrostatic interactions of the protonated nitroxide with the negatively charged bilayer interface. This ionized fraction is likely to be responsible for the appearance of the low field shoulder at pH ≤ 5.0 that is characteristic of a slower and a more restricted nitroxide tumbling. This is expected, as electrostatic interactions would decrease the nitroxide tumbling rate.

Note that the most significant changes in EPR line shapes of IMTSL-PTE occur from pH = 6.0 to 4.0 and also below pH = 3.0 (Fig. 2, right). The first transition corresponds to protonation of the nitroxide probe, whereas the second one is attributed to protonation of the lipid phosphatidyl group (reported pK_a ≈ 2.9 (1)). Thus, only EPR spectra from pH = 3.0–7.0 were analyzed using the two-site slow exchange model (28,34).

The fraction, f, of the nonprotonated form of IMTSL-PTE was derived from the least-squares decomposition of a series of EPR spectra by calculating the double integrals of the individual components (see the Supporting Material). An example of such spectral decomposition is shown in Fig. 3. The experimental f versus pH data (Fig. 3) were fitted to the Henderson-Hasselbalch titration equation yielding pK_aⁱ = 5.70 ± 0.05 at 17.0°C and pK_aⁱ = 4.91 ± 0.02 at 48.0°C (Table 1). Note that the latter pK_aⁱ value was obtained for the lipid sample pH-equilibrated at 40°C. When the equilibration was performed at 20°C, a significantly lower pK_aⁱ = 4.33 ± 0.05 was observed (Fig. 3, right). A likely reason for such a discrepancy is that the binding constants of counterions and/or protons to DMPG could be affected by the lipid bilayer phase state. Then, pH and electrolyte concentration of the aqueous phase for the DMPG sample equilibrated at 20°C when the bilayer is in the gel phase would not necessarily remain the same after heating the same sample to 48°C and changing the bilayer phase to fluid. This is particularly important for samples with high lipid content such as 20 vol % used in this study. Thus, equilibration of lipid bilayers with electrolytes and buffers and the consequent biophysical measurements should always be carried out at the same temperature, or at least without changing the bilayer phase.

Figure 3.

(Left) (A) An EPR spectrum of 1 mol % IMTSL-PTE in DMPG MLVs equilibrated at 48°C with 50 mM buffer at pH = 4.42. Least-squares decomposition of the spectrum (A) into components corresponding to protonated (B) and nonprotonated (C) forms of the nitroxide. (D) Residual of the fit, i.e., the difference between the experimental and the sum of simulated spectra. Panels B and C are the actual reference spectra scaled by amplitude to yield the data in panel A. (Right) Fraction f of the nonprotonated nitroxide as a function of pH at 17°C (▴) and 48°C equilibrated with buffers at 40°C (○) and 20°C (●), respectively. (Solid lines) Fitting of these data to the Henderson-Hasselbalch titration equation with $\text{p}{K}_a^i$ indicated next to the curves.

Table 1.

Interfacial pK_a for IMTSL-PTE in large multilamellar DMPG vesicles

T, °C	Electrolyte, mM	IMTSL-PTE/DMPG, pKai	ΔpKapol	ΔpKael	Ψexp, mV	ΨGC, mV
17.00 ± 0.02	50	5.70 ± 0.05	−0.81 ± 0.03	3.18 ± 0.11	−183 ± 5	−163
17.00 ± 0.02	100	5.25 ± 0.02	−0.81 ± 0.03	2.73 ± 0.04	−157 ± 3	−145
17.00 ± 0.02	150	4.87 ± 0.08	−0.81 ± 0.03	2.35 ± 0.08	−135 ± 4	−135
48.00 ± 0.04	50	4.91 ± 0.02∗	−0.94 ± 0.04	2.52 ± 0.05	−161 ± 3	−163
48.00 ± 0.04	50	4.33 ± 0.05†	−0.94 ± 0.04	1.94 ± 0.06	−124 ± 3	−163

pK_aⁱ from EPR titration experiments, ΔpK_a^pol the polarity induced shift determined using Triton X-100 micelles as an uncharged reference interface at 23.0 and 48.0°C (28), electrostatic shift ΔpK_a^el, and corresponding surface electrostatic potential Ψ_exp, and the surface electrostatic potential Ψ_GC calculated from the GC theory (ε = 78).

^∗pH equilibrated at 40°C.

^†pH equilibrated at 20°C.

