Bleb Nucleation through Membrane Peeling

We study the nucleation of blebs, i.e., protrusions arising from a local detachment of the membrane from the cortex of a cell. Based on a simple model of elastic linkers with force-dependent kinetics, we show that bleb nucleation is governed by membrane peeling. By this mechanism, the growth or shrinkage of a detached membrane patch is completely determined by the linker kinetics, regardless of the energetic cost of the detachment. We predict the critical nucleation radius for membrane peeling and the corresponding effective energy barrier. These may be typically smaller than those predicted by classical nucleation theory, implying a much faster nucleation. We also perform simulations of a continuum stochastic model of membrane-cortex adhesion to obtain the statistics of bleb nucleation times as a function of the stress on the membrane. The determinant role of membrane peeling changes our understanding of bleb nucleation and opens new directions in the study of blebs.

Figure 1

Membrane peeling from the cortex. (a) Schematics of the adhesion between the membrane and the cortex by springlike molecular linkers (zigzag lines). The contact line at $s_c$ connects the unbound membrane patch (left) to the adhered membrane (right), forming a contact angle $\theta$. (b) Normal force balance at the contact line: Adhesion balances the vertical pulling of the unbound membrane [Eq. (4)]. (c) Geometry of the unbound membrane patch, a spherical cap of radius $R_b=2\gamma /f$, and detached radius $r=R_b\sin \theta$.

Figure 2

Bleb nucleation through membrane peeling. (a) Evolution of a detached membrane patch of radius $r$ subject to a pressure $f$. Membrane-cortex adhesion is healed for $r<r_p$ (red region), and the membrane is peeled from the cortex for $r>r_p$ (green and blue regions) [Eq. (5)]. Classical bleb nucleation would occur only for $r>r_n$ (blue region). (b) Energy of formation of a bleb of detached radius $r$ [Eq. (6)] for some values of the pressure $f$, including a typical equilibrium pressure $f_{\mathrm{eq}}$ (solid lines). Membrane peeling may effectively strongly reduce the nucleation energy barrier (dashed lines). Parameter values are $\gamma =5\times {10}^{-5}\mathrm{N}/\mathrm{m}$ [13], $d=30\mathrm{nm}$, $k=10^{-4}\mathrm{N}/\mathrm{m}$ [14], $\delta =1\mathrm{nm}$ [15], ${\rho }_0={10}^{14}{\mathrm{m}}^{-2}$ [14], and $\chi =10^{-3}$ [20].

Figure 3

Statistics of bleb nucleation times. (a) Snapshot of membrane undulations $\delta u$ from simulations. (b) Probability distribution of bleb nucleation times for two values of the pressure $f$. The long-time tails are fitted by an exponential $P(t_{\mathrm{nuc}})\sim e^{-\nu t_{\mathrm{nuc}}}$. (c) The average bleb nucleation time decreases with pressure on the membrane, and so does the characteristic time scale of the process, $1/\nu$. Only pressures very close to the unbinding transition at $f^{*}$ are explored because of computational time limitations. In addition to those in Fig. 2, parameter values are $\kappa =10^{-19}\mathrm{J}$ [19], ${\eta }_c=10^{-2}\mathrm{Pa}·\mathrm{s}$ [6], $\eta =50\mathrm{Pa}·\mathrm{s}/\mu \mathrm{m}$ [14], $k_{\text{on}}={10}^4{\mathrm{s}}^{-1}$ [20], $L=2\mu \mathrm{m}$, $n=1024$, and $\mathrm{\Delta }t=10^{-2}{k}_{\text{on}}$.