Effect of Membrane Tension on the Electric Field and Dipole Potential of Lipid Bilayer Membrane

Abstract

The dipole potential of lipid bilayer membrane controls the difference in permeability of the membrane to oppositely charged ions. We have combined molecular dynamics (MD) simulations and experimental studies to determine changes in electric field and electrostatic potential of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayer in response to applied membrane tension. MD simulations based on CHARMM36 force field showed that electrostatic potential of DOPC bilayer decreases by ~45 mV in the physiologically relevant range of membrane tension values (0 to 15 dyn/cm). The electrostatic field exhibits a peak (~0.8×10⁹ V/m) near the water/lipid interface which shifts by 0.9 Å towards the bilayer center at 15 dyn/cm. Maximum membrane tension of 15 dyn/cm caused 6.4% increase in area per lipid, 4.7% decrease in bilayer thickness and 1.4% increase in the volume of the bilayer. Dipole-potential sensitive fluorescent probes were used to detect membrane tension induced changes in DOPC vesicles exposed to osmotic stress. Experiments confirmed that dipole potential of DOPC bilayer decreases at higher membrane tensions. These results are suggestive of a potentially new mechanosensing mechanism by which mechanically induced structural changes in the lipid bilayer membrane could modulate the function of membrane proteins by altering electrostatic interactions and energetics of protein conformational states.

1. Introduction

A major challenge is identification of the mechanisms by which the mechanical forces are converted into a sequence of intracellular biochemical signals in cells. Numerous studies have demonstrated that in many cases mechanochemical signal conversion originates at the cell membrane[1–3]. It has been recently reported by us that the bradykinin B₂ receptor and PTH1 receptor [4], all G protein-coupled receptors (GPCR), change conformation when stimulated by fluid shear stress (FSS), in the absence of any ligand[5]. These and other studies that showed the importance of lipid-protein interactions for function of membrane proteins[6–9] suggest that the lipid bilayer membrane itself plays a major, possibly primary, role in mediating mechanochemical signal transduction, supporting the hypothesis that changes in the physical properties of the bilayer can have significant effects on signaling dynamics. It has been recognized that mechanical perturbation of the lipid bilayer membrane may lead to changes in static and dynamic properties of the membrane such as membrane thickness[10, 11], polarity[12], structural order[13–15] and fluidity[16, 17]. However, the direct effects of mechanical perturbation on the electrical properties of the lipid bilayer membrane have not been adequately addressed yet (excluding from consideration secondary effects where transmembrane potential is affected by changes in gradients of various ion concentrations due to the downstream activity of membrane channels[18–22]).

The total electrical potential of a membrane is made up of the transmembrane potential (ΔΨ) due to gradients in ion concentrations across the membrane, the surface potential due to lipids with charged headgroups, and the dipole potential (Ψ_D) which arises due to the alignment of dipolar lipid headgroups and water dipoles in the interface region between the hydrophobic membrane interior and the aqueous phase[23–26]. Typical value for ΔΨ across the membrane of a resting cell is around 70 mV, corresponding to the electric field strength of ~ 10⁷ V/m inside the ~ 5 nm thick membrane. In contrast, the dipole potential Ψ_D changes sharply across the headgroup area resulting in much stronger electric fields, on the order of 10⁹ V/m.

It is well established that the total transmembrane potential can modulate and even control functioning of various membrane proteins such as voltage gated ion channels[27, 28], enzymes[29, 30], ligand gated channels[31, 32], ion transporters[33, 34] and very recently GPCRs[35–38]. Application of external potential ΔΨ in these systems affects or even triggers functional conformational transitions. Therefore, it is possible that the mechanically induced changes in the much stronger electric field of the dipolar potential Ψ_D could be capable of exerting strong influence on the conformational dynamics of membrane proteins.

In this paper, we combine molecular dynamics (MD) simulations with experimental studies to estimate the changes in the dipole potential of the lipid bilayer membrane under mechanical stress. We first describe the results of molecular dynamics simulations performed to determine the effects of membrane tension on the dipole potential of the DOPC bilayer; the dipole potential is modeled as the inner or Galvani potential, i.e. the electrostatic potential that is felt by a test point charge. Then, we present the results of experimental studies based on using dipole-potential sensitive fluorescent probes in large unilamelar vesicles (LUV) under variable osmotic stress which is used to induce isotropic membrane tension in the vesicles. Isotropic membrane tension is used to model the response to the FSS since increased membrane tension is one of the consequences of the action of the FSS on plasma membrane in cells. It is assumed throughout the text that the observed mechanosensitive effects are caused by the actual stress induced in the bilayer although we refer to membrane tension as a cause, to facilitate direct link between theoretical studies and experiments.