EPR pH titrations were repeated with electrically neutral DMPC MLVs. The fraction f of the nonprotonated form of IMTSL-PTE was derived as described above yielding pK_aⁱ = 3.96 ± 0.05 at 17°C and pK_aⁱ = 2.95 ± 0.05 at 48°C (see Fig. S1 of the Supporting Material).

The pK_aⁱ values of IMTSL-PTE summarized in Tables 1 and 2 are significantly higher for anionic DMPG versus zwitterionic DMPC MLVs as one expects from the large negative electric potential of the former. Further, pK_aⁱ values of IMTSL-PTE for both DMPG and DMPC MLVs demonstrate significant temperature shifts that are clearly related to the change in the lipid bilayer phase from the gel (17°C) to fluid (48°C). When Triton X-100 micelles were used as a reference to derive ΔpK_a^pol for IMTSL-PTE, the calculated electrical potential for DMPG bilayers showed a measurable drop from Ψ = −183 to −161 mV upon transition from the gel (17°C) to fluid (48°C) bilayer phase. We relate this drop to effects of temperature on the structure of the bilayer interface, including changes in the surface charge density and accessibility of the charged phosphate groups to the ions from the bulk aqueous phase. These effects are further discussed in the following section. In contrast, the pK_aⁱ value of IMTSL-PTE in micelles formed from nonionic surfactant Triton X-100 was changed by only $\Delta \text{p}{K}_a^i=0.13\pm 0.03$ pH units over essentially the same temperature interval (28).

Table 2.

Interfacial pKⁱ_a for IMTSL-PTE in large multilamellar DMPG and DMPC vesicles

T, °C	IMTSL-PTE/DMPC, pKai	IMTSL-PTE/DMPG, pKai	ΔpKapol	ΔpKael	Ψexp, mV	ΨGC, mV
17.00 ± 0.02	3.96 ± 0.05	5.70 ± 0.05	0.63 ± 0.06	1.74 ± 0.08	−100 ± 4	−162 (7)
48.00 ± 0.04	2.95 ± 0.05	4.91 ± 0.02	−0.38 ± 0.06	1.96 ± 0.07	−125 ± 4	−163 (2)

Samples were equlibrated with 50 mM electrolyte, ΔpK_a^pol, the polarity induced shift determined using DMPC vesicles as a nonpolar reference interface, electrostatic shift ΔpK_a^el, and the corresponding surface electrostatic potential Ψ_exp and surface electrostatic potential Ψ_GC calculated from the GC theory (ε = 78).

Certain factors could contribute to the observed differences in pK_aⁱ of IMTSL-PTE in electrically neutral Triton X-100 and DMPC.

Firstly, electrically neutral DMPC is, in fact, a zwitterionic lipid as its polar headgroup contains spatially separated charges of opposite signs. The reporter nitroxide moiety tethered to the lipid’s polar headgroup (Fig. 1) is expected to be mostly influenced by the positively charged trimethylammonium groups of the choline moiety.

Secondly, the positively charged trimethylammonium groups attract negatively charged ions from the bulk solution, thus establishing a diffuse double layer, which provides an electrostatic screening for the protonated amino group of the nitroxide. Then the interfacial pK_aⁱ reported by IMTSL-PTE would be affected by the local electric potential, which could deviate from zero as it is controlled by interplay of these two factors.

In contrast, nonionic surfactant Triton X-100 lacks any charged moieties and, therefore, appears to be a more appropriate reference system for determining the polarity-induced ΔpK_a^pol shift. Thus, using IMTSL-PTE titration data for Triton X-100 micelles and the intrinsic pK_a⁰ = 3.33 ± 0.03 (28), ΔpK_a^pol was estimated to be −0.81 ± 0.03, and −0.94 ± 0.04 at 17°C and 48°C, respectively (Table 1).

Further, experimental pK_aⁱ of IMTSL-PTE in DMPC MLVs at 17°C (Table 2) indicates that DMPC vesicles are unsuitable as electrically neutral references for measurement of bilayer electrostatic potential. Indeed, if we assume that for IMTSL-PTE in DMPC ΔpK_a^el = 0, then the polarity shift for this probe is ΔpK_a^pol = 0.63 ± 0.09 (Eq. 1) when the bilayer is in the gel phase at 17°C. However, such a shift ΔpK_a^pol > 0 would contradict an expectation for the effective dielectric permittivity constant, ε_eff, at the bilayer interface to be of an intermediate value between that of water (ε ≈ 78) and the bilayer core (ε ≈ 2 or 4). Then ΔpK_a^pol > 0 would reflect an increase in the effective dielectric permittivity versus that of water because such an environment would stabilize the protonated form of the nitroxide probe resulting in an increase of the observed pK_aⁱ. The latter trend was previously reported for IMTSL-PTE titration in water/iso-PrOH mixtures of various compositions (28).

