2.1 Chemicals and reagents

1,2-dioleoyl-sn-glycero-3-phospho-(1´-rac-glycerol) (sodium salt) (DOPG), and 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) were purchased from Avanti Polar Lipids Inc. (Alabaster, AL). Gramicidin A (GrA) from Bacillus brevis, 4-(2-Hydroxyethyl) piperazine-1-ethanesulfonic acid (HEPES), 1,4-Piperazinediethanesulfonic acid (PIPES), Tetraethylammonium chloride (TEAC), Bovine serum albumin (BSA), and O,O´-Bis (2-aminoethyl) ethyleneglycol-N,N,N´,N´, -tetraacetic acid (EGTA), potassium chloride (KCl), sodium chloride (NaCl), glucose, and sucrose were purchased from Sigma-Aldrich (Germany).

2.2 Synthesis of GUVs

DOPG/DOPC/GrA (40/60/0.01)-GUVs, where the numbers indicate the molar ratio, were prepared using the natural swelling method [34]. To prepare the samples, we started by adding 80 μL of 1 mM DOPG and 120 μL of 1 mM DOPC, both dissolved in chloroform, into a 5 mL glass vial. After that, it was added 20 μL of 1 μM GrA, which was dissolved in ethanol, to the same vial. The DOPG, DOPC, and GrA components mixed together naturally due to their high diffusion rates in the solvent. Additionally, we gently shook the vial by hand to ensure thorough mixing. At this stage, it was allowed the mixture to sit for approximately 10 minutes. This process was repeated for another vial to prepare a total of two vials for each experiment. Then the solvents were evaporated using a gentle flow of nitrogen gas. To ensure complete drying, the glass vials were placed in a vacuum desiccator connected to a rotary vacuum pump for at least 12 hours. Next, 20 μL of MilliQ water was added to each vial, and the vials were pre-hydrated by incubating them at ~48°C for 8 minutes in a mini water bath. Afterward, 1 mL of buffer A (10 mM HEPES, 150 mM KCl, pH 7.5, and 1 mM EGTA) containing 0.10 M sucrose was added to each vial. The samples were then incubated at 37°C for 2.5 hours. To separate the GUVs from aggregates, the samples were subjected to centrifugation using 13000×g (here g is the acceleration due to gravity) at 20°C for 20 minutes using a centrifuge machine (NF 800R Centrifuge, Nuve, Turkey). Subsequently, the GUV suspension underwent purification using the membrane filtering method [35]. The purified GUV suspension was transferred to a solution of buffer A containing 0.10 M glucose. The dynamics of the GUVs were observed using a phase contrast microscope (IX 73 Olympus, Japan) with a 20× objective at a temperature of 25 ± 1°C (Tokai Hit Thermo Plate, Japan). The images of the GUVs were recorded using a charged coupled camera (CCD) (DP22, Olympus) at a speed of 25 frames per second.

2.3 Generating negative membrane potential (φ_m)

The purified GUVs were transferred to a microchamber of the volume of 200 μL, and the GUVs were diluted using buffer T (10 mM HEPES, 150 mM TEAC, pH 7.5, and 1 mM EGTA) containing 0.10 M glucose. To prevent any effects of osmotic pressure, a similar osmolarity was maintained by keeping the combined concentration of KCl and TEAC inside and outside of the GUVs. Different concentrations of K⁺ ions were used to establish a concentration gradient between the inside and outside of the membrane, thereby generating various membrane potentials [20]. In order to prevent strong attachment between the GUVs and the glass surface of the microchamber, a pre-coating step was performed using a 0.10% (w/v) solution of BSA. The membrane potential across the membrane was calculated using the Nernst equation [36]: (1) where, [K⁺]_out and [K⁺]_in are the concentrations of K⁺ ions outside and inside the GUVs, respectively. The generation of membrane potential is illustrated in Fig 1.

An example to generate φ_m = −30 mV is given here. The inside [K⁺]_in = 150 mM, and hence the final concentration in the outside of GUV is required, [K⁺]_out = 150× e ^-25.7/30 = 46.67 mM. If the final volume of the microchamber was 200 μL, the required purified GUVs is (200 μL×46.67 mM)/150 mM = 62.23 μL, which was diluted with (200 − 62.23) μL = 137.77 μL of buffer T. The same procedure was followed for generating −60 mV and −90 mV. A study successfully demonstrated the establishment of the resulting membrane potential (φ_m) using a specific technique. In the technique, the intensity of the rim of GUV, as indicated by a membrane potential-sensitive dye 3,3’-dihexyloxacarbocyanine iodide DiOC6(3), was employed as a marker of the membrane potential [20]. The study examined the interaction between 2 nM DiOC6(3) and individual DOPG/DOPC/GrA (40/60/0.01)-GUVs in the presence of various membrane potential conditions. We utilized the relevant literature and employed the Nernst equation to calculate the membrane potential in our experiment.