2. Methods

2.1 Simulations of the pure lipid bilayer

Initial structure of a system comprised of 128 DOPC lipids and 5763 water molecules (total 34,953 atoms) was obtained from CHARMM-GUI [39]. Molecular Dynamics simulations were performed at 310 K using NAMD program (version 2.7b) [40] at different membrane tension values (γ = 0, 1, 2, 3, 4, 6, 8, 10, and 15 dyne/cm). We have used a flexible periodic simulation cell that allows fluctuations of cell boundaries in all dimensions. The ratio of the x and y dimensions of the cell were fixed to keep the shape constant in x-y plane (perpendicular to bilayer normal). Simulations were performed on NP_zγT ensemble using combination of Nosé-Hoover constant pressure method[41] and Langevin piston method [42] as implemented in NAMD program in order to keep the pressure normal to bilayer (P_z) at 1 atm and the surface tension constant at the values studied. CHARMM36 force field for lipids was used. The Lennard-Jones (LJ) potential was switched and truncated from 10 – 12 Å. The particle mesh Ewald (PME) [43] method was employed for calculation of long range electrostatic interactions. The contribution of LJ and PME to the energy and forces were updated every step. The temperature was held constant by using Langevin thermostat method with a 1 psec⁻¹ coupling constant. A time step of 2 fsec was used. The coordinates were saved every 1 psec. Simulations were performed on Teragrid supercomputer (Lonestar) using 256 cores or locally on a 48 core Linux cluster based on Xeon 5500 processors. Each simulation was run for 50 ns. The first 10 nsec of each run were intended for equilibration only and were omitted from subsequent analysis. Degree of equilibration of the bilayer was determined by monitoring the value of the area per one lipid molecule.

2.2 Simulations of dipole potential probes in the lipid bilayer

The initial structures for the simulations of the dynamics of fluorescent probes in 128 DOPC bilayer were generated by replacing one phospholipid molecule in the middle of the lipid bilayer described above either with F4N1 or di-8-ANEPPS molecule (see Fig. 3A and B). Initial probe molecular structures were built using Maestro (Schrödinger, Inc.) and conformational search was performed in MacroModel (Schrödinger, Inc.) to determine the lowest energy conformation of the molecules. The preferred conformers of the probes were further optimized using Gaussian 03 software package [44] at the B3LYP6-311G(d,p) level of theory. Partial charges were calculated using CHELPG algorithm as implemented in Gaussian 03[44] for the fragments of the probes that do not include the aliphatic tails and also the head group in the case of di-8-ANEPPS (shown in red, Supplementary Data, Fig. S5). The partial charges for the aliphatic tails for both probes and the head group for the F4N1 were set to the same value as the saturated part of the DOPC aliphatic tail and head group, respectively, to be consistent with the CHARMM36 force field (Supplementary Data, Figure S5). Atom types were assigned manually by analogy with chemically similar fragments found in CGenFF[45].

Figure 3.

F4N1 and di-8-ANEPPS fluorescent probes. (A) Structure of F4N1 probe and its location in DOPC bilayer; CHELPG charges were calculated for the fragment colored in red and CHARMM partial charges were used for the fragments colored in black to make the charges compatible with the CHARMM forcefield. (B) Structure of di-8-ANEPPS probe and its location in DOPC bilayer; CHELPG charges were calculated for the fragment colored in red and CHARMM partial charges are use for the fragments colored in black to make the charges compatible with the CHARMM force field.

F4N1 molecule has a final charge of +1, therefore one Cl⁻ ion was added to the system randomly to neutralize it using autoionize plugin in VMD[46]. Molecular dynamics simulations were carried out as described above for the pure lipid with applied membrane tension of 0 dyn/cm and 10 dyn/cm with F4N1 or di-8-ANEPPS embedded in lipid bilayer. Both systems were minimized and heated to 310 K, followed by 10 ns equilibration and multiple 40 ns production runs.

2.3 Experimental Materials and Methods

The F4N1 fluorescent probe was synthesized according to the synthetic route reported earlier[47]; the purity of the compound was confirmed using LC-MS to be higher than 99.9 %. The di-8-ANEPPS probe was purchased from Life Technologies (Molecular Probes).

Unilamelar vesicles were prepared by hydrating lipid/probe mixture (~ 5 mg/ml) in 605 mOsm/kg Li₂SO₄/sodium phosphate (25 mM) buffer (pH 7.3) followed by ~10 extrusions through 100 nm polycarbonate filters (Avanti Polar Lipids). For both di-8-ANEPPS and F4N1 the DOPC/probe molar ratio was 200. LUV size distributions were checked by dynamic light scattering using DynaPro99 molecular sizer (Protein Solutions, Inc.); LUVs were consistently found to be on average ~ 100 nm in diameter with size distribution width of ~ 50 nm.

The medium osmolality was varied by changing concentrations of the Li₂SO₄ in the suspension medium by either diluting with low osmolarity buffer or by adding variable amounts of buffer containing higher concentration of Li₂SO₄. The freezing point depression method was used to obtain osmolality values (Micro Osmometer 3300, Advanced Instruments). Osmotic pressure (ΔP) was be estimated from the osmolality difference (ΔP=ΔM·RT ) which enabled estimation of the resulting membrane tension (T) from the Young–Laplace equation: T = rΔP/2, where r is the vesicle radius.

Fluorescence excitation (di-8-ANEPPS) and emission (F4N1) spectra of DOPC/probe vesicles in suspension were recorded using a Fluorolog-3 spectrofluorimeter (Jobin Yvon) in a 3×3×10 mm fused silica cell. Fluorescence excitation ratio for the vesicles with di-8-ANEPPS probe (R) was calculated as a ratio of fluorescence emission intensity at 620 nm when excited at 440 nm and 530 nm. Fluorescence emission ratio for the vesicles with the F4N1 probe was calculated as ratio of fluorescence emission intensity at 572 nm and 488 nm when excited as at 420 nm.