Note that pK_aⁱ of IMTSL-PTE in zwitterionic DMPC MLVs is significantly higher than that in Triton X-100 micelles. It is likely that this observation reflects the presence of a large permanent electric dipole formed by the choline (net charge + | e₀ | ) and phosphate (net charge − | e₀ | ) groups of DMPC. Notably, when unrealistically high local values of the ε_eff ≫ ε_water ≈ 80 for the interfacial region of zwitterionic lipid bilayer were predicted from theoretical calculations, they were also explained by the presence of permanent and partially ordered dipoles (35). Finally, when using DMPC as a reference interface, the surface potential of negatively charged lipid bilayers would be greatly underestimated versus those predicted by the GC theory (Table 2). To conclude, IMTSL-PTE data presented here provide convincing arguments against using DMPC as a neutral reference interface in measurements of bilayer surface potentials.

Surface potential calculation using the Gouy-Chapman theory

Experimental results were compared with the surface potentials, Ψ_GC, calculated using the GC theory (36),

$${\Psi }_{\text{GC}}=\frac{2kT}{e}\text{asinh}\left(\frac{{\lambda }_{\text{D}}e\sigma }{2{\epsilon }_0\epsilon kT}\right),$$ (3)

where σ is the lipid surface charge density, λ_D is the Debye screening length, ε₀ is the permittivity of vacuum, and ε is the dielectric constant of the medium.

The Debye screening length is given by

$${\lambda }_{\text{D}}=\sqrt{\frac{{\epsilon }_{0}ekT}{2000{\epsilon }_0^2{N}_{\text{A}}{C}_{el}}},$$ (4)

where N_A is Avogadro’s number and C_el is the bulk molar electrolyte concentration.

The surface charge density was estimated as

$$\sigma =-\frac{e\alpha }{A_L},$$ (5)

where A_L is the surface area per ionizable group of a lipid and α is the degree of dissociation of the phosphatidyl group. For DMPG, the pK_a of this group is 2.9 pH units (37) and, therefore, α ≈ 1 at pH ≥ 3.8. Using A_L = 0.48 and 0.62 nm² for the bilayer in the gel and fluid phase (38), respectively, the corresponding surface charge densities were calculated to be σ = −0.334 and −0.258 C/m². For C_el = 0.05 M, the Debye screening length at 17°C is λ_D = 1.34 nm and λ_D = 1.41 nm at 48°C. Then the GC theory predicts essentially the same surface potential values ${\text{Ψ}}_{\text{GC}}^{17{}^{\text{o}}\text{C}}$ = −162.7 mV and ${\text{Ψ}}_{\text{GC}}^{48{}^{\text{o}}\text{C}}$ = −163.2 mV for DMPG at 17 and 48°C (Table 1). Notably, the potential measured in this work by IMTSL-PTE (Ψ_exp = −183 mV) deviates by only ≈10% from the ${\text{Ψ}}_{\text{GC}}^{17{}^{\text{o}}\text{C}}$ value calculated for 17°C (Ψ_GC = −163mV), whereas the potential calculated for 48°C shows an exceptional agreement with the experiment (−163 vs. −161 mV).

Clearly, an increase in the area occupied by the lipid polar head upon bilayer melting (as much as ≈29% (31,38)) and the corresponding decrease in the surface-charge density accounted for in our calculations are still insufficient to explain ≈20 mV (or ≈15%) drop in Ψ observed experimentally. The latter discrepancy is a likely consequence of the simplified nature of the GC approach that assumes a static charged interface. Specifically, the GC theory does not account for changes in the structure of the bilayer interface and the phosphate groups’ accessibility to ions from the aqueous phase occurring upon the transition of the lipid bilayer from the gel to fluid state. It has been reported that even at physiological temperatures thermal energy (kT) could cause rather noticeable deformations of the lipid membrane (39). Thus, at 48°C the thermal energy could modify the interfacial structure of the lipid bilayer resulting in a higher molecular accessibility of the charged groups of the polar head region to the bulk counterions. Indeed, changes in the lipid bilayer phase and surface area are known to dramatically affect molecular accessibility parameters across lipid bilayers. For example, when studying the accessibility of lipophilic oxygen to bilayers doped with 5-doxyl stearic acid, in which the nitroxide reporter group is positioned at a level just below the DMPC polar head, about a 4.5-fold increase in the accessibility parameter (from 139 ± 1 to 620 ± 1 mG, measured as broadening of EPR line) has been reported as temperature was increased from 18 to 36.5°C (40).

