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). Besides, gramicidin A (GrA) (produced by Bacillus brevis and extracted from its culture), 1,4-piperazinediethanesulfonic acid (PIPES), bovine serum albumin (BSA), O,O´-bis (2-aminoethyl) ethyleneglycol-N,N,N´,N´-tetraacetic acid (EGTA), calcein, sodium chloride (NaCl), glucose, and sucrose were obtained from Sigma-Aldrich (Germany).

2.2. Preparation of GUVs under physiological conditions

Giant unilamellar vesicles (GUVs) with DOPG/DOPC compositions and varying mole fractions of GrA (e.g., 0, 0.01, 0.05, 0.1, 1, 3, 5) were synthesized using the natural swelling method [29]. The membranes of the GUVs were composed of varying molar ratios of DOPG, DOPC, and GrA, such as DOPG/DOPC/GrA (40/60/0), (40/59.99/0.01), (40/59.95/0.05), (40/59.9/0.1), (40/59/1), (40/57/3), and (40/55/5). To synthesize GUVs with different GrA%, DOPG and DOPC lipids (dissolved in chloroform) and GrA (dissolved in ethanol) were mixed gently in a glass vial, with a total volume of 200 μL. The components were allowed to mix naturally due to diffusion, and the vial was gently shaken by hand to ensure homogeneity. The mixture was left undisturbed for 10 minutes. Another vial was prepared in the same manner to ensure consistency across experiments. Following this, the solvents were evaporated under a gentle nitrogen flow, and the vials were placed in a vacuum desiccator connected to a rotary vacuum pump for at least 12 hours to ensure complete drying. Subsequently, 20 µL of MilliQ water was introduced into each vial, and the samples were pre-hydrated by incubating at ~ 48°C for 8 minutes in a mini water bath. After pre-hydration, 1 mL of buffer (10 mM PIPES, 150 mM NaCl, pH 7.0, and 1 mM EGTA) containing 0.10 M sucrose was added to each vial, and the samples were incubated at 37°C for 2.5 hours to facilitate vesicle formation. The choice of temperatures in the GUV preparation method was based on optimizing different stages of vesicle formation. The pre-hydration step was carried out at ~ 48°C to enhance lipid mobility and promote uniform swelling of the dry lipid film, as elevated temperatures above the lipid phase transition temperature facilitate membrane hydration and lamellar separation. The subsequent incubation step for vesicle growth was conducted at 37°C to mimic physiological conditions and ensure that the formed GUVs were in a fluid phase suitable for later electroporation experiments. To separate GUVs from any formed aggregates, the samples underwent centrifugation at 13,000 × g (where g represents gravitational acceleration) at 20°C for 20 minutes using a centrifuge (NF 800R Centrifuge, Nuve, Turkey). After the gentle centrifugation step, the supernatant was carefully collected for subsequent experiments, as it contains the intact GUVs, while the pellet mostly comprises lipid aggregates and multilamellar vesicles. In contrast to our previous protocol using phase-contrast microscopy to visualize GUVs in the region of uniform electric field between the anode and cathode, we encountered optical disturbances in the present experiments. Specifically, in some trials, bubble formation—likely due to electrode surface corrosion—occurred near the electrodes during field application. These bubbles occasionally interfered with the optical path and compromised the quality of phase-contrast images. To circumvent this limitation, we employed fluorescence microscopy by incorporating a fluorescent probe into the GUV interior, which allowed unambiguous vesicle visualization despite the occasional presence of bubbles. This modification ensured consistent image quality and reliable rupture time determination across all experimental conditions. In case of preparing the fluorescent probe (calcein) encapsulated GUVs, vesicles were produced in a solution with 1 mM calcein and 0.10 M sucrose in buffer. The resulting GUV suspension was further purified using a membrane filtration technique [30–32]. The purified GUVs were then transferred to a fresh buffer solution containing 0.10 M glucose. GUV dynamics were examined using a phase-contrast fluorescence microscope (IX 73 Olympus, Japan) equipped with a 20 × objective. The observations were carried out at 25 ± 1°C, maintained by a Tokai Hit Thermo Plate (Japan). A charge-coupled device (CCD) camera (DP22, Olympus) was used to capture images of the GUVs at a frame rate of 25 frames per second.