3. Results

The aim of MD simulations was to determine the effect of membrane tension on the electrical properties of the lipid bilayer, namely the magnitude and the spatial profile of the electric field and the electrostatic potential. Furthermore, MD simulations of dipole potential sensitive fluorescent probes were used to estimate changes in location of these probes with applied membrane tension; this was relevant since fluorescence changes due to applied mechanical stress could potentially be attributed to changes in location of these probes as well as to change in the dipole potential of the membrane.

3.1 Electric field and Dipole Potential

The electric field, E(z), and electrostatic potential, Ψ(z), were calculated by integrating the charge density (ρ(z)) along the bilayer normal (z) as follows:

$$E(z)=\frac{1}{2{\epsilon }_0}[\underset{-l}{\overset{z}{\int }}\rho (z^{\prime }){dz}^{\prime }-\underset{z}{\overset{l}{\int }}\rho (z^{\prime }){dz}^{\prime }]$$ (1)

$$\psi (z)=-\underset{-l}{\overset{z}{\int }}E(z^{\prime }){dz}^{\prime }.$$ (2)

The simulation box was divided into slabs of 0.25 Å in the z-direction. The charge density calculated at each slab was averaged over each frame in the MD trajectory and both leaflets of the bilayer. ε₀ is the vacuum permittivity and dz is the thickness of the slab. The potential was chosen to be zero at the center of the bulk water (z = −l, z = l).

Figure 1A shows that electric field peaks at the distance of ~17 Å from the center of the bilayer which approximately corresponds to the average positions of ester oxygen atoms; the magnitude of the maximum electric field is 0.8×10⁹ V/m. As the membrane tension is increasing, the peak location of the electric field shifts towards the center of the bilayer by ~ 0.9 Å; this shift increases linearly with increasing surface tension (Figure 1B). Note, that at selected locations in the bilayer headgroup area the electric field changes by up to ~ 2×10⁸ V/m at the highest membrane tension used(Fig. 1A). The peak values of the dipole potential show a decrease with increasing surface tension (Figure 2A). Figure 2B shows contributions of DOPC lipid and water molecules to the total dipole potential plotted separately; the contribution from lipids is negative while that from water is positive but the amplitude of both contributions is decreasing with membrane tension. Figure 2C indicates that the maximum value of the dipole potential depends linearly on the applied membrane tension; when membrane tension increases from 0 and 15 dyn/cm the dipole potential decreases by ~ 45 mV (−7.4 %). The absolute value of the electrostatic potential difference between the bulk water and the bilayer-center without applied membrane tension is positive (~ 607 mV).

Figure 1.

Time-averaged electric field (E(z)) change with increasing surface tension. (A) Time-averaged electric field profile along the bilayer normal (z) at zero (black) and 15 dyn/cm (red) applied membrane tension; green line indicates the difference in electric field profile between the 0 dyn/cm and 15 dyn/cm. (B) Shift of the position of the maximum E(z) peak with respect to the bilayer center with increasing membrane tension.

Figure 2.

Time-averaged dipole potential change with increasing membrane tension. (A) Time-averaged dipole potential profile calculated from simulations with (red, green, and blue) and without (black) applied membrane tension; (B) Contributions to the time-averaged dipole potential profile from lipids (Ψ_DOPC(z)) and water (Ψ_Water(z)); (C) Decrease in dipole potential (Ψ(z)) with increasing membrane tension.

3.2 Validation of MD Simulations

Bilayer thickness and area per lipid values are often used for validation of lipid bilayer simulations. The average bilayer thickness was calculated as the average distance between phosphate groups in the two leaflets of the bilayer. The thickness value obtained from the simulations at zero membrane tension was 38.5 Å which is in good agreement with previously reported experimental value of 38 Å [48]. As expected, bilayer thickness decreased by 4.7 % to 36.7 Å when membrane tension increased to 15 dyn/cm (Supplementary Data, Figure S1). The bilayer thickness exhibited fluctuations with standard deviation (σ) of 0.25 Å around the average value while the individual lipid molecules fluctuated by ± 4 Å along the z dimension. Average area per lipid calculated from the simulation without applied membrane tension (68.8 Ų/lipid) was also in agreement with the experimentally reported value (67.4 ± 1.0 Ų/lipid) [49] as well as the value reported from another simulation performed under similar conditions (69.0 Ų/lipid)[50]. The standard deviation of area per lipid fluctuations was 1.37 Ų/lipid. The area per lipid was observed to increase with increasing surface tension (Supplementary Data, Figure S2), as reported previously for PC bilayers [50, 51]. The area per lipid increased from 68.8 Ų to 73.2 Ų (total increase of 6.4%) when membrane tension increased from 0 to 15 dyne/cm yielding the area expansion modulus (K_A) of 234.5 dyn/cm; this theoretical value of K_A agrees well with the experimental value of 265±12 dyn/cm reported earlier for DOPC bilayer[51]. The volume of the bilayer increased by only 1.4 % consistent with high volumetric compressibility moduli of the lipid bilayers[10].

