To Close or to Collapse: The Role of Charges on Membrane Stability upon Pore Formation

Abstract Resealing of membrane pores is crucial for cell survival. Membrane surface charge and medium composition are studied as defining regulators of membrane stability. Pores are generated by electric field or detergents. Giant vesicles composed of zwitterionic and negatively charged lipids mixed at varying ratios are subjected to a strong electric pulse. Interestingly, charged vesicles appear prone to catastrophic collapse transforming them into tubular structures. The spectrum of destabilization responses includes the generation of long‐living submicroscopic pores and partial vesicle bursting. The origin of these phenomena is related to the membrane edge tension, which governs pore closure. This edge tension significantly decreases as a function of the fraction of charged lipids. Destabilization of charged vesicles upon pore formation is universal—it is also observed with other poration stimuli. Disruption propensity is enhanced for membranes made of lipids with higher degree of unsaturation. It can be reversed by screening membrane charge in the presence of calcium ions. The observed findings in light of theories of stability and curvature generation are interpreted and mechanisms acting in cells to prevent total membrane collapse upon poration are discussed. Enhanced membrane stability is crucial for the success of electroporation‐based technologies for cancer treatment and gene transfer.

The transmembrane potential built during the pulse is given by Ψ( ) = 3 2 |cos | [1 − exp (− )] [1] , where is the vesicle radius, is the field strength, is the tilt angle between the electric field and the surface normal, t is time and = ( 1 + 1 2 ) is the charging time with the membrane capacitance and the conductivities of the solutions inside and outside the vesicle, and , respectively. Above the electroporation threshold, the transmembrane potential Ψ cannot be further increased and the membrane becomes permeable to ions at a certain critical transmembrane potential, Ψ  1V; see e.g. [2] . In the experimental conditions explored in this work, ≅ 10 S/cm, ≅ 4-300 S/cm (see also Table S1), ≅ 0.01 F/m 2 , the transmembrane potential reaches Ψ for vesicles with radii above 7-10 m. Table S1. Conductivity values of the solutions used. Values were obtained from three individual measurements of each solution from a single batch using a conductivity meter SevenEasy (Mettler Toledo, Switzerland).

Sucrose (200 mM)
10.1 ± 0.2 Glucose (200 mM) 3.9 ± 0.1 Glucose + 1 mM NaCl 177.0 ± 1.   To assess trends in the tube thickness, the tubes were imaged using identical microscope settings and a dye (DPPE-Rh, 0.1 mol%) that displays no curvature preference [3] . No variation in the fluorescence intensity of the vesicle containing different fractions of charged lipids were detected (before and after poration). (A) Images of lipid tubes formed after complete vesicle bursting (burst) or partial vesicle bursting (partial burst) where the tubes remain attached to the mother GUV. The POPG fraction in the membrane varies from 20 to 50 to 100 mol% from left to right. The images show weaker intensity associated with thinner tubes as the PG fraction increases. Scale bars: 5 m. (B) Tube fluorescence intensity profiles from the vertical lines shown in (A). Line profiles were always taken in the same direction to minimize polarization issues. (C) Area-integrated peak intensities measured on tubes formed upon bursting (burst) or still attached to partially burst GUVs for increasing POPG mol%. Each open circle corresponds to a measurement on an individual tube. Measurements were performed on several GUVs per composition (occasionally, multiple measurements from independent tubes from the same GUV). A minimum of 3-4 GUVs per composition were studied. Mean and standard deviation are also shown (red). The decrease in intensity is associated with decreased tube diameter.  Following the protocol in [4] , GUVs were immobilized in 1% (w/v) isotonic agarose gel to slow down pore closure and were exposed to a single DC pulse (

Text S2: Edge tension measurements
Pore dynamics in vesicles follows four well-defined stages; (i) quick opening, (ii) maximum size stage that is relatively stable, (iii) slow closure, limited by leak-out, and (iv) rapid closure as theoretically modeled in [5] . According to this model, the slow closure (third stage) of a circular pore of radius in a GUV of radius , can be directly related to the edge tension through 2 ( ) = −(2 3 ⁄ ) + , where is the medium viscosity ( = 1.133×10 -3 Pa.s for the conditions studied here), is time and is a constant. is assumed roughly constant during pore closure and measured after resealing of the macropore(s). The edge tension is directly calculated from the slope of the linear dependence of 2 ( ) with time, see also Fig. S9. Vesicles with radius deviation larger than 5 % were discarded for