To conclude, although the GC theory is in a reasonable agreement with experimental surface potentials Ψ, the theory does not predict a significant (≈15%) drop reported by IMTSL-PTE upon bilayer melting.

Surface electrostatics of POPG bilayers

Electrostatic properties of bilayers formed from unsaturated lipids with longer acyl chains (versus DMPC or DMPG) were studied using vesicles composed of pure and mixed POPC and POPG (T_m ≈ −2°C) and summarized in Table 3 and Fig. 4. The samples were pH-equilibrated using Method 1. Estimates for POPG surface area do vary widely in the literature (e.g., from A_L = 0.53 (41) to 0.65 (42) and even 0.70 nm² (43)). Notably, even for smallest A_L = 0.53 nm², the GC theory underestimates the bilayer surface potential for all the lipid compositions studied (Table 3).

Table 3.

Interfacial pK_a (pKⁱ_a) of IMTSL-PTE in mixed POPG and POPC MLVs

Mol % of POPG	pKai	ΔpKael	Ψexp, mV	ΨGC, mV	ΨGC, mV
				AL = 0.53 nm2	AL = 0.70 nm2
100%	5.49 ± 0.03	2.97 ± 0.05	−171 ± 3	−158	−144
60%	5.25 ± 0.02	2.73 ± 0.05	−157 ± 3	−132	−119
40%	4.74 ± 0.03	2.22 ± 0.05	−128 ± 3	−112	−99
20%	4.38 ± 0.04	1.86 ± 0.06	−107 ± 3	−79	−67
0%	3.50 ± 0.03	0.98 ± 0.05	−56 ± 3	0	0

Measured at 17°C, with the corresponding experimental electrostatic potential, Ψ_exp, and Ψ_GC predicted by the GC theory for different areas per polar headgroup. Triton X-100 micelles were used as an uncharged reference.

Figure 4.

Dependence of the calculated (○) (A_L = 0.65 nm²) and experimental (●) surface electrostatic potentials,Ψ, and the pK_a value of IMTSL-PTE (▴) on the fraction of POPG lipids in the vesicles composed of POPG/POPC mixtures of various ratios. (Solid line) Guide to the eye. Lipid bilayers were in the fluid state at 17°C. Electrostatic surface potentials for pure POPC are not shown.

Surface charge density of DMPG and POPG bilayers

Bilayer surface charge density, σ, was estimated from experimental surface potentials using the GC theory. If we accept a monovalent electrolyte as an approximation of our experimental conditions, then σ is given by

$$\sigma =\sqrt{8000kT{\epsilon }_0\epsilon C_{el}{N}_{\text{A}}}·\text{sinh}\left(\frac{e\Psi }{2kT}\right).$$ (6)

For C_el = 0.05 M, ε = 78 for pure water, and Ψ_exp = −183 mV for DMPG vesicles at 17°C, the calculated surface charge density of σ_exp = −0.50 C/m² is somewhat higher than −0.29 or −0.40 C/m² predicted from Eq. 5 for lipids below T_m using A_L = 0.40 or 0.55 nm², respectively. If we assume that the environment of the nitroxide of IMTSL-PTE is less polar (e.g., ε = 60 as in Riske et al. (17)) than pure water, Eq. 6 would yield a more realistic σ_exp = −0.44 C/m². Notably, ε = 60 of Riske et al. (17) is the same as ε ≈ 60 estimated for the interfacial location of the reporter nitroxide of IMTSL-PTE incorporated into Triton X-100 micelles (28). Calculated values of σ_exp for other lipid systems studied are given in Table 4.

Table 4.