2.3. Electric field-induced membrane tension in GUVs

Following the transfer of purified GUV suspension into a microchamber, an external electric field (E) was applied to induce electro-permeabilization. When GUV was exposed to an electric field, a transmembrane voltage (V_m) developed across the lipid bilayer, leading to the generation of lateral membrane tension (σ_e) within the membrane. This tension can be mathematically expressed as [33]:

(1)

where ε_m is the membrane permittivity (approximately 4.5), ε₀ is the permittivity of free space, h represents the membrane thickness (~ 4 nm), h_e is the membrane dielectric thickness (~ 2.8 nm). Eq (1) follows from electro-mechanical coupling principles, where the stored electrostatic energy per unit area in the membrane is proportional to its effective capacitance and the square of Vₘ. Since the experimented GUVs are typically spherical, the angle (θ) between the applied electric field direction and the normal to the bilayer surface varies across the vesicle’s membrane, ranging from 0° to 90°. The transmembrane voltage (V_m) at a given θ is given by: V_m = 1.5RE|cosθ|, where R is the radius of the vesicle. The highest value of V_m occurs when θ = 0°, leading to V_m = 1.5 RE. The expression V_m = 1.5RE|cosθ| is derived from the analytical solution of Laplace’s equation for a spherical vesicle placed in a uniform external electric field, as originally described by Schwan [34] and further developed by others [35–37]. This formulation assumes: (i) the vesicle behaves as a thin dielectric shell with uniform thickness h, (ii) the conductivity of the inner and outer aqueous media is much greater than that of the membrane, and (iii) the field is applied in the low-frequency (DC or quasi-static) limit. In such conditions, the potential difference across the membrane is maximal at the poles (θ = 0° and 180°), where V_m = 1.5RE, and decreases with ∣ cosθ ∣ toward the equator (θ = 90°). This critical voltage, denoted as V_c, determines the threshold for vesicle rupture. By substituting V_m into Eq. (1), an expression for lateral membrane tension is obtained [38]:

(2)

where R is the radius of the GUV (m), E is the magnitude of applied electric field (V/m). The rupture threshold is influenced by both vesicle size and the intensity of the applied electric field. For instance, if R = 10 μm and E = 553 V/cm, the resulting transmembrane voltage is V_m = 0.83 V, while the induced lateral membrane tension is σₑ = 7 mN/m.

In the investigations, the choice of σₑ = 8 mN/m was motivated by the need to probe rupture kinetics within a physiologically relevant and experimentally accessible membrane tension range. In electroporation theory, the induced membrane tension influences both the lifetime of metastable prepores and the rate of pore expansion. Tensions in the range of 6–10 mN/m are sufficiently high to induce pore formation on experimentally observable time scales (sec), but not so high as to cause immediate catastrophic rupture that would prevent kinetic analysis [38]. Suppose, at tensions significantly above 10 mN/m, vesicles rupture almost instantaneously, preventing reliable determination of rate constants and pore-edge tension. Therefore, membrane tension σₑ = 8 mN/m was chosen as a representative, controlled condition that allows robust statistical comparison across different GrA%, enabling the effective study of rupture kinetics of GUVs with varying GrA content in the membrane. When a ‘single GUV’ is placed in an external electric field, dielectric polarization occurs due to the permittivity contrast between the lipid bilayer and the surrounding aqueous medium. This polarization leads to the development of a transmembrane potential (Vₘ), which is not uniform but varies with the angle θ relative to the field direction. The induced Vₘ causes the accumulation of charges at the membrane–water interface, giving rise to an electrocompressive Maxwell stress. This stress translates into an in-plane (lateral) membrane tension (σₑ) that acts to stretch the membrane.

2.4. Experimental setup for applying the electric field to GUVs

To investigate the impact of an external electric field on an individual GUV, experiments were conducted using vesicles (containing different mole fractions of GrA in membrane) suspended in solutions. The schematic representation of the experimental setup utilized for applying the electric field is depicted in Fig 1(A), while the microchamber dimensions and electrode configuration are illustrated in Fig 1(B). A pulsating DC signal with a frequency of 1.1 kHz was employed throughout the study (Fig 1C). Since vesicle suspensions naturally contain GUVs of varying sizes, each experiment was performed on a ‘single GUV’ carefully selected from the suspension having nearly same contrast and diameter. The chosen GUVs for analysis had diameters ranging between 28–32 μm. To ensure statistical reliability, multiple trials were conducted by examining many individual GUVs using several microchambers. Prior to applying the electric field, the diameter of each selected ‘single GUV’ was measured. Using this measurement, the required membrane tension was determined based on Eq. (2). The same technique was utilized in our several investigations [27,38–44]. For each GrA concentration, at least 12–18 (N = 12–18) individual GUVs were examined and analyzed in each independent trial (n = 2–4) under identical conditions.

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Fig 1. Experimental setup for applying an electric field to GUV.

(A) Laboratory setup showing the microchamber positioned on the microscope stage during experiments. (B) Schematic illustration of the microchamber and the arrangement of gold-coated electrodes. The microchamber was constructed by placing a U-shaped silicone rubber spacer on a glass slide to maintain structural integrity. (C) Graph depicting the applied pulsating DC signal with a frequency of 1.1 kHz over time (ON time 200 μs). (D) Diagram representing a single GUV suspended between the gold-coated electrodes, where E denotes the applied electric field. The transmembrane potential (V_m) is dependent on the angle (θ) relative to the electric field direction. (E) Phase-contrast microscope image of an intact GUV before exposure to the electric field. (F) Phase-contrast image showing the same GUV after undergoing rupture due to applied electric field.

https://doi.org/10.1371/journal.pone.0338817.g001

The corresponding electric field strength (E) applied to the vesicles ranged between 250–450 V/cm. The membrane tension (σ_e) was maintained for a maximum duration of 60 s during each experiment. Fig 2(D) provides a schematic representation of an individual GUV positioned between two gold-coated electrodes. The moment at which the vesicle underwent complete rupture was recorded as the onset of pore formation. A representative image of a GUV before the application of the electric field is presented in Fig 1(E), while Fig 1(F) illustrates the same GUV after rupture.

