Effects of osmotic pressure on the irreversible electroporation in giant lipid vesicles

Irreversible electroporation (IRE) is a nonthermal tumor/cell ablation technique in which a series of high-voltage short pulses are used. As a new approach, we aimed to investigate the rupture of giant unilamellar vesicles (GUVs) using the IRE technique under different osmotic pressures (Π), and estimated the membrane tension due to Π. Two categories of GUVs were used in this study. One was prepared with a mixture of dioleoylphosphatidylglycerol (DOPG), dioleoylphosphatidylcholine (DOPC) and cholesterol (chol) for obtaining more biological relevance while other with a mixture of DOPG and DOPC, with specific molar ratios. We determined the rate constant (kp) of rupture of DOPG/DOPC/chol (46/39/15)-GUVs and DOPG/DOPC (40/60)-GUVs induced by constant electric tension (σc) under different Π. The σc dependent kp values were fitted with a theoretical equation, and the corresponding membrane tension (σoseq) at swelling equilibrium under Π was estimated. The estimated membrane tension agreed well with the theoretical calculation within the experimental error. Interestingly, the values of σoseq were almost same for both types of synthesized GUVs under same osmotic pressure. We also examined the sucrose leakage, due to large osmotic pressure-induced pore formation, from the inside of DOPG/DOPC/chol(46/39/15)-GUVs. The estimated membrane tension due to large Π at which sucrose leaked out was very similar to the electric tension at which GUVs were ruptured without Π. We explained the σc and Π induced pore formation in the lipid membranes of GUVs.