Average mass density profiles for the lipid bilayer groups (Supplementary Data, Figure S3) are similar to what have been reported previously for PC bilayers [15, 50, 52]. The deuterium order parameter profiles, $S_{CD}=\langle \frac{3}{2}co{s}^2\theta -\frac{1}{2}\rangle =\langle P_2(\mathit{cos}\theta )\rangle$, where θ is the angle between each C-H bond and the bilayer normal) display a trend of decreasing order towards the center of the bilayer and exhibit a prominent dip close to the double-bond (carbon atoms 9 and 10) (Supplementary Data, Figure S4), similar to observed experimentally for DOPC using DROSS NMR technique[53] and in MD simulations[52]. Very similar S_CD profiles have been observed both experimentally and from MD simulations for related PC bilayers (e.g. POPC)[50, 54].

Analysis of the above properties confirms that our bilayer model based on CHARMM36 force field behaves as expected, providing additional validation of our MD simulations.

3.3 Position of the probes

The location of the fluorescent probes used in this study determine their suitability to measure changes in local electric fields in the lipid bilayer under membrane tension[55]. Due to the structural similarity of these probes to phospholipids, they are expected to be located in the membrane with their amino (in F4N1) and sulfonate (in di-8-ANNEPS) groups in the polar head region of the lipids and their aliphatic groups in the lipid tail region (Fig. 3). In order to determine whether that was the case in our simulations with or without applied membrane tension (γ = 0 or 10 dyn/cm), the z coordinates (along the bilayer normal) of the selected lipid groups as well as center-of-mass (COM) of the probes and the DOPC bilayer were plotted as function of time (see Figure 4A–B); these simulation data confirm that the probes stay anchored in the lipid bilayer with their polar groups located in the head group region and hydrophobic groups in the lipid tail region irrespective of applied membrane tension. Note that, although the average position of the probes changes by less than 1 Å, the observed fluctuations of the COM of the probes exceed 10 Å at 310 K while the mass density profiles of both probes extend over 20 Å (Supplementary Data, Figure S3A–B). The average mass density profiles calculated for the lipid groups and the probes also show that the probes are located between the head groups of the bilayer and the center of the bilayer in both the simulations with and without applied surface tension (Supplementary Data, Figure S3). The average COM position of the F4N1 probe moves towards the center of the bilayer by ~ 0.5 Å when membrane tension is increased to 10 dyn/cm (Supplementary Data, Figure S3A). The increase in membrane tension does not significantly affect the average COM z coordinate of the di-8-ANEPPS probe, although it leads to broadening of the probe’s bimodal mass density profile whereby on average the mass density of the di-8-ANEPPS shifts both towards the center of the bilayer and towards the head groups area (Supplementary Data, Figure S3B).

Figure 4.

Position of lipid groups and the probes along the bilayer normal (z-coordinates) for simulations without (0 dyn/cm) and with applied membrane tension (10 dyn/cm). (A) Plot of z-coordinates of F4N1 in the bilayer with respect to time from simulations without (0dyn/cm) and with applied membrane tension (10 dyn/cm). The nitrogen, phosphate and ester oxygen (sn-2 chain only) atoms of the lipid head groups are colored in blue, orange and red respectively. The center-of-mass (COM) of DOPC and F4N1 are colored in grey and green respectively. (B) Plot of z-coordinates of di-8-ANEPPS in the bilayer with respect to time from simulations without (0 dyn/cm) and with applied membrane tension (10 dyn/cm). The nitrogen, phosphate and ester oxygen (sn-2 chain only) atoms of the lipid head groups are colored in blue, orange and red respectively. The center-of-mass (COM) of DOPC and di-8-ANEPPS are colored in grey and green respectively.

Note that an earlier experimental study of the F4N1 probe [56] suggested that this probe assumes vertical orientation in the bilayer based on quenching measurements using nitroxide-labeled lipids; this observation lends additional support to our MD simulation results (see Fig. 3A).

3.4 Determination of Dipole Potential Changes under Membrane Tension in DOPC Vesicles

It has been shown that potential-sensitive fluorescent membrane probes can be used to detect changes in the dipole potential [47, 56–64]; the fluorescence excitation ratio of di-8-ANEPPS and the emission ratio of the F4N1 have been shown to be sensitive to changes in the dipole potential[57, 58]. More specifically we used styrylpyridinium dye (di-8-ANEPPS–excitation ratiometric dye)[23, 57, 59, 64] and the charged 3-hydroxyflavone (3HF) derivative (F4N1 - dual emission ratiometric dyes)[47, 58, 60]. When these dyes are bound to lipid bilayer, their chromophore is located in the headgroup area and therefore is exposed to the electric field of the dipole potential which leads to modulation of their fluorescence excitation (di-8-ANEPPS)[23, 57, 59, 64] or fluorescence emission (F4N1)[47, 58, 60] spectra.

To investigate whether mechanical membrane tension has an effect on dipole potential of the lipid bilayer, DOPC/di-8-ANEPPS or DOPC/F4N1 (molar ratio 200:1) vesicle suspensions were exposed to osmotic differentials induced by lithium sulphate (Li₂SO₄), selected due to its low membrane permeability[65]. Furthermore Li₂SO₄ is known not to cause dehydration of the lipid bilayer via direct binding, preferential hydration or steric exclusion effects[66]. Fluorescence spectra of di-8-ANEPPS and F4N1 under isoosmotic conditions were unchanged when liposomes were prepared in sodium phosphate (25 mM) buffer without addition of Li₂SO₄.