2.4 Electric field-induced membrane tension

After 10 min of transferring GUVs and buffer T into the microchamber, an electric field (E) was applied to the GUVs. When an electric field is applied to GUVs, transmembrane voltage (V_m) is generated across the lipid bilayer. Such voltage leads to induce the lateral electric tension σ_c in the membrane as follows [37]: (2)

In the equation, ε_m represents the membrane permittivity (~ 4.5), ε₀ is the permittivity of free space, h is the thickness of the membrane (~ 4 nm), and h_e is the membrane dielectric thickness (~ 2.8 nm). When a spherical GUV is exposed to an E, the angle (θ) between the direction of E and the normal to the bilayer surface can range from 0 to 90°. This means that the orientation of E relative to the GUV’s membrane can vary throughout the vesicle’s surface. The relationship between V_m and θ can be expressed as: V_m = 1.5RE|cosθ|. The value of V_m is maximum when θ = 0°, corresponding to V_m = 1.5RE, which is referred to as the "critical membrane voltage for the breakdown of vesicle" (V_c). By substituting the value of V_m in Eq (2), the following equation can be obtained [38]: (3) where, R is the radius of the GUVs [m], E is applied electric field [V/m]. Thus, the tension at which a GUV breaks down is influenced by both the applied E and the size of the GUV. If R = 10 μm and E = 553 V/cm, V_m = 0.83 V and σ_e = 7 mN/m.

2.5 Experimental setup to apply the electric field on the GUVs

We examined the effects of electric field on a ‘single GUV’ placed in solutions with different membrane potentials (e.g., φ_m = 0, −30, −60 and −90 mV). The experimental setup for applying the electric field is presented in Fig 2(A). The size of the microchamber and electrode configuration is shown in Fig 2(B). A pulsating DC signal of frequency 1.1 kHz is used in the investigations (Fig 2C). Usually, vesicle suspension contains different sizes of GUVs. We examined a ‘single GUV’ in each microchamber, in which the size range of GUVs was 30−35 μm. To obtain statistically reliable results, we repeated the same experiment several times by examining different ‘single GUVs’ in different microchambers. To apply an electric field to the GUVs, first measured the size of each selected ‘single GUV’, and then determined the required electric tension using Eq (3). The corresponding range of E was 250–450 V/cm. The electric tension σ_e was applied for a maximum time 60 s. Fig 2(D) shows an illustration of a ‘single GUV’ between the two gold-coated electrodes. The time when the GUV was completely ruptured is defined as the time of pore formation. Before applying the electric field to the GUVs shown in Fig 2(E) and after rupture of the same GUV shown in Fig 2(F).

3.1 Electroporation in DOPG/DOPC/GrA (40/60/0.01)-GUVs in the presence of various membrane potentials

At first, we investigated the effects of membrane potential (φ_m) on the electroporation in DOPG/DOPC/GrA (40/60/0.01)-GUVs. Fig 3 shows the experimental results of the rupture of GUVs at 0 and −90 mV at σ_e = 6 mN/m. Without applying electric field (i.e., 0 s), the GUVs become intact and spherical in shape, as shown in Fig 3(A) and 3(B). At φ_m = 0, the GUV remains intact until 40.62 s (Fig 3A). GUV starts to rupture at 42.99 s, and at 43.2 s, it becomes completely ruptured as the structure of the GUV disappears. Similarly, at φ_m = −90 mV, GUV is started to rupture at 18.26 s (Fig 3B). The rupture occurs due to the rapid increase in the radius of the pores formed in the GUV membranes. The starting time of rupture indicates the time of pore formation, signifying the point at which the structural integrity of the GUV disappears.

The same experiments were carried out for several ‘single GUVs’ (number of examined GUVs was N = 12−18) in each independent experiment (number of independent experiments was n = 2−4) under the same conditions. The rupture time (t_rup) for several GUVs in one independent experiment is different both for 0 mV and −90 mV, indicating the stochastic nature of rupture (Fig 3C and 3D). The required rupture time of several GUVs at 0 mV is relatively larger compared to −90 mV. In Fig 3(C), 15 GUVs rupture out of 18 GUVs at 0 mV, whereas 17 GUVs rupture at −90 mV (Fig 3D). The time required to rupture the GUVs is defined as the rupture time of vesicles (t_rup). A ‘single GUV’ was observed until 60 s, whether the GUV ruptured or not. If any GUVs didn’t rupture within 60 s, they are considered intact and indicated by a symbol (×) mark at the top of the bar (Fig 3C and 3D). A similar rupture along with stochastic rupture of DOPG/DOPC/GrA (40/60/0.01)-GUVs is also observed for −30 mV and −60 mV at σ_e = 6 mN/m.