Introduction
Lipid vesicles are closed and spherical structures formed by phospholipid bilayers which are used as model of biological cells [1]. When cells/vesicles are transferred into a hypotonic solution, the swelling of cells/vesicles occurs due to osmotic pressure (P). The swelling induces a lateral tension in the membranes of cells/vesicles. Such membrane tension plays an important role in various physiological functions and mechanical properties of bio/lipid membranes [2][3][4]. Different types of responses such as an increase in volume, and leakage of internal contents have been investigated under P using large unilamellar vesicles (LUVs) and giant unilamellar a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 vesicles (GUVs) [5][6][7][8][9][10][11]. The elastic properties of membranes were measured by investigating the changes of volume in presence of P using dynamic light scattering [5,6]. Since the static and dynamic change in size and shape of a 'single GUV' can be visualized using the optical microscope, vesicles with sizes 10 μm or more have been using in various researches [12,13]. When GUVs are transferred to a hypertonic solution, the shrinkage of GUVs occurs. The analysis of the time-dependent decrease in volume of each GUV provides the water permeability of lipid membranes [14,15]. The main advantage to use the GUVs is that any change of a 'single GUV' can be measured independently, while not possible for the case of LUVs as it provides an ensemble average of many small nanometers sized vesicles. Therefore, the size of GUVs provides the opportunity to observe the phenomena occurring at the single individual vesicle.
Irreversible electroporation (IRE) is a cell/tumor ablation technique that uses direct current (DC) pulses of length 100 μs to 1 ms, electric field of magnitude hundreds to thousands of V/ cm, and frequency of around 1.1 kHz (i.e, electrical pulses of width 200 μs are delivered once per 909 μs). The electric field induces lateral tension in the membranes of GUVs, resulting in the permanent permeabilization of the membranes of vesicles [16,17]. If the lateral tension reaches a critical value, pore formation occurs in membranes and subsequently vesicles are ruptured. The permeabilization due to transient pores or transmembrane pores is used for various medical and bioengineering purposes [18][19][20]. The continuous trajectory of pore formation in vesicles under applied tension or electrical stress is described by a theoretical model. The waiting time for the formation of a pore follows a nonmonotonous function of lateral tension in which the waiting time drops from infinity at zero tension to a minimum at any other tensions. On contrary, electric tension causes the waiting time to decrease monotonously [21]. The results of molecular dynamic (MD) simulations show that the kinetics of pore formation follows a linear dependency of activation energy of prepore formation under the applied field [22]. The pore life cycle due to the electric field describes the pore opening, construction and closing. The time of pore opening depends strongly on the gradient of electric field across the membrane interface and that the pore closing time is weakly dependent on the pore-initiating electric field. The pore closing time is much higher than the pore opening time [23]. The formation of a pore starts with the creation of single-file-like water defects penetrating the membranes under electric tension [24]. The metastability of a small hydrophilic pore is investigated by MD simulations, which is due to the compensating of positive and negative curvature effects at the edge of a pore [25]. Therefore, the research on the electric filed-induced pore formation is rapidly growing due to its potential applications in biology, biotechnology and medicine [18,26]. It has been reported that GUVs prepared by hybrid films of agarose and lipids exhibit altered mechanical properties [27]. The presence of agarose meshwork inside the GUVs prevents the creation of pores in response to electric pulses and keep the membrane highly permeable. Incorporation of membrane proteins and cytoskeleton network in GUVs further improve the understanding of these elements in electropermeabilization.
It is well reported that plasma membranes of mammalian cells contain an amount of 20-50% cholesterol [28], which is an important element of lipid rafts involves in signal transduction and endocytosis [29,30]. Since IRE technique is used for the ablation of tumor/cancer cells, it is important to consider the GUVs prepared by lipids and cholesterol for obtaining biological relevance. The presence of cholesterol increases the value of breakdown potential. The greater stability of membranes with cholesterol results in an increase of critical pore radius [31]. Also, the rate of pore formation is much slower for cholesterol containing membranes subjected to the electric field due to the substantial increment of membrane cohesion [32]. An addition of cholesterol increases the electroporation threshold that often links to the rise of the stiffness of bilayer [33]. The effects of cholesterol on the electric tension-induced pore formation is investigated where the line tension of a pore increased with the increase of cholesterol in the membranes [34]. Therefore, it is very important to study the GUVs under osmotic pressure at a more physiologically relevant condition. Here, we investigated the influence of osmotic pressure on the cholesterol containing charged membranes of GUVs along with the cholesterol free charged membranes of GUVs in a buffer containing a physiological concentration of ions. We used GUVs comprising a mixture of three elements: DOPG, DOPC and cholesterol, and also two elements: DOPG and DOPC. The electrostatic interaction due to the surface charges of membranes [35,36] of DOPG/DOPC/chol (46/39/15)-GUVs and DOPG/ DOPC (40/60)-GUVs is comparable.
We investigated the constant electric tension (σ c )-induced rate constant (k p ) of rupture of GUVs under different P. From the analysis of these investigations, the lateral membrane tension (σ oseq ) due to P at swelling equilibrium is evaluated. The experimentally estimated value of membrane tension is compared with the value calculated theoretically. The values of membrane tension of DOPG/DOPC/chol (46/39/15)-GUVs and DOPG/DOPC (40/60)-GUVs at a particular P is found almost same. We also investigated the large osmotic pressure-induced sucrose leakage from the inside of DOPG/DOPC/chol (46/39/15)-GUVs. The sucrose leakage occurred owing to the formation of pores in the membranes of vesicles. Finally, we explained the σ c and P induced pore formation in GUVs.

Preparation of GUVs
DOPG/DOPC/chol (46/39/15)-GUVs (46/39/15 indicates molar ratio) and DOPG/DOPC (40/ 60)-GUVs were prepared in a buffer (10 mM PIPES, 150 mM NaCl, pH 7.0, 1 mM EGTA) containing 100 mM sucrose using the well-known natural swelling method [37,38]. The surface charge density of DOPG/DOPC (40/60)-GUVs is O PG ¼ eX a DOPG = -0.10 Cm -2 where, X (= 0.40) is the DOPG molar fraction in membranes, e is the electronic charge and a DOPG (= 72.5 Å 2 /molecule) is the cross sectional area of DOPG [39]. After the addition of cholesterol, the membranes become condensed [40][41][42][43]. Hence, the value of a DOPG is about 50 Å 2 /molecule for 15 mole% cholesterol [44,45]. The cross sectional area of cholesterol, a ch , is about half of a DOPG i.e., 33-38 Å 2 //molecule [41]. Based on these values the surface charge density of DOPG/DOPC/chol (46/39/15) Therefore, the surface charge density of cholesterol containing membrane is slightly higher than the cholesterol free membrane. For preparing DOPG/DOPC/chol (46/39/15)-GUVs, a mixture of 1 mM DOPG, DOPC and cholesterol of amount 200 μL and for DOPG/DOPC (40/60)-GUVs a mixture of 1 mM DOPG and DOPC of amount 200 μL were taken into a 4.5 mL glass vial. The mixture was dried with a mild flow of nitrogen gas for producing a thin and homogeneous film. After that the vial was placed in a vacuum desiccator for overnight. Next, an amount of 20 μL MilliQ water was added into the vial and pre-hydrated for 8 min at 45˚C, and then the sample was incubated for 3 h at 37˚C with the same buffer containing 100 mM sucrose. An amount of 280 μL buffer solution containing various glucose concentrations which were smaller than sucrose concentration was taken into a U-shaped silicon microchamber that was inserted into a slide glass. An amount of 20 μL unpurified GUVs suspension was provided into the solution of microchamber and then waited about 20-25 min for settle down the GUVs suspension into the bottom of microchamber and also for the swelling equilibrium of vesicles in the presence of P. As we used a concentration gradient between sucrose and glucose solution, an osmotic gradient was created between the inside and outside of GUVs. To prevent the strong attraction between the GUVs and the glass surface of slide glass, the chamber was coated using a 0.10% (w/v) BSA dissolved in the same buffer containing same glucose concentrations. The GUVs were visualized using an inverted phase contrast microscope (Olympus IX-73, Japan) with a 20× objective at 25 ± 1˚C (Tokai Hit, Japan). The images of GUVs were recorded using a charge-coupled device camera (Olympus DP22, Japan).