Figure 5A shows the fluorescence excitation ratio (R) of the di-8-ANEPPS fluorescent dipole potential probe while Fig. 5B shows the fluorescence emission ratio of the dual-wavelength ratiometric dipole potential probe F4N1 incorporated into DOPC liposomes as function of osmolarity of the suspension buffer. The data show that hypotonic stress leads to a larger change in the fluorescence excitation ratio of the di-8-ANEPPS than the hypertonic stress. The emission ratio of the F4N1 exhibits peak at isoosmotic conditions. The most important observation using either probe is that the dependence of the dipole potential on osmolality gradient is asymmetric with respect to the isotonic point.

Figure 5.

(A) Dependence of fluorescence excitation ratio on osmotic stress in 100 nm liposomes using di-8-ANEPPS probe. (B) Dependence of fluorescence emission ratio on osmotic stress in 100 nm liposomes using F4N1 probe. Hypotonic stress corresponds to membrane stretching.

Gross et al. have used known modulators of the dipole potential, 6-ketocholestanol and phloretin to calibrate the fluorescence excitation ratio (R) of di-8-ANEPPS[57]. It is important to note that the calibration by Gross et al. was in turn based on the seminal study by Franklin et al.[67] which relied on measurements of binding and translocation rates of hydrophobic ions in response to modulation of the dipole potential by 6-ketocholestanol and phloretin molecules coupled with the data analysis based on a total membrane potential model by Flewelling et al.[25]. The total membrane potential model used by Franklin et al.[67] relied on a set of fitted and calculated parameters such as point dipole moments of lipids, their orientation, density, distance form bilayer center and dielectric constant of bilayer interior leading to considerable uncertainty in the predicted value of the dipole potential; additional assumptions were made regarding location, orientation and dipole moments of 6-ketocholestanol and phloretin in the bilayer. Hence we use the calibration data of dipole potential based on the response to by 6-ketocholestanol and phloretin to only qualitatively assess the magnitude of dipole potential change due to osmotically induced membrane tension. According to calibration by Gross et al. the normalized fluorescence excitation ratio of di-8-ANEPPS changes by 0.8 units for a 100 mV change in dipole potential[57]. Thus, based on the R dependence on hypoosmotic stress presented in Fig. 5A, the decrease in DOPC dipole potential at the highest value of hypoosomotic stress corresponds to 5 ± 0.5 mV. The lysis tension of pure DOPC lipid bilayers has been reported to be ~ 9.9 ± 2.6 dyn/cm[68]. Therefore, in our experiments the lysis tension should only be reached for the average 100 nm vesicles when the osmolality difference was ~ 170 mOsm/kg. However, the finite distribution of vesicle sizes (± 50%) prepared by the extrusion procedure leads to corresponding distributions of membrane tensions and lysis pressures and this results in less steep dependence of dipole potential on hypoosmotic stress value. Moreover, despite relatively low permeability of Li₂SO₄,[65] the leakage from the vesicles can further reduce the actual osmolality gradient. Hence the estimated value of dipole potential change (5 mV) should be taken as the lower limit.

4. Discussion

Using MD simulations and experimental measurements we found that the maximum value of the dipole potential of DOPC bilayer decreases with increasing membrane tension while the profile of underlying electric field inside the bilayer undergoes significant changes.

In order to explain how a mechanical perturbation of the lipid bilayer membrane could affect the Ψ_D, it is necessary to review the relationship between the structure of the lipid bilayer membrane and the dipolar potential. It is commonly accepted that the dipole potential is a manifestation of a nonrandom organization of the electric dipole moments in the membrane -water interface region. More specifically it is believed that the dipole potential originates from (a) the oriented dipole moments of polar headgroups of lipids (e.g. phosphatidylcholine (PC) type lipids have dipole moment of 18–25 Debye), (b) carbonyl group of acyl chains (dipole moment ~2.5 Debye), and (c) the oriented water molecules (dipole moment of water molecule ~ 1.8 Debye) adjacent to the bilayer[23–26, 69] (note that dipole moment of water molecules in TIP3P model we used is ~ 2.35 D). It has been determined that the dipole moment of the PC headgroup is oriented more parallel to the surface of the bilayer with the normal component of 6 ± 3 Debye pointing towards the aqueous phase[70, 71] (i.e. negative charge towards interior of the bilayer). Therefore it has been suggested that in most cases the dipole moments of lipid bound water molecules are responsible for the positive sign of internal dipole potential[24, 69, 72], despite the fact that removal of carbonyl groups lowers the dipole potential by ~100 mV[24, 73]. Our simulations confirm that electrostatic potential contributions are negative from lipids and positive from water molecules (see Fig. 2B) suggesting that CHARMM 36 force field qualitatively reproduces the electrostatic properties of the DOPC bilayer. The sign of these contributions is opposite but their magnitude is rather similar (Fig. 2B). Hence the dipole potential arises due to difference in two large and opposing contributions which makes it very sensitive to the structural changes in the bilayer, the force field and the method used to calculate electrostatic interactions.

Multiple experimental studies have shown that values of dipole potential for PC bilayers are positive (109 – 575 mV) [23, 25, 69, 74]. Our MD simulations confirm that maximum dipole potential value of DOPC bilayer is positive but somewhat larger than the average value expected for a PC bilayer. This has been recently addressed in a molecular dynamics study of DPPC bilayers under similar conditions and was attributed to limitations of CHARMM 36 force field [50]. Another recent study showed that a lower value of dipole potential, more inline with experimental values, can be obtained by incorporating electronic polarizability into the force field by using classical Drude oscillator model[75]; although the same study admits that the better agreement with experimental value could be fortuitous since other polarizable force fields produce quite different results[76].