To determine the rate constant of rupture of GUV (k_r) for different negative membrane potentials at a fixed σ_e, the time course of the fraction of intact GUVs without rupture among all the examined GUVs, P_intact (t), is determined, which indicates on how much fraction of GUVs became intact with time and is represented as P_intact (t) = 1- P_rup (t). If 18 single GUVs are examined at σ_e = 6 mN/m in which 9 GUVs rupture within 60 s observation, P_intact (t) = 1- P_pore (t) = 1−9/18 = 0.5. Fig 4(A) shows the time course of P_intact (t) for different membrane potentials at 6 mN/m. It shows that the decrement of experimental data for P_intact (t) vs. time is a factor when membrane potential changes from 0 to −90 mV. The P_intact (t) vs. time graph is well fitted by a single-exponential decay function, (4)

where, t is the duration of time to apply the tension in GUVs. From the fitted curves, the values of k_r are obtained 6.2×10⁻³, 10.4×10⁻³, 21.8×10⁻³, and 36.7×10⁻³ s^-1 for 0, −30, −60 and −90 mV, respectively. The same experiments were carried out for several ‘single GUVs’ (N = 12−18) in each independent experiment (n = 2−4). The values of average k_r are (7.5 ± 1.6)×10⁻³, (10.9 ± 2.3)×10⁻³, (16.9 ± 2.6)×10⁻³, and (35.6 ± 5.5)×10⁻³ s^-1 for 0, −30, −60 and −90 mV, respectively, at 6 mN/m. Hence, the values of k_r increase with the increase of negative membrane potential (Fig 4B).

We have calculated the probability of rupture (P_rup) and the average time of intact (t_intact) of DOPG/DOPC/GrA (40/60/0.01)-GUVs for different φ_m at 6 mN/m. The values of P_rup were 0.41 ± 0.05, 0.47 ± 0.02, 0.52 ± 0.02, and 0.68 ± 0.04 for 0, −30, −60, and −90 mV, respectively (Fig 4C). P_rup increases with the increase of φ_m. The average times of intact GUVs (t_intact) are 50.25 ± 2.1, 43.88 ± 2.0, 39.50 ± 3.1, and 28.11 ± 2.0 s for 0, −30, −60, and −90 mV, respectively, at 6 mN/m. Less intact time of GUVs is observed in higher φ_m (Fig 4D).

Now, we quantify the change in rate constant of rupture, probability of rupture, and the average time of intact DOPG/DOPC/GrA(40/60/0.01)-GUVs at σ_e = 6 mN/m with the change in membrane potential. Table SI 1 in S1 File represents the values of different parameters in the presence of φ_m. Table SI 2 in S1 File is extracted from Table SI 1 in S1 File, which presents the changes in k_r, P_rup, and t_intact due to the changes in φ_m. The average values of Δk_r/Δφ_m, ΔP_rup/Δφ_m, and |Δt_intact|/Δφ_m are obtained 1.1×10⁻⁴ (s^-1/mV), 2.3 (mV⁻¹), and 22.3×10⁻² (s/mV), respectively, at σ_e = 6 mN/m and at φ_m = −30 mV.

3.2 Electroporation in DOPG/DOPC/GrA (40/60/0.01)-GUVs in the presence of various electric tensions at φ_m = −30 mV

In this section, we have investigated the electric tension (σ_e) dependent electroporation in DOPG/DOPC/GrA (40/60/0.01)-GUVs at φ_m = −30 mV, and presented the results in Fig 5. The phase contrast images of two separate ‘single GUVs’ at 5 and 7 mN/m are presented in Fig 5(A) and 5(B), respectively in the presence of φ_m = -30 mV. Both the GUVs remain intact and spherical before applying the electric filed (i.e., 0 s). The complete rupture of these GUVs occurs at 51.02 and 37.12 s at 5 and 7 mN/m, respectively. The stochastic rupture of several ‘single GUVs’ for both conditions is shown in Fig 5C and 5D. The unruptured GUVs are indicated by (×) mark at the top of the respective bar diagram. The number of ruptured GUVs at 5 mN/m is relatively smaller compared to 7 mN/m.