Method of applying constant electric tension on GUVs under osmotic pressure
As mentioned in the preparation section of DOPG/DOPC/chol (46/39/15)-GUVs the sucrose concentration inside the GUVs was 100 mM. We calculated the osmolarity (mOsm/L) from the concentration of sucrose and glucose in mM according to the reported paper [11]. The equations of osmolarity for sucrose and glucose in buffer are defined as y = 1.029C + 292.9 and y = 1.010C + 294.2, respectively, where C is the molar concentration of sucrose or glucose. According to the equation, 100 mM sucrose concentration is equal to 396 mOsm/L. However, at the time of pre-hydration an amount of 20 μL MilliQ water was used. Therefore, the osmolarity of the inside sucrose of GUVs (C 0 in ) was 396×1000/1020 = 388 mOsm/L. Here, we describe the experimental technique on the electric field-induced rupture of vesicles in the presence of different P. A MOSFET based IRE circuit was used for generating direct current (DC) pulses of frequency 1.1 kHz and pulse width 200 μs in which electric signal was controlled with a microcontroller. The detail of the method is described in our reported papers [38,46]. The gold coated electrode was used for applying the electric field on GUVs.
To apply the constant electric tension on GUVs, initially the electric filed (E) was kept at around 320 V/cm and targeted a 'single GUV' located between the electrodes. Next, the value of E increased quickly (~7 s) to a definite level, and this E was kept constant until time 60 s. The experimental set-up for applying the electric field on GUVs under P is illustrated in Fig 1. Due to the application of E on a 'single GUV' with radius R, the internal and external free charges of buffer became polarize as the lipid membranes are impermeable to ions. The accumulation time of free charges is calculated by the Maxwell-Wagner equation [47]. According to the Maxwell stress tensor, accumulation of free charges induces a lateral electric tension in the membranes given by the following equation [47][48][49].
We applied electric field, E = 320-560 V/cm in the experiment. For R = 10 μm and E = 553 V/cm, V m = 0.83 V. The applied electric tension was considered constant as a fixed value of E was applied for the corresponding R. By choosing the appropriate value of E, various constant tensions were applied on GUVs.

Rate constant of tension-induced pore formation in GUVs under osmotic pressure
Under osmotic pressure, the electric field induced a total tension, σ t = σ c + σ oseq , in the membranes of GUVs, where σ c is the tension due to electric field and σ oseq is the tension due to P at swelling equilibrium. Using the mean first passage time approach the rate constant (k p ) of tension-induced pore formation in the membranes of GUVs is determined as follows [55]: where A F is the pre-exponential factor, Γ is the line tension of membrane and B is the electrostatic interaction term due to charges of membrane. The theoretical Eq (3) was used to fit the experimental data on k p vs. σ t for both DOPG/DOPC/chol (46/39/15) and DOPG/DOPC (40/ 60)-GUVs.