Surface charge densities σ_exp of DMPG, DMPC, POPG, and POPC MLVs

Lipid	T, °C	Ψexp., mV	εeff	σexp, C/m2	AL, nm2	σL, C/m2
DMPG	17.00 ± 0.02	−183 ± 5	78	−0.50	0.48	−0.33
			60	−0.44
DMPG	48.00 ± 0.04	−161 ± 4	78	−0.25	0.62	−0.26
			60	−0.22
DMPC	17.00 ± 0.02	−83 ± 3	78	−0.065	—	0
			60	−0.057
DMPC	48.00 ± 0.04	−36 ± 4	78	−0.019	—	0
			60	−0.016
POPG	17.00 ± 0.02	−171 ± 4	78	−0.39	0.53	−0.30
			60	−0.35	0.65	−0.25
					0.70	−0.23
POPC	17.00 ± 0.02	−56 ± 3	78	−0.036	—	0
			60	−0.031

Calculated using the GC theory for two values of the effective dielectric constant in the interfacial location of the nitroxide and experimental surface potentials determined by EPR; the value σ_L was predicted from Eq. 5 for different lipid surface area A_L.

Effective dielectric constant at the location of the IMTSL-PTE reporter nitroxide

The value of the effective dielectric constant ε_eff at the interfacial location of the reporter probe is a source of uncertainty for determination of ΔpK_a^pol and surface charge density (Eq. 6 and Table 4) regardless of the type of molecular probe (EPR, fluorescence, NMR, etc.). Fortunately, EPR provides additional means for evaluating local polarity and ε_eff through changes in the magnetic parameters of the nitroxide (reviewed in Smirnova and Smirnov (44)). For X-band EPR spectra, the nitrogen hyperfine coupling constants are the most sensitive parameter for local polarity (45). When examined by least-squares simulation of EPR spectra, A_iso for the nonprotonated form of IMTSL-PTE for various lipid systems was found to be essentially the same within experimental error: the lowest A_iso = 14.78 ± 0.04 G was for DMPC at 48°C and pH = 8.0, and the highest was A_iso = 14.87 ± 0.04 G for POPG at pH = 7.0 and 17°C. Thus, we conclude that the local polarity of the nitroxide moiety of IMTSL-PTE is not affected to any significant degree by temperature, phase state of lipid bilayer, or its composition.

We note that the magnitude of A_iso = 14.83 ± 0.04 G is significantly lower than one would anticipate for the imidazolidine nitroxide at the lipid-water interface, with ε_eff expected to take an intermediate value of water (ε ≈ 78) and a hydrocarbon phase (ε ≈ 2). For example, A_iso of nonprotonated IMTSL-2-mercaptoethanol adduct (IMTSL-ME, an analog of IMTSL-PTE that would not form micelles (28)) in 60/40 isopropyl alcohol-aqueous buffer solution mixture (ε = 40.85) is A_iso = 15.29 ± 0.02 G (28).

To decrease uncertainty in determination of A_iso from simulations of EPR spectra of liquid samples, rigid-limit spectra that are free from dynamic effects were acquired by rapidly freezing aqueous IMTSL-PTE/lipid suspensions in liquid nitrogen to 77 K. These spectra yielded parameter A_zz (see Fig. S3) that is measurably affected by local dielectric constant and formation of hydrogen bonds with the N-O^⋅ moiety (46). Notably, for all the lipid compositions, A_zz of IMTSL-PTE was found to be essentially the same ranging from 34.45 ± 0.05 G for POPG to 34.85 ± 0.08 G for POPC (see Table S1 in the Supporting Material). These data verify that the local dielectric environment of IMTSL-PTE was not affected by the lipid compositions we employed.

Local environment of the nitroxide fragment of IMTSL-PTE in POPG bilayers consists mostly of glycerol residues of the lipid headgroup. To mimic such an environment, we have acquired rigid-limit EPR spectra of the model compound IMTSL-ME in a pure glycerol and water-glycerol mixture (20:80 vol %). The value A_zz for IMTSL-ME in glycerol at 77 K was 33.15 ± 0.07 G. The value A_zz for water-glycerol mixture increased to 35.86 ± 0.11 G, indicating a more polar environment. Notably, A_zz of IMTSL-PTE in POPG or POPC is measurably higher than A_zz for pure glycerol that has ε = 42.6.