S7
GUVs with resealing pores. The obtained mean edge tension values and standard deviations are given in Table S2. In the case of partial bursting where the vesicle size decreases as the pore closes (data in magenta in Fig. 4), the edge tension was evaluated considering the initial and final vesicle radius and averaged (error bars in Fig. 4 show the corresponding deviations resulting from vesicle size changes). Figure S9. Pore edge tension measurement for negative POPC:POPG (1:1) GUVs. (A, B) Phase contrast snapshots of a GUV before, during and after pore closure, respectively, for typical pore closure (upper row) and partial bursting cases (lower row). The third snapshots in the rows are processed images (same as the second snapshots) used for measuring the pore radius . The processing of the phase contrast images involves background subtraction and binarization as introduced in [6] . (C) Edge tension measurements showing the pore opening and closure and the fit for the slow closure stage (red lines) according to 2 ( ) = −(2 3 ⁄ ) + for typical (blue data) and partial bursting cases (black data). In the graph, the pore size in µm is rescaled by = 1 µm. Pore closure is significantly slowed down for the case of partial bursting. Accordingly, the edge tension extracted from the vesicle with a typical macropore is 17 pN, while the one obtained from the vesicle exhibiting partial bursting is only 7 ± 2 pN.  The energy of a porated vesicle of radius is a sum of the Helfrich and the rim energy: = 2 ∫ ( − ) 2 + ∫ 2 ⁄ + 2 , (S1) where is the membrane bending rigidity, = 1⁄ is the vesicle mean curvature, is the membrane spontaneous curvature, is the Gaussian curvature modulus, is the pore radius and is the edge tension. The integral in Eq. S1 is over the vesicle (nonporated) area = For a pore to have the tendency to expand, as is the case in bursting PG-containing vesicles, the energy of the system should decrease, i.e.
Above we assumed that the vesicle radius remains constant, which for small changes in the pore radius is indeed the case. We see that the Gaussian curvature contribution (second term in Eq. S1) cancels out, which is understandable because the topology of a vesicle with expanding pore is preserved. Equation S2 implies that the edge tension term is dominated by curvature contributions. PG-containing electroformed vesicles exhibit inward tubes [7] with diameter below the resolution of confocal imaging, 2 < 200nm. The associated spontaneous curvature for inward cylindrical tubes is ≡ − 1 2 ⁄ implying that 1⁄ ≪ and can be ignored. The inequality S2 can then be transformed into −2 < 2 ( √1 2 ⁄ − 1 2 ⁄ ) ⁄ . (S3)

S9
Considering that the pore radius reached at the end of the pulse is of the order of 1 µm, i.e., ≪ , the above expression roughly reduces to | | −1 < √2 ⁄ .
(S4) For 50 mol% PG membranes, we have = 23 pN (see data in Fig. 4B) and = 31 kBT [8] . We thus obtain that the diameter of tubes stabilized by spontaneous curvature at which the vesicles tend to burst should be smaller than 105 nm. This result is consistent with the suboptical tube diameters we observe upon poration (Fig. S3). The predicted relatively high spontaneous curvature is plausibly generated by the asymmetric distribution of PG in the membrane resulting from the vesicles preparation method [7] .
As a consistency check, for pure PC membranes where the pores tend to close, the energy of the systems should satisfy the opposite condition ⁄ > 0, i.e. it is energetically unfavorable for the pores to open. These single-component PC membranes are intrinsically symmetric and exhibit zero spontaneous curvature ≈ 0, which from Eq. S2 implies that 2 ⁄ < √( ⁄ ) 2 − 1. Taking for = 40 pN (Fig. 4B) and ≈2.1×10 -19 J [9] , we see that this condition is indeed satisfied.

