Figure 1

Tension vs the ratio between the real area of the vesicle at zero tension, $N{a}_0$, and the apparent area of the vesicle, $A_p$, as deduced from Eq. (8). The parameters are given in Table . The equation is drawn for $A_p=4\pi$ ${\left(30\mu \mathrm{m}\right)}^2$ (solid line) and $A_p=4\pi$ ${\left(8\mu \mathrm{m}\right)}^2$ (dotted line, distinct from the solid line only for $\sigma <{10}^{-8}\mathrm{N}∕\mathrm{m}$). Tension is a function of $N$ and $A_p$ but depends only of $N∕A_p$ provided that $\sigma ∕k_{\mathrm{courb}}⪢{\pi }^2∕A_p$.Reuse & Permissions

Figure 2

Evolution of the radius of a vesicle under constant illumination. This radius decreases by 40% in $7\min$, which corresponds to the loss of about $2∕3$ of the vesicle surface before its bursting. At first, the solubilization is quick $(\tau =215\mathrm{s})$ and a pore is stabilized for $90\mathrm{s}$ (Stage 1). Then, the solubilization becomes slower $(\tau =715\mathrm{s})$ and a cascade of short-living transient pores is observed (Stage 2). $\tau$ is obtained by the exponentially decreasing fits of the vesicle radius decay during each stage 1 (solid line for stage 1 and dotted line for stage 2). ▵: measured pore radius, symbols are linked when they correspond to a single pore that remains open. ◻: measured vesicle radius.Reuse & Permissions

Figure 3

Fluorescence microscopy image of a giant vesicle exhibiting a long-living transient pore. The bar represents $10\mu \mathrm{m}$ and the pore remained open for more than $80\mathrm{s}$.Reuse & Permissions

Figure 4

Cascade of pores on a single vesicle. Each pore (indicated by a white arrow) opens and reseals after less than $2\mathrm{s}$. Image 3 shows the closing of the pore of image 2. The bar represents $20\mu \mathrm{m}$.Reuse & Permissions

Figure 5

Statistical studies made over 141 pores. (a) pore duration, (b) correlation between the duration of the pore and its rank in a succession of pores on a single vesicleReuse & Permissions

Figure 6

Leakage of a vesicle during the formation of a long-lived pore. A small vesicle (indicated by a white arrow) is expelled through the pore and allows measuring the leaking velocity. The bar represents $20\mu \mathrm{m}$.Reuse & Permissions

Figure 7

Leakage of numerous large vesicles inside a bigger one, which finally reseals. The bar represents $20\mu \mathrm{m}$.Reuse & Permissions

Figure 8

Simulation of the pore opening and closing. The line tension is set to $\zeta =3\mathrm{pN}$. For all simulations, we decided not to model the energy barrier for the nucleation of a nanometric hydrophilic pore (Ref. 32) because poorly controlled defects in the membrane can help overcome this barrier (Ref. 25). For this reason, a minimal pore radius of $2\mathrm{nm}$ was maintained in the simulations. A pore expands as soon as it reaches a minimum radius $r_{\min }$ obtained for $\sigma =\zeta ∕r_{\min }$. For $\zeta =1–10\mathrm{pN}$, a nanometric pore expands for $\sigma =0.5-5\mathrm{mN}∕\mathrm{m}$, which is close to the measured rupture surface tension for DOPC bilayers (Ref. 22). (a): Strong solubilization regime (characteristic solubilization time $\tau =60\mathrm{s}$). (a1): Evolution of the radius of the vesicle (dotted line) and pore (solid line): a long-lived pore remains open and its size is above optical resolution for $100\mathrm{s}$. (a2): Evolution of the surface tension in time: the solubilization causes an increase of the surface tension until it reaches the rupture tension. The tension is then relaxed in few milliseconds when the pore opens and the internal medium leaks out. The leak outflow becomes slow and the solubilization rate is high enough to compete with it and prevents the pore’s closing for tens of seconds. (b): Slow solubilization regime (characteristic solubilization time $\tau =800\mathrm{s}$). (b1): Evolution of the radius of the vesicle (dotted line) and pore (solid line): a cascade of short-living transient pores is predicted. (b2): Evolution of the surface tension in time: a new short-lived pore opens as soon as the tension reaches a threshold values close to the rupture surface tension value of a DOPC bilayer.Reuse & Permissions

Figure 9

Correlation between the solubilization rate and the regime of pore that is observed. ▵ corresponds to experiments in which a cascade of short-lived pores is observed. ◻ corresponds to experiments in which a single long-lived pore is observed. The position of the symbols on the time axis corresponds to the characteristic solubilization time $\tau$ deduced from a decreasing exponential fit of the measured area of the vesicle.Reuse & Permissions

Figure 10

Comparison between our model’s predictions and an experiment. The line tension is set to $\zeta =3\mathrm{pN}$. The best match between the vesicle radius evolution of the vesicle from our experiment and our simulation [Eq. (16)] is obtained for $t_1=60\mathrm{s}$, $t_2=855\mathrm{s}$, $p_1=0.41$, and $p_2=0.59$. In that case our simulation predicts the succession of a long-lived pore and a cascade of transient pores. 엯: measured pore radius, symbols are linked when they correspond to a single pore that remains open. ▵: measured vesicle radius. Dotted line: computed vesicle radius. Solid line: computed pore radius.Reuse & Permissions

Figure 11

Force radius time derivative $f^{*}(r_{\text{pore}},n,R_{\mathrm{ves}},\zeta )$ as a function of $r_{\text{pore}}$ for various $n$ with $R_{\mathrm{ves}}=30\mu \mathrm{m}$ and $\zeta =3\mathrm{pN}$. For $n>n_c=1.0502$, $f^{*}(r_{\text{pore}},n,R_{\mathrm{ves}},\zeta )<-0.1\mu \mathrm{m}∕\mathrm{s}$ for all $r_{\text{pore}}$ and no long-lived pore is expected. For $n<n_c$, $f^{*}(r_{\text{pore}},n,R_{\mathrm{ves}},\zeta )=-0.1\mu \mathrm{m}∕\mathrm{s}$ for two $r_{\text{pore}}$ values. The larger corresponds to a stable long-lived pore.Reuse & Permissions

Figure 12

Critical $n_c$ $(n=N{a}_0∕4\pi R_{\mathrm{ves}}^2)$ for $\zeta =3\mathrm{pN}$ (solid line) and $\zeta =7\mathrm{pN}$ (dotted line).Reuse & Permissions