Although observed trends in both A_iso and A_zz are indicative of an environment with the effective ε significantly lower than ε = 78, such a low ε value would be unrealistic for the interfacial position of the N-O^⋅ moiety of IMTSL-PTE. The observed A_iso and A_zz could be explained by assuming that the hydroxyl groups of the glycerol residue effectively form hydrogen bonds with the tertiary amino group of the imidazolidine heterocycle of the nitroxide. Such hydrogen bonding would have an effect on the nitroxide electronic structure that is similar to protonation of the amino group and decrease both A_iso and A_zz. Indeed, A_zz data for MTSL-PTE confirm this hypothesis. The nitroxide moiety of this phospholipid is similar to IMTSL-PTE (Fig. 1), but the structure of the pyrroline heterocycle is lacking a protonatable tertiary amino group. MTSL-PTE doped at 2 mol % in either DMPC or POPG lipid bilayers showed essentially the same A_zz values of 35.91 ± 0.05 and 35.98 ± 0.05 G, respectively. Note that A_zz of MTSL-PTE exceeds that of IMTSL-PTE by ∼1 G. Even greater effect was observed for A_zz of glycerol solutions of MTSL-2-mercaptoethanol adduct (MTSL-ME) when compared with A_zz of IMTSL-ME (ΔA_zz ≈ 2.7 G, see Table S1).

Surface electrostatics of bilayers with mixed lipid composition

To the best of the authors’ knowledge, only limited data are available on the electrostatics of mixed lipid bilayers. For example, Khramtsov et al. (18) employed EPR of partitioning spin probes to assess Ψ for two DMPC/DMPG MLVs’ compositions at a low and, thus, nonbiological, ionic strength (10 mM NaOAc buffer solution). Other authors reported that an increase in the fraction of DMPC from 0 to 20 mol % in DMPC/DMPG bilayers results in only a 6% decrease in the electrostatic surface potential (47). The latter measurements were carried out in 25 mM glycine buffer solution at pH = 2.8 using a fluorescence method described in Winiski et al. (48).

Here, using the IMTSL-PTE method, we report that dilution of DMPG with an equimolar concentration of zwitterionic DMPC results in an unexpectedly small change in the surface electrostatic potential from ∼−183 to −164 mV when the bilayer is in the gel phase at 17°C (Tables 1 and 5). That is, an increase in the fraction of DMPC lipids to 50 mol % results in only a ∼10% decrease in the electrostatic surface potential. Although this trend is in general agreement with data reported by Chakraborty and Sarkar (47), the GC model predicts a significantly larger drop in the electrostatic potential of the 50/50 mol % DMPG-DMPC mixture to Ψ_GC = −128.26 mV (i.e., by 30%). One of the possible reasons for such a discrepancy is that the GC model neglects the DMPC electric dipole caused by the charge separation in the polar head region.

Table 5.

Interfacial pK_a (pKⁱ_a) of IMTSL-PTE

T, °C	pKia	ΔpKael	Ψexp, mV	ΨGC, mV	ΨGC, mV
				AL = 0.48 nm2	AL = 0.62 nm2
17 ± 0.02 C	5.37 ± 0.06	2.85 ± 0.05	−164 ± 3	−128	—
48 ± 0.04 C	4.63 ± 0.05	2.24 ± 0.03	−143 ± 3	—	−125

Measured in MLVs composed of 50/50 mol % of DMPG and DMPC, electrostatic shift ΔpK_a^el, surface electrostatic potential Ψ_exp, and Ψ_GC from the GC theory.

This dipole could produce a negative electric potential that contributes to the net surface potential of the interface of bilayers containing DMPC. Indeed, measurements of electrophoretic mobility demonstrated that, in electrolyte solutions, zwitterionic (electrically neutral) DMPC vesicles behave as if they are negatively charged (49). Computational studies have shown that a negative (∼−50 mV) potential across the headgroup region of DMPC could be induced by a charge separation in the phosphatidylcholine moiety (50). If we assume that the difference between $\text{p}{K}_a^i$ values of IMTSL-PTE in Triton X-100 and DMPC (2.52 vs. 3.96 pH units, respectively, see Voinov et al. (28) and Table 2) is mainly determined by such an electric potential, then, given that the ΔpK_a^pol = −0.81 (Table 1) and the intrinsic pK_a of IMTSL-PTE is pK_a⁰ = 3.33, one can use Eq. 1 to derive ΔpK_a^el for DMPC at 17°C. This ΔpK_a^el = 1.44 corresponds to an electrostatic surface potential of Ψ_exp = −82.89 mV.