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Fig 2. Electric field-induced rupture of DOPG/DOPC/GrA-GUVs at different GrA% under σ_e = 8 mN/m.

Typical fluorescence microscopic images illustrate the rupture progression of (A) DOPG/DOPC (40/60)-GUVs, (B) DOPG/DOPC/GrA (40/59.9/0.1)-GUVs, and (C) DOPG/DOPC/GrA (40/57/3)-GUVs. The applied electric field (E) is directed as indicated by the arrow on the left. The time in seconds after applying the electric field is noted in each image.

https://doi.org/10.1371/journal.pone.0338817.g002

3.1. Effects of GrA% on the electroporation of GUVs

To investigate the influence of GrA on the electroporation process in DOPG/DOPC/GrA-GUVs, we conducted a series of experiments to examine the rupture dynamics under an applied electric field. Fig 2 presents representative experimental outcomes for GUVs rupture at σ_e = 8 mN/m, comparing vesicles with 0, 0.1, and 3 mole% GrA in their membranes. At the start of the application of electric field (i.e., at t = 0 s), the considered GUV remained their original spherical and intact structures as observed in Fig 2(A). At 0% GrA, the GUV remained almost stable up to 3 s, after which it was ruptured at 4 s, evidenced by the disappearance of its structural integrity. In contrast, for 0.1% GrA, the vesicle remained almost intact for a significantly longer duration (38 s) before rupturing at 39 s (Fig 2B). A different trend was observed at 3% GrA, where the rupture was occurred at 15 s (Fig 2C). Noteworthy, the rupture time and rate constant were obtained from time-lapse image sequences (1 s/frame) for each vesicle. Data are presented as mean ± standard deviation (SD).

The breakdown of vesicles is associated with the formation and growth of pores in the membrane under the applied electric field. The rupture initiation time corresponds to the onset of detectable membrane destabilization, marking the loss of GUV structural stability. During this process, a gradual decrease in lumen fluorescence intensity of the encapsulated calcein dye was observed prior to complete rupture. This fluorescence decrease likely reflects an early stage of membrane permeation or localized leakage, followed by a rapid loss of intensity as the vesicle disintegrates. The accompanying minor shape fluctuations observed just before rupture suggest transient perturbations of the membrane but do not allow us to directly resolve the underlying molecular mechanism. Therefore, while the observed fluorescence dynamics are consistent with previously proposed models involving nanopore formation and subsequent membrane disintegration [45], the present experiments do not directly test this mechanism. The onset of rupture was operationally defined as the time point corresponding to the pronounced drop in lumen fluorescence intensity.

In our experiments, membrane rupture was identified by a pronounced and irreversible decrease in the luminal fluorescence intensity of calcein dye encapsulated within the GUVs. This decrease directly reflects the loss of membrane integrity and the consequent leakage of the fluorescent probe into the external medium. Such a correlation between fluorescence decay and membrane rupture has been well established in previous peptide–membrane interaction and electroporation studies [46,47]. We previously demonstrated that the sudden drop in internal fluorescence corresponds to vesicle rupture or large pore formation [48]. We employed the same criterion and confirmed that the fluorescence decrease coincides with the morphological collapse of GUVs, as captured by time-lapse microscopy. Therefore, the sharp decline in luminal fluorescence intensity in the present study reliably indicates physical membrane rupture.

The imaging time resolution of 1 s/frame and the spatial resolution corresponding to a 15 μm scale bar were selected to appropriately capture the mesoscale (intermediate scale — between the microscopic (molecular) and macroscopic (bulk) levels.) dynamics of vesicle deformation and rupture, rather than the nanoscopic events of individual channel opening. The open time of a single GrA channel typically lies in the microsecond to millisecond range, and the pore diameter (at initial stage) is on the order of few nanometers—well below the optical resolution limit of conventional microscopy. In contrast, the formation and expansion of electroporation-induced pores in GUVs occur over hundreds of milliseconds to several seconds, and at spatial scales from submicron to tens of microns. Therefore, a temporal resolution of 1 s/frame provides sufficient sampling to resolve the global morphological transitions (e.g., swelling, rupture, and membrane retraction) without excessive photo-bleaching or data redundancy. The chosen optical magnification and scale (15 μm) ensure the full vesicle contour remains in the field of view while preserving adequate pixel resolution for quantitative image analysis of rupture kinetics. Thus, the selected temporal and spatial resolutions were optimized for the characteristic spatiotemporal scales relevant to GUV electroporation and peptide-induced membrane destabilization, rather than for direct observation of transient molecular channel events.