Theoretical membrane tension of GUVs in presence of osmotic pressure
The theoretical aspect of membrane tension of GUVs in presence of P is described in our previous paper [10]. Here, we present a brief description of the theory under P. Let us consider a 'single GUV' of initial radius r 0 and the initial osmolarity inside the GUV is C 0 in . The unit of osmolarity (mOsm/L) is the same as mM (mmol/L or mol/m 3 ). If the GUVs are transferred to a hypotonic solution of concentration C out (mOsm/L), P is induced in the GUV, resulting the radius of GUVs increases to Δr eq at swelling equilibrium. The osmolarity difference at initial condition between the inside and the outside of GUV becomes DC 0 ¼ C 0 in À C out and then P = RTΔC 0 , where R is the gas constant and T is the absolute temperature. The membrane tension at swelling equilibrium is defined as follows [10]: where, K A is the area compressibility modulus of the membranes of GUVs. We reported the value of K A = 141 ± 5 mN/m for DOPG/DOPC (40/60)-GUVs [12]. Using the same method (i.e., micropipette aspiration technique), we measured the value of K A = 154 ± 4 mN/m for DOPG/DOPC/chol (46/39/15)-GUVs.

Constant electric tension-induced stochastic rupture of DOPG/DOPC/ chol (46/39/15)-GUVs under different osmotic pressures
We investigated the constant electric tension-induced rupture of GUVs at different osmotic pressures. To apply P, DOPG/DOPC/chol (46/39/15)-GUVs suspension is transferred from an isotonic solution to a hypotonic solution. The initial osmolarity difference between the inside and outside of GUVs governs the values of P. The value of osmolarity of sucrose solution was C 0 in = 388 mOsm/L. An amount of 20 μL GUVs suspension was provided with the same buffer of amount 280 μL containing 76.6 mM glucose concentration. Hence, the outside concentration of DOPG/DOPC/chol (46/39/15)-GUVs was 78 mM, which had osmolarity value C out = 373 mOsm/L. The osmolarity difference between the inside sucrose and the outside glucose concentration of GUVs was ΔC 0 = 388-373 = 15 mOsm/L. After providing the GUVs suspension into the microchamber, it was waited 20-25 min for homogeneous mixing of the solutions and also for the swelling equilibrium of GUVs in the presence of P. At first, we applied a constant electric tension of value σ c = 6.5 mN/m on a 'single DOPG/DOPC/chol (46/39/15)-GUV' for time 60 s. Before applying the electric tension due to the electric field, the GUV had a high contrast in an inverted phase contrast image as shown in Fig 2A(i) due to the difference in refractive indexes of sucrose and glucose solution (i.e., sucrose in the inside of GUVs and glucose in the outside of GUVs). During application of σ c , the spherical-shaped GUV was also intact until the time 13 s. At time 13.6 s, GUV initiated to rupture and at time 14 s GUV was ruptured completely (Fig 2A(i)). Therefore, the spherical structure of GUV was permanently disappeared due to the rupture of vesicle. In our several previous papers, we explained the rupture of GUVs in such a way that at first a nanopore is formed in the membranes whose radius rapidly increases to infinity, leading to complete rupture of GUVs [38,46,56]. The time of pore formation is defined as the time when the vesicles started to rupture.
We performed similar experiments for several 'single DOPG/DOPC/chol (46/39/15)-GUVs' (the number of examined GUVs, n 1 = 15-24). Here, we present only three GUVs. Fig  2A(ii) and 2A(iii) represent the rupture of the 2 nd and 3 rd GUVs, in which the rupture occurs at time 9 s and 21 s, respectively. The starting time of rupture is indicated by asterisk mark ( � ). The rupture of several 'single GUVs' followed stochastic nature, which means that the rupture occurred at different times.
These results clearly indicate that as the external tension decreased from 6.5 to 5.0 mN/m, the probability of rupture became smaller for DOPG/DOPC/chol (46/39/15)-GUVs.

