Membrane Buckling Induced by Curved Filaments

We present a novel buckling instability relevant to membrane budding in eukaryotic cells. In this mechanism, curved filaments bind to a lipid bilayer without changing its intrinsic curvature. As more and more filaments adsorb, newly added ones are more and more strained, which destabilizes the flat membrane. We perform a linear stability analysis of filament-dressed membranes and find that the buckling threshold is within reasonable in vivo parameter values. We account for the formation of long tubes previously observed in cells and in purified systems. We study strongly deformed dressed membranes and their bifurcation diagram numerically. Our mechanism could be validated by a simple experiment.

Figure 1

Illustration of the proposed buckling mechanism. Overbent filaments are represented in blue, underbent filaments in red, and the membrane in yellow. Wedges of the membrane were removed for visualization. (a) Curved filaments with an affinity for each other and the membrane form membrane-bound circular arrays. The tension and bending modulus of the membrane tend to stabilize flat arrays. (b) Buckling, on the other hand, allows the binding of more filaments and the relaxation of those already bound to their preferred (yellow) radius. These stabilizing and destabilizing effects balance at the buckling threshold. (c) The formation of long tubes allows the binding of an arbitrarily large number of filaments close to their preferred radius.

Figure 2

Normal modes $z_n(R)$ of the dressed membrane. (a) Spatial structure of the first four normal modes at their respective buckling thresholds for $K=2.5$. (b) Thin black lines: buckling thresholds as a function of $n$, $K$, and $\Sigma$. Thick black line: stability limit of long, cylindrical dressed membrane tubes. Protrusions are obviously more stable at small $\Sigma$, where the destabilizing influence of the filaments overrides the stabilizing effect of the membrane. Therefore, the $n$th normal mode of the flat dressed membrane is linearly unstable for parameter regimes located under the $n$th thin black line and long tubes exist only under the thick black line. Thin cyan (gray) line: parameter regimes compatible with the experimental data of Ref. 7. Symbols are referred to in the main text.

Figure 3

Numerically computed mechanical properties of strongly deformed dressed membranes for $K=2.5$. (a) Parametrization and profiles. (b) Force-extension curves ($L=\ell /u$). (c) Black lines: bifurcation diagram for the $F=0$ problem. Cyan (gray) lines: changes induced by a weak asymmetry of the dressed membrane. In both cases, thick (thin) lines represent stable (unstable) solutions. (d) Activation energy $\Delta \mathcal{F}$ a flat dressed membrane needs to reach the $\ell =+\infty$ buckled solution.