Now, we determine the values of k_r of DOPG/DOPC/GrA (40/60/0.01)-GUVs under various σ_e. We follow the same procedure as in Section 3.1 for determining the k_r. The experimental data on the time course of P_intact for various σ_e are presented in Fig 6(A). The experimental data for each tension is fitted using Eq (4), and the values of k_r are obtained as 7.1×10⁻³, 10.4×10⁻³, and 17.9×10⁻³ s^-1 for 5, 6 and 7 mN/m, respectively. The average values of k_r (N = 18−20, n = 2−4) are obtained as (7.1 ± 1.3)×10⁻³, (10.4 ± 1.5)×10⁻³, and (17.9 ± 4.3)×10⁻³ s^-1 for 5, 6, and 7 mN/m, respectively, at −30 mV. It shows the increasing of k_r with the increase of σ_e at −30 mV (Fig 6B). Now, we compare these rate constants with those obtained at 0, −60, and −90 mV. At 5 mN/m, the k_r values are (4.1 ± 1.2)×10⁻³, (7.1 ± 1.3)×10⁻³, and (20.1 ± 5.8)×10⁻³ s^-1 for 0, −30, and −90 mV, respectively. The similar differences in k_r for different φ_m are also observed at 6 and 7 mN/m (Fig 6B). Thus, at a fixed tension σ_e, φ_m greatly increases the kinetics of vesicle rupture. We have calculated the probability of rupture (P_rup) for various φ_m and σ_e. At σ_e = 6 mN/m, the values of P_rup are found as 0.35 ± 0.05, 0.47 ± 0.07, and 0.68 ± 0.07 for 0, −30, and −90 mV, respectively. The same trend of increasing the values of P_rup with φ_m is obtained for 5 and 7 mN/m. The σ_e dependent P_rup for various φ_m is presented in Fig 6(C), indicating that the presence of higher φ_m increases the probability of rupture of GUVs irrespective of membrane tension. In a similar way, the values of the average time of intact (t_intact) are obtained as 37.4 ± 4.8, 29.7 ± 2.8, and 19.8 ± 2.7 s for 5, 6, and 7 mN/m, respectively, at −30 mV. At 0 mV, the values of t_intact are obtained 41.4 ± 2.8, 35.4 ± 2.7, and 29.2 ± 2.4 s for 5, 6, and 7 mN/m, respectively. Similarly, at −90 mV, these values are obtained as 19.6 ± 2.7, 14.5 ± 3.0, and 13.7 ± 2.2 s for the corresponding tensions. It is observed that less time is required for vesicle rupture at higher φ_m at a particular tension (Fig 6D).

3.3 Estimation of pore edge tension (Γ) of DOPG/DOPC (40/60)-GUVs under various conditions

Lipid membranes, composed of lipid molecules, exhibit continuous fluctuations in their lateral density. These fluctuations can lead to localized regions of decreased lipid density known as prepores or local density rarefactions [39,40]. The presence of an electric field (E) induces lateral tension (σ_e) in the membranes. Thermal energy further contributes to variations in the lateral density of lipid molecules, causing local condensation and rarefaction within the membrane [38]. When a rarefaction in the membrane exceeds a critical radius, r_c, it transitions into a prepore with a radius, r. If r is smaller than r_c, the prepore closes rapidly. Conversely, if r is greater than or equal to r_c, the prepore transforms into a transmembrane pore. These phenomena are depicted and visualized in Fig 7. Vesicle rupture occurs within a very short time, approximately 1 s, as the radius, r, approaches infinity. The free energy of a prepore, U(r, σ_e), comprises a term -πr²σ_e that favor prepore expansion and the term 2πrΓ that favor prepore closure, where Γ represents the free energy per unit length of a prepore (i.e., pore edge tension or line tension of a pore). According to the classical theory of pore formation, the free energy of a prepore can be expressed as [41]:

(5)

In our previous paper [42], a similar equation for the free energy of a prepore in the context of IRE was utilized. In that study, we specifically considered the toroidal structure of the prepore [43]. The parameter B represents the electrostatic interaction arising from the surface charge of membrane. In our case, B is considered to be 1.76 mN/m since the surface charge density of the DOPG/DOPC/GrA (40/60/0.01)-GUVs and the ion concentration in the buffer match those of DOPG/DOPC (40/60)-GUVs [41]. The energy barrier, or activation energy, for pore formation is determined by the maximum value of U(r) at r = r_c, denoted as U_b. At r_c = Γ/ (σ_e + B), U_b, is expressed as follows [44,45]: (6)

The Arrhenius equation for the rate constant (k_r) can be derived from Eq (6) and can be expressed as follows [46]: (7) where, A is the frequency factor, k_B is the Boltzmann constant, and T is the absolute temperature. By rearranging Eq (7), we can derive the revised expression as follows: (8)

The experimental data on lnk_r vs. 1/(σ_e + B) for several membrane potentials are fitted using Eq (8) as shown in Fig 8. The best-fit values were obtained for Γ = 4.80 ± 1.98, 6.14 ± 2.23, 6.47 ± 3.18, and 5.48 ± 2.12 pN at 0, −30, −60, and −90 mV respectively. The change in Γ is negligible and often unchanged with respect to the change of φ_m. Therefore, it can be assumed that the value of Γ is almost same for DOPG/DOPC/GrA (40/60/0.01)-GUVs with the change in φ_m.