Constant electric tension induced rate constant of rupture in DOPG/ DOPC/chol (46/39/15)-GUVs under different osmotic pressures
To calculate the rate constant of rupture of GUVs induced by constant electric tension, we determined the time-dependent fraction of intact GUVs without rupture among all the examined GUVs, P intact (t). It basically indicates the fraction of GUVs that are still intact after time 't' and is defined as P intact (t) = 1-P pore (t) [57,58]. Fig 3(A) shows the time course of P intact (t) for DOPG/DOPC/chol (46/39/15)-GUVs at σ c = 6.5 (square), 6.0 (triangle) and 5.0 mN/m (circle). As the value of σ c decreases from 6.5 to 5.0 mN/m, the P intact (t) with time is slower. The time-dependent P intact (t) is well fitted by a single-exponential decay function (solid line in Fig 3A): where k p is the rate constant for rupture (i.e., pore formation) and t is the duration of constant electric tension applied to a GUV (tension is started at t = 0). The values of k p were obtained 1.  Fig 3(B). As a control experiment, the σ c dependent k p value at ΔC 0 = 0 mOsm/L (green open square) for DOPG/DOPC/chol (46/39/15)-GUVs is also presented in Fig 3(B). The experimental data of σ c dependent k p for DOPG/DOPC/chol (46/39/15)-GUVs under different osmolarity differences is provided in S1 Table of S1 File. The ΔC 0 dependent membrane tension for DOPG/ DOPC/chol (46/39/15)-GUVs is shown in Fig 3(C). Tables 1 and 2 Fig 4(D) shows the σ c dependent k p values under different ΔC 0 . The value of k p increased with the increase of applied tension for a particular osmotic pressure. The experimental data of σ c dependent P pore (60 s) and σ c dependent k p for DOPG/DOPC (40/60)-GUVs under different osmolarity differences are provided in S2 Table of S1 File. The ΔC 0 dependent membrane tension for DOPG/DOPC

Analysis of constant electric tension-induced rupture of GUVs under different osmotic pressures
Now we analyze the results of Fig 3(B) for estimating the membrane tension (σ oseq ) induced by osmotic pressure at swelling equilibrium. The total membrane tension, σ t = σ c + σ oseq , where the tension σ c was due to the external electric field and the tension σ oseq was due to P. The rate constant of rupture was determined for σ t . Hence, the shifting of the k p vs. σ c curve from the    Table 2). Using this value, we obtained the theoretical curve for k p as a function of σ t (Fig 3B, pink line). Fig 3(C) shows that the experimental σ oseq increases with an increase in ΔC 0 . The ΔC 0 dependent experimentally estimated membrane tension and theoretical tension are provided in Fig 3(C). The experimental data on σ oseq corresponds to the theoretical tension.
The similar procedure was followed for the experimental estimation of σ oseq for DOPG/ DOPC (40/60)-GUVs. Using the relation σ t = σ c + 2.1 mN/m and the same parameter as those used for ΔC 0 = 0, we obtained the theoretical curve for k p as a function of σ t using Eq (3) ( Fig  4D, blue line) under ΔC 0 = 13 mOsm/L, which fitted well to the experimental data. Similarly, using the relation σ t = σ c + 3.5 mN/m and the same parameter as those used for ΔC 0 = 0, we obtained the theoretical curve for k p as a function of σ t using Eq (3) (Fig 4D, red Tables 1 and 2, respectively. Similarly, the theoretical estimation of σ oseq for DOPG/DOPC (40/60)-GUVs under ΔC 0 = 13 and 17 mOsm/L is provided in Tables 3 and 4, respectively. By the comparison of experimental and theoretical values of σ oseq shown in Tables  1-4, it has been considered that these values agree with each other within the experimental error. The error of theoretically estimated σ oseq was calculated based on the errors of ΔC 0 , C 0 in , C out , and K A . The error of osmotic pressure for the solutions of sucrose and glucose was ± 2.8 mOsm/kg. The relative errors in the osmolarity values of C out , C 0 in , ΔC 0 , and K A for ΔC 0 = 13 mOsm/L were estimated 0.0072, 0.0095, 0.43, and 0.035, respectively. The values of ΔC 0 with errors for DOPG/DOPC/chol (46/39/15)-GUVs were ΔC 0 = 15 ± 4 mOsm/L, and ΔC 0 = 19 ± 4 mOsm/L whereas for DOPG/DOPC (40/60)-GUVs they were ΔC 0 = 13 ± 4 mOsm/L, and ΔC 0 = 17 ± 4 mOsm/L.

Comparison of the results of IRE technique with micropipette technique
To compare the electric tension-induced rupture of DOPG/DOPC(40/60)-GUVs to that of mechanical tension-induced rupture of the similar vesicles, it is important to show the results of the estimated membrane tension at different osmotic pressures. The procedure to apply the tension into the vesicles in two different techniques is totally different. In the IRE technique, the tension was applied using the Eq (1) whereas in the micropipette technique, tension was applied using an external force. In the latter case, the induced tension was calculated by the formula, σ = ΔPd/4(1−d/D), where ΔP is the difference in pressure between the exterior and the interior of a micropipette, d is the inner diameter of the micropipette and D is the diameter of the spherical part of the GUV exterior to the micropipette.