3.2. Stochastic nature of GUV rupture and dependence on GrA concentration

To ensure statistical reliability, multiple independent experiments were conducted, where 12–18 GUVs (N = 12–18) were analyzed per experimental run (n = 3–4 independent experiments) under identical conditions at σ_e = 8 mN/m. The rupture time (t_rup) exhibited variability among individual GUVs within an independent experiment, indicating a stochastic rupture behavior that depends on the GrA%, as illustrated in Fig 3(A, B, C). A comparative analysis of rupture times revealed that GUVs with 0% GrA ruptured faster compared to those with 0.1% GrA. Interestingly, GUVs containing 3% GrA ruptured more quickly than those with 0.1% GrA, suggesting a non-monotonic dependence of rupture time on GrA content. The rupture time is defined as the duration required for the complete disintegration of a GUV under the applied electric field (when the GUV’s lumen-intensity decreased remarkably). Each ‘single GUV’ was monitored for up to 60 s, regardless of whether rupture occurred or not. A similar rupture trend was observed for vesicles containing other GrA content (0.01%, 0.05%, 1%, and 5%) at σ_e= 8 mN/m. The probability of rupture P_rup, which is defined as the ratio of the number of ruptured GUVs to the total number of GUVs analyzed under identical conditions as a function of GrA% is depicted in Fig 3(D). The data reveal that P_rup initially decreases with increasing GrA%, but beyond a certain threshold, it begins to rise, indicating that higher GrA levels may promote membrane instability beyond a critical point.

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Fig 3. Analysis of rupture time (t_rup) of DOPG/DOPC/GrA-GUVs at different GrA% under σ_e = 8 mN/m.

(A–C) Stochastic rupture behavior of many ‘single GUVs’ in one independent experiment at (A) 0% GrA, (B) 0.1% GrA, and (C) 3% GrA. The x-axis represents the GUV label number (m). (D) Probability of rupture (P_rup) as a function of GrA%, showing an initial decrease followed by an increase with higher GrA%.

https://doi.org/10.1371/journal.pone.0338817.g003

3.3. Rate constant of rupture in DOPG/DOPC/GrA-GUVs with varying GrA% at fixed membrane tension

To quantify the rupture kinetics of GUVs at different GrA% while maintaining a constant membrane tension (σ_e), we analyzed the time-dependent fraction of intact vesicles (P_intact) that remained unruptured throughout the observation period. This fraction represents the fraction of GUVs that retained their structure over time and is mathematically expressed as:

(3)

where P_rup denotes the cumulative probability of rupture at a given time t. For instance, if a total of 18 GUVs were examined at σ_e = 8 mN/m, and 9 GUVs ruptured within 60 s, the corresponding P_intact would be: P_intact = 1 − P_rup = 1 − 9/18 = 0.5. Fig 4(A) illustrates the experimental time course of P_intact for different GrA% at 8 mN/m. The data reveal that the decay in P_intact varies as GrA% increases from 0% to 5% in the membrane, suggesting a GrA-dependent rupture process. The decay behavior follows a single-exponential function, given by:

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Fig 4. Rupture kinetics of DOPG/DOPC/GrA-GUVs at different GrA% under σ_e = 8 mN/m.

(A) Time-dependent fraction of intact GUVs (P_intact) for 0, 0.01, 0.05, and 5% GrA, showing the exponential decay behavior. The coefficient of determination (R²) was evaluated for the goodness of fit shown in (A). The values of R² were obtained 0.90, 0.91, 0.91, and 0.79 for 0, 0.01, 0.05, and 5% GrA, respectively. (B) GrA%-dependent variation in k_r, highlighting a non-monotonic trend in rupture susceptibility. The error bars in (B) represent the standard error of the mean rate constants derived from 3–4 independent experiments for each GrA%.

https://doi.org/10.1371/journal.pone.0338817.g004

(4)