Note that the decrease in dipole potential with increasing membrane tension is also expected due to changes in bilayer thickness. Assuming a very simplified bilayer model based on a three layer slab of a dielectric of thickness d, with a charge density profile consisting of a constant positive charge density (ρ₀) core between −d/4 to d/4 and a constant negative charge density (−ρ₀) in the interface regions −d/2 to −d/4 and d/4 to d/2 (to guarantee total charge neutrality), the equations (1) and (2) can be integrated to yield the following expression for the electrostatic potential profile within such a slab of dielectric:

$$\{\begin{array}{c}\psi (z)=\frac{{\rho }_0}{{\epsilon }_0\epsilon }\left({\left(\frac{d}{4}\right)}^2-\frac{z^2}{2}\right),z\in \left\{-\frac{d}{4},\frac{d}{4}\right\}\\ \psi (z)=\frac{{\rho }_0}{2{\epsilon }_0\epsilon }\left(z^2-d\mid z\mid +{\left(\frac{d}{4}\right)}^2\right),z\in \left\{-\frac{d}{4},-\frac{d}{4}\right\},\left\{\frac{d}{4},\frac{d}{2}\right\}\end{array},$$ (3)

which assumes that bilayer is centered at z = 0 and that charge density is zero outside the interval z = −d/2 and d/2. According to eqs. (3) the electrostatic potential profile within such bilayer model is a bell-like curve with potential value being zero at the boundary points, z = −d/2 and d/2, and the maximum value reached at the center of the bilayer at z = 0:

$${\psi }_{\mathit{max}}=\frac{{\rho }_0{d}^2}{16{\epsilon }_0\epsilon }.$$ (4)

Equation (4) shows that maximum value of the potential varies as a square of bilayer thickness (assuming that dielectric constant and charge density are constant). Based on the changes in thickness (− 4.7%) and volume (+1.4%) obtained in MD simulations (see above), and assuming that charge density is inversely proportional to the bilayer volume, the eq. (4) predicts that the maximum value of the potential should decrease by 8.9 % in the membrane tension range 0 to 15 dyn/cm. Despite apparent simplicity of such bilayer model, the predicted decrease in the maximum value of potential is rather close to – 7.4 % obtained from our MD simulations (Fig. 2C) giving additional confidence that our MD simulations correctly reproduce trends in response of dipole potential to membrane tension. Note, that the square dependence of the maximum potential at z = 0 on the bilayer thickness is not specific for the above “three layer” model. For example a dielectric slab model consisting of a homogenous charge density profile (ρ(z) = ρ₀, z ∈{−d/2, d/2} of one type (e.g. positive), yields a similar value for the maximum potential at z=0: ${\psi }_{\mathit{max}}=\frac{{\rho }_0{d}^2}{8{\epsilon }_0\epsilon }$; i.e. the existence of spatially-distributed excess charge density of one type of charge within the bilayer interior contributes to the finite potential value within the bilayer. A recent MD study of a DPPC bilayer also showed that dipole potential of the DPPC bilayer is decreasing when area per lipid is increased [77]. Note, that new CHARMM 36 force field used in our simulations has been designed to correct a number of deficiencies of the older lipid force fields such as inability to reproduce fine structure of water at the lipid water interface, underestimation of area expansion modulus and underhydration of the headgroup region [50].

A recent study suggested that dipole potential is sensitive to density of lipid dipoles implying that any disruption of acyl chain packing can lead to changes in the dipole potential[26]. When the lipid bilayer is stretched, the lipids become more loosely packed while lipid tails become more disordered[15], which has been detected as increased membrane fluidity[17] and hydration[12]; in this case changes in dipole potential are expected due to the change in packing density of lipids (i.e. area per lipid). Increase in area per lipid with increasing membrane tension observed in our MD simulations (Supplementary Data, Figure S2) is consistent with such interpretation. Thus, although the precise molecular origin of dipole potential remains controversial[26, 78], it seems that the orientation and packing density of dipolar molecules in the interface region are the key factors that control the magnitude and spatial dependence of the Ψ_D. Our MD simulations data presented in Fig. 2B confirm that mechanosensitivity of electrostatic potential of DOPC bilayer is due to the membrane tension induced changes in the potentials of both, lipids and water molecules; these data indicate that in the membrane tension range 0 – 15 dyn/cm the values of the dipole potential of lipid molecules in the center of the bilayer increases by 110 mV and the dipole potential of the water molecules decreases by 155 mV, resulting in overall decrease of the total dipole potential by 45 mV. Thus, the decrease of dipole potential by 7.4 % is close to the 6.4 % decrease in the area per lipid within the same membrane tension range.