Similar to DMPC/DMPG mixtures, dilution of negatively charged POPG lipids with zwitterionic POPC results in a gradual decrease of the electrostatic potential, Ψ_exp (Table 3, Fig. 4). And, similar to Ψ_exp of pure POPG bilayers, experimental IMTSL-PTE data for mixed POPG/POPC lipids are in a better agreement with Ψ_GC calculated for the smallest A_L = 0.53 nm² (Table 3). This is consistent with the results of theoretical studies showing significantly smaller A_L for POPG versus POPC lipids (41). The counterintuitive trend for POPG was attributed to formation of interlipid ion bridges and strong intra- and intermolecular hydrogen bonding that overcomes electrostatic repulsion (41).

Notably, experimentally measured potentials for both DMPG/DMPC and POPG/POPC mixed bilayers demonstrate significant deviations from the GC predictions. We relate this disagreement to the simplified nature of the GC theory that does not account for either the electric dipole of PC lipids or the diffuse nature of the bilayer interface that could be more pronounced for the shorter DMPC and DMPG lipids than for the longer POPC and POPG lipids.

Another observation is that large changes in Ψ_exp are measured upon adding relatively small fractions of negatively charged lipids to bilayers whereas an increase in POPG fraction from ∼60 to 100 mol % affects Ψ_exp rather insignificantly. This could be the biophysical basis for achieving effective regulation of bilayer surface potentials by small-to-moderate mol % of negatively charged lipids found in cellular membranes.

Effect of electrolyte

Addition of electrolyte (NaCl) to DMPG MLVs results in a strong electrostatic screening effect and a gradual decrease in the observed pK_aⁱ and the surface electrostatic potential, Ψ (Table 1 and Fig. 5). Experimentally determined Ψ_exp for DMPG MLVs at 17°C changes linearly (R = 0.9988) with the salt concentration within the studied concentration range (Fig. 5, solid circles and solid line). Notably, theoretical Ψ_GC values show a nonlinear dependence on concentration when either the dielectric constant ε = 78 of the bulk water (dash-dotted line) or a lower ε = 60 (dashed line) were assumed for the location of the reporter nitroxide (28). By comparing the experimental data and theoretical curves shown in Fig. 5, it is clear that adjusting the effective dielectric constant alone would not bring the experimental data into agreement with the theory as the experimental data show a steeper dependence on the electrolyte concentration than predicted by the GC model.

Figure 5.

Surface electrostatic potential, Ψ_exp, of the large multilamellar DMPG vesicles measured at 17°C plotted versus concentration of the electrolyte (NaCl). Experimental data obtained from IMTSL-PTE titrations are shown (●) with corresponding linear regression (solid line). GC theoretical predictions are shown (dash-dotted and dashed lines) for dielectric constants ε = 78 and 60, respectively.

Conclusions

Overall, comparison of the experimental surface potentials measured by EPR of IMTSL-PTE showed a remarkable (<±2%) agreement with the GC theory for anionic lipid bilayers in the fluid phase such as POPG at 17°C and DMPG at 48°C. The agreement was within ≈10% for DMPG vesicles in gel phase (17°C). Further, the surface potential of DMPG vesicles was found to decrease linearly with electrolyte concentration within the biologically relevant 0.05–0.15 M range whereas the GC theory predicted a nonlinear and less steep dependence. Even larger deviations (∼30%) have been noticed for bilayers formed from mixtures of DMPC and DMPG whereas deviations for POPC/POPG mixtures were significantly less (<7%). The main difference between DMPC/DMPG and POPC/POPG is the length of the acyl chain. The latter should result in a larger hydrophobic effect making POPC/POPG bilayers much more stable and the aqueous interface better defined and possibly less dynamic. Thus, although the simplified GC approximation works satisfactory well for longer chain phospholipids such POPC and POPG, it might be less acceptable for shorter lipids such as DMPC and DMPG based on the experimental data presented here.

To conclude, the studies presented here allowed us to identify experimental conditions and systems for which the GC theory works exceptionally well for describing electrostatic phenomena at the lipid bilayer interface that is assumed to be flat and static in nature. At the same time, it appears that this theory starts to show measurable deviation when describing systems composed of shorter phospholipids, mixed lipid bilayers, or when considering effects of electrolyte concentration. We expect that an understanding of interfacial electrostatic phenomena in more comprehensive models of cellular membranes (which, for example, include sterols and integral proteins and account for nanoscale curvature effects) would require further experimental and theoretical efforts.