Large osmotic pressure-induced leakage of sucrose from GUVs
Here, we investigated the large osmotic pressure-induced sucrose leakage from the inside of DOPG/DOPC/chol (46/39/15)-GUVs. In that case, the concentration gradient was ΔC 0 = 388-359 = 29 mOsm/L. The images of GUVs were taken after 20-25 min of the addition of GUVs suspension into the glucose solution. A phase-contrast image of GUVs under P is shown in Fig 6. In the presence of ΔC 0 , several GUVs labeled by 1, 2 and 3 leaked out sucrose. The sucrose leakage was confirmed by observing the contrast between the inside and outside of GUVs. It is to be noted that a few GUVs were still intact (no sucrose leakage occurred) under this osmolarity difference. The leakage of sucrose can be explained by the way that at first, GUVs were swelled as water molecules passed through the membranes from the outside of vesicles, and then, pores were formed in the membranes of GUVs for releasing the membrane tension in presence of P. The same result was also obtained for several independent experiments (the number of independent experiments was 10). The fraction of GUVs in which sucrose leakage occurred during the first 20-25 min among all the examined GUVs was 0.55 ± 0.04 at ΔC 0 = 29 mOsm/L. The membrane tension at ΔC 0 = 29 mOsm/L was calculated theoretically using Eq (4) which was 8.0 mN/m.