3.4 Electroporation in DOPG/DOPC (40/60)-GUVs in HEPES and PIPES buffer in the absence of membrane potential

In this experiment, the electric field-induced rupture of DOPG/DOPC (40/60)-GUVs prepared in HEPES buffer (10 mM HEPES, 150 mM KCl, pH 7.5, and 1 mM EGTA) is investigated in the absence of membrane potential. Fig 9 shows the experimental results of GUV’s rupture under different tensions. Initially, at 0 s, both GUVs (shown in Fig 9(A) and 9(B)) remain intact and exhibit a spherical shape with high contrast in the phase contrast image, indicating their stability. However, when an electric tension of σ_e = 5 mN/m is applied to the GUV shown in Fig 9(A), rupture occurs at 51.6 s. Similarly, when a higher electric tension of σ_e = 7 mN/m is applied to the GUV shown in Fig 9(B), rupture occurs at 24.46 s. The stochastic rupture of several GUVs at σ_e = 5 mN/m and σ_e = 7 mN/m is presented in Fig 9C and 9D, in which the horizontal axis indicates the GUV label number (m) and the vertical axis indicates the rupture time (t_rup). The GUVs that did not rupture within this time frame is indicated by the cross (×) mark on top of the bar (Fig 9C and 9D).

To determine the k_r of DOPG/DOPC (40/60)-GUVs, the time-dependent P_intact is shown in Fig 10(A). The P_intact vs. time graph is fitted using Eq 4, and the k_r value is obtained 5.8×10⁻³ s^-1 for 5 mN/m. Similarly, the values of k_r are 10.4×10⁻³ s^-1 and 15.1×10⁻³ s^-1 for 6 and 7 mN/m, respectively. The average values of k_r with (± SE) from the several independent experiments (e.g., N = 12−18, n = 2−4) are obtained (4.8 ± 1.6)×10⁻³ s^-1, (9.1 ± 3.2)×10⁻³ s^-1 and (16 ± 5.4)×10⁻³ s^-1 for 5, 6, and 7 mN/m, respectively (Fig 10B). This is clearly indicating the increasing rate constant with applied field. The values of P_rup are obtained 0.36 ± 0.05, 0.45 ± 0.06, and 0.54 ± 0.06 for 5, 6, and 7 mN/m, respectively (Fig 10C). It is found that the P_rup increases with the increase in applied tension. As mentioned above, all the examined GUVs were not ruptured in some cases. The average time of intact (t_intact) GUVs were 56.32 ± 1.6, 48.33 ± 2.3, and 43.03 ± 2.8 s for 5, 6, and 7 mN/m, respectively (Fig 10D). The intact time is comparatively shorter at higher membrane tensions.

We also performed the similar experiments in PIPES buffer (10 mM PIPES, 150 mM NaCl, pH 7.5, and 1 mM EGTA) and the results follow the same trend as those obtained in HEPES buffer (Fig 11). The values of k_r, P_rup and t_intact at σ_e = 5 mN/m in PIPES buffer are obtained (8.5 ± 1.7)×10⁻³ s^-1, 0.36 ± 0.05, and 34.5 ± 3.5 s, respectively, whereas the corresponding values in HEPES buffer are obtained (4.8 ± 1.6)×10⁻³ s^-1, 0.48 ± 0.04, and 56.3 ± 1.8 s. These differences are due to the presence of different salts and other chemicals in the two buffers. The experimental data on lnk_r vs. 1/(σ_e + B) is presented in Fig 11, and the data points have been fitted using Eq (8). The best-fit values of Γ are obtained as Γ = 10.4 ± 0.9 pN for PIPES buffer and Γ = 6.8 ± 1.3 pN for HEPES buffer. Hence, the Γ for DOPG/DOPC (40/60)-GUVs in PIPES buffer is 1.5 times larger than that of HEPES buffer. The value of Γ for DOPG/DOPC(40/60)-GUVs in the PIPES buffer is very similar to that obtained in the literature [31].