where t represents the time duration for which the membrane tension is applied. The experimentally fitted decay curves allowed for the determination of the rupture rate constant (k_r) at different GrA%. For a single typical experiment, the extracted values of k_r for 0%, 0.01%, 0.05%, and 5% GrA were 24.3 × 10 ⁻ ² s ⁻ ¹, 2.8 × 10 ⁻ ² s ⁻ ¹, 1.9 × 10 ⁻ ² s ⁻ ¹, and 11.5 × 10 ⁻ ² s ⁻ ¹, respectively (Fig 4A). Fig 4(A) illustrates the experimental time course of P_intact for different GrA% at 8 mN/m. The time dependent P_intact for 0.1, 1, and 3% GrA is provided in the Supporting Information (S1 File). To ensure the robustness of our findings, multiple independent trials were conducted. The averaged values of k_r obtained for 0, 0.01, 0.05, 0.1, 1, 3, and 5% GrA at σ_e = 8 mN/m were (22.5 ± 1.40)×10 ⁻ ² s ⁻ ¹, (3.1 ± 0.19)×10 ⁻ ² s ⁻ ¹, (1.8 ± 0.10)×10 ⁻ ² s ⁻ ¹, (2.4 ± 0.14)×10 ⁻ ² s ⁻ ¹, (3.4 ± 0.18)×10 ⁻ ² s ⁻ ¹, (7.2 ± 0.30)×10 ⁻ ² s ⁻ ¹, and (12.5 ± 0.9)×10 ⁻ ² s ⁻ ¹, respectively for N = 12–18 and n = 2–4. Thus, k_r decreases sharply from 22.5 × 10 ⁻ ² s ⁻ ¹ at 0% GrA to a minimum of 1.8 × 10 ⁻ ² s ⁻ ¹ at 0.05% GrA, before rising again to 12.5 × 10 ⁻ ² s ⁻ ¹ at 5% GrA, demonstrating a clear nonmonotonic dependence on GrA content. Thus, the k_r values reveal a nonlinear dependence on GrA%. Initially, the rupture rate constant decreases as GrA content increases, reaching a minimum at 0.05% GrA. However, beyond this point, a further increase in GrA content leads to a progressive increase in k_r, indicating an enhanced susceptibility of the vesicle membrane to rupture (Fig 4B). These findings suggest that at lower GrA%, the membrane peptide may stabilize the membrane, reducing rupture likelihood. However, at higher contents, the presence of GrA may facilitate membrane destabilization, possibly by altering bilayer mechanical properties or increasing membrane permeability, thus accelerating rupture kinetics.

3.4. Rate constant of rupture in DOPG/DOPC/GrA-GUVs under varying GrA% and membrane tensions

This section presents the analysis of membrane tension (σ_e)-induced rupture in DOPG/DOPC/GrA-GUVs under varying GrA% and membrane tensions. The results are summarized in Fig 5. The same experimental approach described in Section 3.3 was employed to evaluate the rupture rate constant (k_r) for varying GrA% and different values of σ_e. The mean values of k_r for DOPG/DOPC/GrA-GUVs are displayed in Fig 5, illustrating a clear increase in k_r with higher electric tension across all GrA%. Moreover, at a constant σ_e, the presence of GrA significantly affects the rupture kinetics of vesicles, suggesting that GrA incorporation alters membrane stability and influences the rupture process. The trend shows that k_r increases as σ_e rises across all GrA%. At a fixed σ_e, k_r exhibits a biphasic dependence on GrA%, initially decreasing with lower GrA% and then increasing at higher GrA levels. Error bars represent standard errors, indicating variations from multiple independent measurements. As shown in Fig 5, the rupture rate constant (k_r) increases with higher membrane tension (σ_e) because elevated tension lowers the energy barrier for pore formation, making it more likely for prepores to expand into irreversible transmembrane pores. Physically, higher σ_e contributes an additional destabilizing term in the pore free energy, which accelerates the rupture process.

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Fig 5. Rate constant of rupture of DOPG/DOPC/GrA-GUVs at different GrA% and electric tensions.

Different symbols indicate distinct GrA% in the membranes. Error bars represent standard deviations.

https://doi.org/10.1371/journal.pone.0338817.g005

3.5. Estimation of pore-edge tension (Γ) in DOPG/DOPC/GrA-GUVs under different GrA%

Lipid bilayers, composed of amphiphilic lipid molecules, continuously undergo spontaneous fluctuations in lateral packing density. These fluctuations create localized regions of lower lipid density, often referred to as prepores or transient density rarefactions [35,49]. When subjected to an external electric field (E), the membrane experiences an induced lateral tension (σ_e), which promotes pore formation. Additionally, thermal energy contributes to fluctuations in lipid density, leading to localized condensation and expansion within the bilayer [50]. If a rarefied region surpasses a critical radius (r_c), it evolves into a prepore with a characteristic radius (r). When r < r_c, the prepore rapidly closes. Conversely, when r ≥ r_c, the prepore transitions into a transmembrane pore, eventually leading to vesicle rupture. These dynamic events, including the transition from prepore to full membrane rupture, are schematically illustrated in Fig 6. Vesicle rupture occurs within ~1 s as the radius of the prepore expands indefinitely. It refers to the timescale of the irreversible transition from a critical prepore to full membrane rupture under the applied membrane tension. Specifically, once a prepore reaches the critical radius r_c, it becomes energetically favorable for the pore to expand without bound, leading to vesicle rupture. The process is extremely rapid, occurring on the order of ~1 s, and does not imply that the pore remains open for 1 s. Instead, this duration reflects the transient period between the prepore surpassing r_c (critical radius), and the complete collapse of the vesicle.

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Fig 6. The energy landscape of a system undergoing conformational changes in the process of pore formation.