Discussion
We investigated the constant electric tension (σ c )-induced rupture of GUVs under different osmotic pressures, and then estimated the membrane tension (σ oseq ) due to P at swelling equilibrium from the analysis of results. If σ oseq is greater than a critical value, the pore formation occurred in the membranes of GUVs. It is generally considered that the lipid membrane is an ensemble of lipid molecules in which local thermal fluctuation in the lateral density is always existing. The region where the lateral density is lower than their regular one is defined as a local density rarefaction or prepore of radius r [59,60]. Under electric field and osmotic pressure, the total membrane tension σ t = σ c + σ oseq is induced in the membrane. It is to be noted that if P = 0, σ t = σ oseq . If the size of such a rarefaction crosses a critical radius (r c ), the region converts into a prepore of radius, r. If r < r c the prepore closes rapidly, and if r � r c the prepore converts into a transmembrane pore. If r goes to infinite within a very short time (~1 s), GUVs become ruptured. The free energy of a prepore U(r, σ t ) can be expressed as [38,56,57] U(r,σ t ) = 2πrΓ−πr 2 σ t , where Γ is the free energy per unit length of a prepore (i.e., line tension) that is favoring the closure of a prepore. A similar equation of a prepore free energy for IRE technique was used in our previous paper [38] where toroidal structure of a prepore was considered [61,62]. For DOPG/DOPC/chol (46/39/15)-GUVs and DOPG/DOPC (40/60)-GUVs, the free energy of a prepore can be written as, where B is the electrostatic interaction term due to charged membranes [35,56]. At the critical radius of a prepore, r c ¼ G s t þB , the energy barrier of a prepore free energy is expressed as The time-dependent P intact (t) data was fitted with a single-exponential decay function ( Fig  3A), which suggested that the rupture can be considered as an irreversible two-state transition [56,58]. From the fitted curve, we calculated the values of k p , which increased with σ c . On the other hand, the value of activation energy was determined by investigating the constant mechanical tension-induced pore formation [56,58]. The tension-dependent activation energy clearly indicated that the classical theory of pore formation was correct [56,58]. On the basis of classical theory, we explained the σ c induced rupture of GUVs under different P.
It is necessary to judge whether the values of σ oseq and σ c have the same effect for generating the lateral tension on the membranes or not. In the constant electric tension-induced rupture of GUVs (Figs 2-4), both σ oseq and σ c were applied to the GUVs, and hence the total membrane tension of vesicles was σ t = σ c + σ oseq . In the absence of P, the values of k p were obtained for the tensions 7.0, 8.0 and 9.0 mN/m for DOPG/DOPC/chol (46/39/15)-GUVs. When we applied such an osmotic gradient in GUVs which had a critical value of about 7 mN/m (according to Eq 4), rupture of GUVs occurred. In this regard, we investigated the sucrose leakage from the inside of GUVs under large P, in which it was used only σ oseq (i.e., σ t = σ oseq ). In the sucrose leakage experiment, we applied a value of σ oseq = 8.0 mN/m for DOPG/DOPC/ chol (46/39/15)-GUVs. Such investigation confirms the validity of the additive nature of σ c and σ oseq (i.e., σ t = σ c + σ oseq ). If we compared the values of σ t = σ c (green open square in Fig  3B) and those of σ t = σ c + 2.3 (cyan open triangle in Fig 3B) and σ t = σ c + 4.0 (pink open circle in Fig 3B) (Fig 4F). Such an additivity nature of tensions was also used when GUVs were induced by mechanical tension in the micropipette aspiration technique under different osmotic pressures [10,11].
We can reasonably consider that σ oseq induced leakage of sucrose due to the pore formation in membranes of GUVs occurred in a manner similar to σ c induced rupture of GUVs. However, one important thing has to be discussed here. The electric field-induced rupture of vesicles did not follow the similar fashion of σ oseq induced sucrose leakage, although in both cases pore formation was occurred in the membranes. In the case of σ c induced rupture, at first a nanopore was formed in the membranes and its radius became infinity within a very short time in the presence of electric field, and therefore vesicle was ruptured. On the other hand, in the case of σ oseq induced sucrose leakage, nanopores might not go to infinity within a very short time, and therefore, the vesicles became intact and spherical. Such intact with undetectable breaks of GUVs were also observed in the nanoparticles and antimicrobial peptide induced pore formation in the lipid membranes of GUVs [12,63]. The estimated value of the critical radius of pore was 1.2 to 1.8 nm (as shown in Fig 7), which was very similar to that obtained by other investigations [10,11].
During thermal fluctuation of membranes, if the radius of a prepore reaches to critical radius, transmembrane pore is formed, and hence causes a rapid leakage of sucrose from the inside of GUVs due to the Laplace pressure. Therefore, the internal content of GUVs leaked out (Fig 6), and consequently, the membrane tension vanished. It was reported experimentally the dynamics of closing of a large pore created by tension [64][65][66] and the theories of the evolution of a pore induced by tension explained well the results of closing of large pores [67,68]. Hence, the growing of large P-induced pore can be explained by these theories although it could not give any quantitative information for the closing of pore in this investigation. As the sucrose leakage occurred from the inside of GUVs, the phase contrast image of the leaked GUVs was different to that observed of the intact GUVs (Fig 6). The inside intensity of leaked GUVs labeled by 1, 2 and 3 (Fig 6) was less than that of intact GUVs. The similar intensity difference was also observed in nanoparticles-induced pore formation in GUVs [63]. Therefore, it was easy to differentiate the leaked GUVs from intact GUVs after large osmotic pressureinduced pore formation.
These investigations clearly indicated that the cell-size lipid vesicles such as GUVs became weak in the presence of P. The formation of pore in plasma membranes of cells causes cell death, yet outside solute concentrations of cells change easily. To prevent P induced cell death, cells modify their structure by incorporating mechanosensitive channels [4] into their plasma membranes during the development of life. The mechanosensitive channels open when membranes are stretched by P [2,3], and hence, the possibility of cell death became less in the presence of P.

Conclusions
We investigated the effects of electric field-induced rate constant of rupture of DOPG/DOPC/ chol (46/39/15)-GUVs and DOPG/DOPC (40/60)-GUVs under different osmotic pressure. Theoretical equation was fitted to the tension dependent rate constant of rupture of GUVs in the presence of different P. The membrane tension was determined experimentally at swelling equilibrium under different P using electroporation technique, which is a new approach. The estimated value of membrane tension agreed with the theoretical calculation. In the absence of external tension, a large value of osmotic pressure induced sucrose leakage from the inside of DOPG/DOPC/chol (46/39/15)-GUVs due to pore formation in the membranes of vesicles. The tension due to osmotic pressure and electric field determines the electric tension-induced rate constant of rupture of GUVs. The rupture was explained based on the classical theory of tension-induced pore formation in vesicles. These investigations provided quantitative and valuable information on membrane tension under different P, which was important for research of the effects of P on the activities of membrane proteins and membrane active peptides.