In the present study we have only considered the effects of an isotropic membrane tension. It can be expected that nearly any mechanical perturbation of the lipid bilayer membrane that can affect the structure of the bilayer, could also result in changes of the dipole potential. For example a recent theoretical study showed that when lipid bilayer is exposed to fluid flow shear stress, the orientational order of lipids increases substantially[13]; in particular, this study showed that lipids are tilted by the shear stress (see Fig. 5 in ref.[13]). Since tilting of the lipid can change the normal component of its associated dipole moment, the change in dipole potential could be expected. Lipid bound water molecules may also change their orientation following application of the FSS; such effect could lead to significant changes in the dipole potential since even a relatively small degree of changes in ordering of water molecules can potentially generate significant drops in electrostatic potential over small distances as pointed out earlier by Gawrisch et al.[24].

It is expected that only the hypertonic stress can lead to membrane stretching due to osmotic swelling of the liposomes. The hypertonic stress is not expected to induce significant membrane tension or compression of the membrane because liposomes can respond to an increase in the surface to volume ratio by changing their shape to aspherical although part of the bilayer may be deformed in this case[12]. Since fluorescence excitation ratio of di-8-ANEPPS and emission ratio of F4N1 have been shown to be sensitive to changes in the dipole potential[57, 58], our experimental data suggest that the dipole potential is sensitive to stretching and deformation of lipid bilayer membrane. Note that kosmotropic or surface tension effects of the dissolved solute (Li₂SO₄ in our case) cannot explain the observed asymmetry in the dependence of fluorescence ratio around the isotonic point because the bilayer dehydration or changes in surface tension have been shown to be monotonous (smooth) function of solute concentrations[79]. The influence of ionic strength on the dipole potential has been studied by Gross et al.[57]; they found no significant change in the dipole potential (as measured using di-8-ANEPPS probe) in the ionic strength range from1 μM to 1 M of KCl. This is expected since ionic strength should have a significant affect only on the surface potential. Gross at al. also showed that the di-8-ANEPPS probe is exclusively sensitive to the dipole potential but not to the membrane surface charge density. Moreover, we did not observe any changes in the fluorescence ratio of di-8-ANEPPS and F4N1 measured under isoosmotic conditions in liposomes prepared in low ionic strength buffer (i.e. in the absence of Li₂SO₄) versus those prepared in the higher ionic strength solution used in our osmotic stress experiments.

In MD simulations we did not observe any lysis/pore formation of the DOPC bilayer at membrane tension values up to 25 dyn/cm. The pore formation is a kinetic process[80] and is expected to proceed on time scales beyond the maximum time of 50 ns used in our simulations; this is consistent with previous reports indicating that a high membrane tension of ~ 90 dyn/cm is needed to observe pore formation in the equilibrated DOPC bilayer on the nanosecond time scale[81].

Note that since our MD simulations indicate that there was no major change in the position of the di-8-ANEPPS and F4N1 probes with respect to the bilayer/water interface with applied surface tension, it is tempting to attribute the experimentally detected changes (Fig. 5A and B) mostly to the changes in the dipole potential of the DOPC bilayer due to mechanical stress; the fact that two different probes exhibit similar response (the decrease in their fluorescence ratios) to the increase in membrane tension is consistent with such interpretation. Still, a small shift in the average z position of the F4N1 probe and a change in the shape of the mass density profile of the di-8-ANEPPS could potentially be responsible for the observed experimental differences between the two probes in the hyperosmotic stress range; these changes may also be another reason (apart from deficiencies of the force field used, the above mentioned experimental factors and the type of calibration data used, see Section 3.4) why the experimentally detected change in the dipole potential (~ 5mV) is notably lower than calculated from MD simulations (~ 45 mV). Note that the calibration data for both probes are based on correlation of their fluorescence ratios to a maximum value of dipole potential as measured using dipole potential modulators and lipophilic ion permeability studies[23, 55, 57]. However, since our MD simulations show that both probe molecules, and in particular their chromophore moieties, are located in the bilayer head group area (Fig. 3), they should be primarily sensitive to the electric fields in that area. As bilayer thins due to applied membrane tension (Supplementary Data, Fig. S1) the probes (the F4N1 and the major mass density peak of di-8-ANEPPS, Fig. S3B) translocate towards the center of the bilayer while the lipid head group area also moves closer to bilayer center. The peak electric field also shifts towards bilayer center, thereby reducing the change in field magnitude experienced by the probe molecule; therefore the change in dipole potential as reported by the probes may likely underestimate the change in the maximum value of the dipole potential in the interior of the bilayer under tension. Note that it has been shown that specific molecular interactions do not affect emission spectrum of di-8-ANEPPS and that the shifts in the fluorescence spectra are due to changes in membrane dipole potential[82, 83].

It is of general interest to discuss by which mechanism the above changes in intra-membrane electric field could couple to conformational motion of membrane proteins. The potential answer to this question is suggested by a large number of studies enabled by the fact that the transmembrane potential (ΔΨ) can relatively easily be measured and controlled using electrodes (e.g. patch clamp technique)[84]. It is established that the conformational motion in voltage-gated ion channels is associated with the “gating” currents[28, 85], first predicted by Hodgkin and Huxley[86]. For a membrane channel to open, the “gating” charges - the charged or dipolar residues move in response to changes in membrane electric field causing conformational transition of the channel protein which opens the pore[28, 85]; it is the motion of charged residues (mostly arginines)[79] and reorientation of dipolar residues that gives rise to transient “gating” currents. It has also been suggested that changes in transmembrane potential can lead to reorientation (tilting) of a α-helix due to the interaction of its intrinsic dipole moment[87] with electric field[28]. More importantly, the movement of “gating” charge was recently reported in a GPCR[35, 36]; this seminal study suggested that the external field (due to total ΔΨ) causes a conformational change in the 3rd intracellular loop of GPCR which results in changes in affinity of the receptor to the agonist ligand and, consequently, alters the activity of the GPCR. Thus, the finding that activity of some GPCRs can be modulated by transmembrane potential[35–38, 88] implies a potential sensitivity of GPCR mediated signaling pathways to changes in electrical properties of the lipid bilayer membrane. Therefore, the much stronger field of the dipolar potential may play a significant role in the energetics and conformational dynamics of GPCR receptors.