This consists of a prepore region and the rupture region. The curve illustrates the transition from a stable prepore state to an unstable pore state at the energy barrier U_b, followed by progression toward membrane rupture. The critical pore radius r_c marks the transition point between reversible pore formation and irreversible rupture.

https://doi.org/10.1371/journal.pone.0338817.g006

The free energy associated with a prepore, U(r, σ_e), consists of two opposing terms: (1) A destabilizing term (-πr²σ_e), which promotes pore expansion by reducing the energy barrier. (2) A stabilizing term (2πrΓ), which resists pore expansion and accounts for the pore-edge tension (Γ), defined as the free energy per unit length of the prepore boundary. Following classical pore formation theory, the free energy expression for a prepore is given by [51]:

(5)

where B represents the component of membrane tension-induced by electrostatic interaction due to membrane surface charge. Based on prior findings [51], B is estimated to be 1.76 mN/m, as the surface charge density and ionic conditions of DOPG/DOPC/GrA-GUVs in buffer match those of DOPG/DOPC (40/60)-GUVs. The activation energy barrier (U_b) for pore formation corresponds to the maximum free energy value at r = r_c, expressed as [51]:

(6)

From Eq. (6), the Arrhenius relationship for the rate constant (k_r) can be derived as [52]:

(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)

Experimental data for lnk_r plotted against 1/(σ_e+ B) for different GrA% were fitted to Eq. (8), as shown in Fig 7. The best-fit analysis provided the estimated values of pore-edge tension (Γ) for different GrA%: Γ = 9.6 ± 0.5, 5.6 ± 0.3, 3.4 ± 0.2, 4.5 ± 0.2, 6.5 ± 0.3, 6.3 ± 0.3, 6.8 ± 0.3 pN for 0, 0.01, 0.05, 0.1, 1, 3, and 5% GrA, respectively. These values align well with previous results obtained for DOPG/DOPC (40/60)-GUVs in buffer and are comparable to those reported for DOPG/DOPC/GrA (40/59.99/0.01)-GUVs [53].

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Fig 7. Dependence of lnk_r on 1/(σ_e + B) for DOPG/DOPC/GrA-GUVs at various GrA%.

Each symbol represents a different GrA%, as indicated in the legend. The solid lines represent best-fit theoretical curves based on Eq (8), demonstrating the relationship between membrane tension and rupture kinetics across different GrA conditions.

https://doi.org/10.1371/journal.pone.0338817.g007

3.6. Impact of GrA% on rupture kinetics and membrane stability

Table 1 summarizes the dependence of key parameters—including the rate constant of rupture, probability of rupture, and pore-edge tension—on the mole fraction of GrA in the membrane under σ_e = 8 mN/m. The data reveal a biphasic trend in the variation of these parameters. At lower GrA contents (0–0.05%), a decrease in rate constant, probability of rupture, and pore-edge tension suggests an increase in membrane mechanical stability. This is likely due to GrA-induced changes in lipid packing and lateral interactions, leading to a more rigid bilayer. However, between 0.05%

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Table 1. Rate constant, probability of rupture, and pore-edge tension in DOPG/DOPC/GrA-GUVs with varying GrA% under σ_e = 8 mN/m.

https://doi.org/10.1371/journal.pone.0338817.t001

and 1% GrA, these parameters mostly start to rise again, indicating a reduction in membrane stability. This softening effect at higher GrA contents may result from various physical factors, including excessive ion channel formation, which disrupts lipid organization, increases bilayer fluidity, and weakens membrane integrity.

4.1. Mechanistic insights into electric field-induced pore formation (rupture occurred due to pore formation) in DOPG / DOPC / GrA - GUVs by varying GrA %

The present study elucidates the impact of GrA incorporation into lipid bilayer on the electric field-induced rupture kinetics of DOPG/DOPC/GrA-GUVs under physiological conditions. The experimental results consistently demonstrate a non-monotonic dependence of rupture susceptibility on GrA%, reflecting complex biophysical interactions between membrane mechanics, peptide-induced perturbations, and stochastic pore formation processes. The electric field induces lateral membrane tension (σₑ), modulating the free energy landscape of the bilayer and promoting pore nucleation and growth [35]. The observed rupture behavior as a function of GrA content reveals a biphasic trend: (1) At lower GrA contents (0–0.05%), a substantial reduction in rupture rate constant (k_r) and rupture probability (P_rup) was observed. This suggests that trace amounts of GrA stabilize the membrane, possibly by: enhancing lipid packing via lateral ordering effects [54], altering membrane compressibility, and inhibiting pore expansion. At higher GrA contents (0.05–5%), k_r and P_rup increase gradually. This could result from: GrA-induced thinning of the membrane and increased permeability, enhanced dielectric breakdown susceptibility due to ion channel formation, increased curvature stress or lateral heterogeneity, promoting pore nucleation [55,56]. This non-monotonic response underscores a critical concentration threshold beyond which GrA compromises membrane integrity rather than reinforcing it.

To describe the GrA-dependent pore-edge tension Γ(ϕ), we now introduce the mole fraction of GrA in the bilayer (ϕ) which is defined as the ratio of mole number of GrA in the bilayer to the sum of mole number of phospholipids and mole number of GrA in the membrane. The biphasic behavior suggests a non-monotonic dependence of Γ on GrA content in membrane as follows:

(9)

where Γ₀ is the pore-edge tension of the pure lipid bilayer in the absence of GrA, a is coefficient representing initial membrane stiffening due to GrA (ordering effect), and b is the coefficient representing membrane softening or curvature induction at high ϕ. This parabolic dependence captures the experimental trend: pore edge tension decreases initially, reaches a minimum, and then increases with further GrA enrichment. In Eq. (9) the quadratic term was chosen because our experimental results show that Γ(ϕ) decreases with increasing ϕ up to a certain GrA mole fraction, after which it increases again, suggesting a competition between two mechanisms: (1) Destabilization at low–moderate ϕ due to lipid disordering and hydrophilic exposure at the rim. (2) Re-stabilization at higher ϕ due to possible GrA aggregation, formation of ordered rim-associated peptide domains, or partial shielding of rim hydrophobic exposure.

Substituting Γ(ϕ) into the energy barrier equation (Eq. 6) and then into the rupture rate equation (Eq. 7), we obtain the rupture rate constant as a function of GrA content as follows:

(10)

This equation explicitly links GrA content with rupture rate and accounts for the biphasic kinetic profile observed experimentally (described in results section). This model integrates the membrane mechanics framework with molecular-level interactions induced by GrA incorporation. At lower GrA levels, aϕ dominates, lowering Γ and thus the rupture kinetics, consistent with GrA-induced membrane thinning, hydrophobic mismatch, and increased curvature propensity. As ϕ increases further, the − bϕ² term becomes significant, capturing a stabilizing effect—possibly due to GrA clustering, bilayer stiffening, or formation of more ordered domains. This leads to increase Γ and rate constant. The resulting non-monotonic rupture rate reflects the balance between line tension reduction and steric saturation effects, providing a theoretical explanation for the biphasic kinetics observed in the experiments. This behavior is analogous to previous studies of peptide-lipid interactions where membrane-active agents modulate bilayer rupture through combined mechanical and thermodynamic influences [54–56].

It should be noted here, under classical pore nucleation theory, a decrease in pore-edge tension (Γ) is generally expected to lower the energy barrier for pore formation and hence increase the rupture rate constant (k_r). However, our data for low GrA mole fractions (0–0.05%) suggest that additional factors influence membrane rupture in this regime. At very low GrA contents, we hypothesize that GrA incorporation induces subtle changes in lipid packing and hydration at the pore rim, which could increase local bending rigidity (κ) and/or reduce the effective line tension for pore expansion despite a nominal decrease in the measured Γ. These changes may also alter the initial defect formation probability, such that the nucleation step becomes rate-limiting rather than pore growth. In other words, the decrease in Γ measured under steady conditions may not directly translate into a higher dynamic rupture probability if the pore nucleation barrier is dominated by local lipid-peptide interactions at these low peptide densities. A related possibility is that the lower Γ reflects an average property of the bilayer under tension, but the actual rupture pathway at low GrA content may require cooperative rearrangements of lipids and peptides that are kinetically slower. This could explain the observed decrease in k_r and P_rup despite reduced Γ.

Fig 8 illustrates a conceptual model for the integration of GrA into lipid bilayers and the hypothesized transition to toroidal pore formation under electric stress. This schematic underpins several mechanistic interpretations relevant to the non-monotonic rupture kinetics observed in our experiments. The bilayer scheme shows GrA molecules existing as monomers and dimers embedded within the bilayer. GrA dimers approximately span the bilayer thickness to form cation-selective channels [55], facilitating ion transport. At low molar fractions (0–0.05%), GrA insertion is thought to stabilize the bilayer by promoting lateral ordering and suppressing fluctuations, thereby increasing the energetic barrier for spontaneous pore formation. At higher GrA fractions (0.05–5%), the increased density of GrA dimers may lead to local curvature stress, membrane thinning, and reduced dielectric thickness, which collectively predispose the membrane to electroporation-induced rupture. This is supported by the report that elevated GrA concentrations disrupt lipid packing and increase membrane susceptibility to destabilization [56].

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Fig 8. Schematic representation of GrA incorporation and electromechanical response of the lipid bilayer under an applied electric field.

GrA monomers insert perpendicularly into each lipid leaflet and can dimerize across the bilayer to form ion-conducting channels spanning the membrane. Upon exposure to an external electric field, electric tension (σₑ) acts laterally on the bilayer, promoting local deformation and pore initiation. The balance between the applied σₑ and intrinsic line tension (Γ) governs the stability of the pore edge. Depending on the GrA content and field strength, these perturbations can facilitate membrane thinning and transient pore formation, providing a mechanistic basis for electroporation behavior in peptide-doped membranes.

https://doi.org/10.1371/journal.pone.0338817.g008

The electric field-induced tension and pore nucleation are illustrated. The thermodynamic free energy of a pre-pore is given by eq (5). As GrA content increases, its influence on Γ becomes non-trivial. Our estimated values of Γ from lnk_r versus 1/(σ_e + B) analysis suggest that GrA initially enhances Γ (via membrane ordering), then reduces it beyond a threshold, facilitating pore growth and rupture. Toroidal pore (shown in Fig 8) differs from classical hydrophobic pores by having lipid headgroups lining the pore wall, stabilizing the high-curvature geometry [57]. In the case of GrA-induced pore formation, the toroidal pore configuration is energetically favorable because the lipid headgroups bend inward to line the pore, reducing the exposure of hydrophobic tails to water and thereby lowering the overall free energy.

GrA has been proposed to facilitate such curvature transitions, especially at high contents. The local hydrophobic mismatch and membrane thinning can promote elastic deformations that favor toroidal over cylindrical pore structures [58]. This mechanistic insight aligns with our observation that higher GrA fractions increase rupture probability and rate constants, possibly due to toroidal pore nucleation at GrA-rich microdomains. At higher GrA content, formation of toroidal pores becomes favorable due to enhanced membrane curvature stress and local thinning. The bending energy per unit area of such a curved structure is given by the classical Helfrich bending energy model [59]:

(11)

where κ is the bending rigidity of the membrane, C is the actual local curvature of the membrane, C₀ is the spontaneous curvature induced by embedded molecules like GrA [59–61]. GrA, due to its asymmetric insertion, hydrophobic mismatch, or local perturbation of lipid packing, can increase C₀ in specific domains, thereby reducing the local bending energy and promoting toroidal pore formation [60–62]. The presence of GrA can locally modulate membrane curvature and decrease bending rigidity, facilitating the formation of these high-curvature toroidal pores. Consequently, the local bending energy contribution stabilizes the pore structure, making it more favorable than a classical hydrophobic pore under similar tension. However, an increase in the spontaneous curvature (C₀) may not universally lead to a reduction in local bending energy; the outcome depends on the relationship between C (the actual curvature of the membrane) and C₀, as described by the Helfrich bending energy model. Specifically, when C is close to C₀, the bending energy is minimized, facilitating the formation of curved structures such as toroidal pores. In contrast, if the induced C₀ is far from the prevailing membrane curvature, the bending energy may increase instead. In the context of GrA, its asymmetric insertion, hydrophobic mismatch, and local lipid packing perturbations can induce local C₀ that is comparable to the curvature required for pore formation, thereby lowering the energetic barrier for these events.

In lipid bilayer enriched with GrA, the membrane becomes softer and more prone to curvature instabilities. When with where ϕ is the mole fraction of GrA in membrane, the membrane curvature matches the induced spontaneous curvature, thereby minimizing the energy cost of forming highly curved structures like toroidal pores. These GrA-rich domains thus serve as nucleation hotspots, explaining the observed increase in rupture probability at higher GrA% [63]. The hypothesis presented in Fig. (8) provides a compelling framework for understanding the biphasic effects of GrA on electroporation. At lower contents, GrA acts as a membrane stabilizer, while at higher mole fraction, it becomes a destabilizing agent promoting curvature-driven defects and toroidal pore formation. This model reconciles the observed kinetic trends with molecular-level phenomena and extends previous findings on GrA-membrane interactions.

4.2. Biophysical implications and outlook

Our results provide key insights into how membrane-active peptides such as GrA modulate lipid membrane stability under electric stress. This dual modulation—stabilization at low mole fractions and destabilization at higher concentrations—has several important implications: (i) Optimizing electroporation-based drug delivery: Understanding the concentration-dependent effects of GrA can inform the design of liposome or vesicle carriers that leverage transient membrane permeabilization for controlled cargo release. (ii) Peptide-induced cytotoxicity: The mechanistic insights into GrA’s influence on membrane rupture may help interpret its role in antibiotic activity, channel formation, and selective cytotoxic effects. (iii) Designing synthetic vesicles and vesicle engineering: Our findings offer guidance for engineering vesicles with tunable mechanical robustness and controlled susceptibility to rupture, which is relevant for biomimetic systems and synthetic biology applications. Future studies combining continuum mechanics modeling and molecular dynamics simulations will be valuable to dissect the molecular underpinnings of GrA’s biphasic effects, offering predictive capabilities for peptide-lipid interactions under stress. While the present DOPG/DOPC system provides a controlled platform to understand the effect of GrA, future studies incorporating more complex lipid and protein compositions will be essential to capture the full biophysical diversity of cell membranes relevant to IRE-based cancer therapies.