Supplementary movies
Movie S1. Bursting of a charged GUV upon electroporation observed under phase contrast microscopy. The GUV composed of POPC:POPG (1:1) in sucrose/glucose (in/out) solution was electroporated using a pulse of 3 kV/cm magnitude and 150 s duration. The formed macropore expands, leading to a full collapse of the vesicle, leaving only tubular membrane fragments after bursting. The time stamps correspond to the initial observation time. The GUV was electroporated at time 34 ms. Vesicle diameter is around 25 µm.
Movie S2. Bursting of a charged GUV upon electroporation observed under epifluorescence microscopy. The GUV composed of POPC:POPG (1:1) prepared in sucrose/glucose (in/out) solution and labelled with 0.1 mol% DPPE-Rh was electroporated (3 kV/cm, 150 s). The formed macropore expands by converting the nearly flat membranes into tubular lipids structures. The time stamps correspond to the initial observation time. The GUV was electroporated at time 17 ms. Vesicle diameter is around 30 µm. The much smaller vesicle seen at the end of the movie is another vesicle (already present in the chamber), which is not associated with the main GUV and which is not in focus in the beginning of the movie.
Movie S3. Bursting of a charged GUV upon electroporation observed under confocal microscopy. The GUV composed of POPC:POPG (1:1), labelled with 0.5 mol% DPPE-NBD (green), prepared in sucrose/glucose (in/out) solution and encapsulating 2.5 M SRB (red) was electroporated (3 kV/cm, 150 s). The GUV contains a couple of smaller vesicles inside. Bursting leads to the rapid release of the encapsulated content. These smaller vesicles do not burst because they are shielded by the outer vesicle and are too small for the transmembrane potential to reach the poration threshold (see Text S1). The time stamps correspond to the initial observation time. The GUV was electroporated at time 190 ms. Vesicle diameter is around 30 µm.
Movie S4. Long-lasting macropore in a charged GUV observed under epifluorescence microscopy. The GUV composed of POPC:POPG (1:1) containing 0.1% DPPE-Rh was electroporated (3 kV/cm, 150 s) and the formed macropore remained opened for longer than 2 s. Such a long pore lifetime allowed the release of encapsulated smaller vesicles inside the GUV. Note that the fluorescence around the pore rim is homogenous, suggesting neither enrichment nor depletion of lipids. The time stamps correspond to the initial observation time. The GUV was electroporated at time 60 ms. Vesicle diameter is around 50-60 µm.
Movie S5. Electroporation of a neutral GUV (POPC) labelled with 0.5 mol% NBD-PG and immobilized in 1 wt% agarose. A single DC pulse (4 kV/cm, 8 ms) was applied at time ~1.1 s. The GUV was observed under epifluorescence microscopy. Vesicle size is around 40 µm.
Movie S6. Bursting of a charged GUV, POPC:POPG (1:1), induced by detergent and observed at high temporal resolution under phase contrast microscopy. A concentrated solution of Triton X-100 was added to the chamber (to a final concentration of 1 mM) containing POPC:POPG (1:1) GUVs. The movie is slowed down. The time stamps correspond to the initial observation time. The macropore appears at time 12.5 ms. The expansion of the bursting membrane is very fast and is completed in less than 3 s. Vesicle size is around 50-60 µm.
Movie S7. Bursting of a charged GUV, POPC:POPG (1:1), induced by detergent observed under epifluorescence microscopy. A concentrated solution of Triton X-100 was added to the chamber (to a final concentration of 1 mM) containing POPC:POPG (1:1) GUVs labelled with 0.1 mol% DPPE-Rh. At initial times, Triton X-100 leads to an increase in GUV area (the membranes look floppy). The numbers correspond to the initial observation time. The macropore appears at 3.7 s and leads to vesicle bursting with dynamics identical to that induced by electroporation. At later times, the membrane fragments formed after bursting are solubilized. Vesicle size is around 50-60 µm.
Movie S8. Formation of submicron-sized pores before vesicle bursting. A POPC:POPG (1:1) GUV labelled with 0.5 mol% DPPE-NBD and in the presence of 2.5 M of SRB was incubated with Triton X-100 (1 mM final concentration) and observed under confocal microscopy. The movie is sped up. The vesicle becomes permeable to SRB (at ~ 40 s) before it bursts (at ~3 min). The macropore formation is too fast to be observed with confocal microscopy. Vesicle size is around 30 µm.