The electrostatic potential calculated by Eq. 1 and 2 is the average potential that would act on an infinitesimal test charge of zero volume inserted into bilayer at any given z position; as such it is not directly measurable[75, 89]. The free energy of a finite size probe in the bilayer would certainly contain contributions from exclusion volume and would require calculation of the potential of mean force (PMF) using, e.g. umbrella sampling and weighted histogram method[90–92] or through Jarzynski’s equation using steered MD simulations [93] and it could be significant considering changes in bilayer structure caused by membrane tension. However, the purpose of this work is to explore exclusively the electrostatic contributions to bilayer mechanosensitivity. Such approach is further supported by a recent theoretical study that showed that for the lipid bilayers a similar dipole potential is obtained using finite-size probes versus point test charges[75].

One may raise question if it is appropriate to refer to the electrostatic potential obtained from our MD simulation as the dipole potential. It has been found that the higher order non-dipolar contributions to the inner potential (i.e. quadrupolar) can be dominant for water/hydrocarbon interfaces[89]. However, it has been recently reported that the electrostatic potential of the bilayer membrane is primarily dipolar in nature [75].

Since mechanically induced changes in the dipolar potential can lead to considerably different spatial distribution of the electric field (up to ~ 2×10⁸ V/m change in field magnitude, see Fig. 1A), the resulting changes in electrostatic interaction energy between the dipolar field and the relevant parts of the protein could potentially result in substantial relative shifts of the free energies of different conformational states. This would translate to changes in relative equilibrium populations of these conformational states which, in turn, could lead to changes in activity and physiologically relevant response. Note that expected change in interaction energy of a single uncharged residue (dipole moment ~ 3.5 Debye) with the electric field of 2×10⁸ V/m is on the order of 0.55 k_BT at 37°C (0.34 kcal/mol). Change in electrostatic interaction energies of charged residues are even higher, for e.g. it would take ~ 0.75 k_BT (0.46 kcal/mol) for a charged residue to move ~ 1 Å against the field of the electrostatic potential (~ 2×10⁸ V/m). Thus, depending on the spatial extent of the conformational transition, the number of residues involved and the degree of their exposure to lipids, the overall electrostatic contribution to changes in energies of protein conformational states due to membrane tension could be significant. This is certainly only very qualitative estimate of the expected effect and more detailed studies of specific systems using more rigorous and much more computationally demanding PMF calculations with polarizable force fields will be required for quantitative analysis.

The bilayer parameters such as e.g. thickness or area per lipid exhibit substantial fluctuations. Therefore a question could be asked whether we should compare the magnitude of the membrane tension effect to the magnitude of these fluctuations or to the average macroscopic value of the relevant bilayer parameter (thickness, area per lipid or dipole potential). We believe the answer depends on the time scale of the process of interest. Most of the relevant process such as conformational transitions in membrane proteins happen on microsecond/millisecond time scale; in this case the usage of average values could be justified considering that the time scale of the fluctuations is on picosecond - nanosecond time scale i.e. the membrane protein can be expected to respond mostly to changes in the average value of the bilayer parameter.

In conclusion, our key results are as follows. MD simulations using CHARMM 36 force field showed that the dipole potential of DOPC bilayer linearly decreases by ~ 45 mV in the physiologically relevant membrane tensions range 0 – 15 dyne/cm. In the same range of tensions the peak of the electric field shifts by about 0.9 Å towards bilayer center following the decrease in the thickness of the bilayer by ~ 1.84 Å (−4.7%); the maximum change in the electric field magnitude (~ 2×10⁸ V/m) is the bilayer interface region. We suggest that mechanosensitivity of the dipole potential of DOPC bilayer is in part be due to the membrane tension induced changes in the electrostatic potentials of both, lipid and interfacial water molecules. The area per lipid expands from 68.8 Ų to 73.2 Ų (6.4%) when membrane tension increases from 0 to 15 dyn/cm which enabled us to estimate the value of the area expansion modulus (K_A) to be 234.5 dyn/cm. Experiments using dipole potential sensitive probes indicated that dipole potential of DOPC bilayer decreases with increasing membrane tension by at least ~ 5 mV. These results are suggestive of a potentially new mechanosensing mechanism by which mechanically induced structural changes in the lipid bilayer membrane could modulate the function of membrane proteins by altering electrostatic interactions and energetics of protein conformational states.

Abbreviations

FSS

fluid shear stress

MD

molecular dynamics

LUV

large unilamelar vesicles

DOPC

1,2-dioleoyl-sn-glycero-3-phosphocholine

COM

center of mass

PMF

potential of mean force

PME

particle mesh Ewald method

LJ

Lennard-Jones potential

Appendix: Supplementary Data

Supplementary data to this article can be found online at: