An elastohydrodynamic thin film theory for the onset of compartmentalization of lipid bilayer based model protocells

Vesicles of charged lipid bilayers attached to like-charged surfaces via divalent ions autonomously form daughter vesicles upon removal of the ions from the interface. We hypothesized that the onset of the subcompartment formation may be governed by an elastohydrodynamic instability caused by (1) electrostatic repulsion, (2) attractive van der Waals interactions between the surface and the bilayer, and/or (3) membrane spontaneous curvature, penalized solely by the bending energy of the membrane. To test the three candidates, we have developed an elastohydrodynamic thin film theory that relates the coupling between membrane bending and each of the three mechanisms to the pressure gradients that drive fluid flow underneath the membrane. Our stability analysis rules out the electrostatic effects in the presence of ionic screening and shows that the spontaneous curvature stabilizes a flat interface at the linear order. On the other hand, attractive van der Waals interactions give rise to an instability above a critical wavelength of 250 nm, in agreement with experiments. Our results suggest that molecular van der Waals forces at a range of membrane thickness scale may have played an important role in the formation of lipid membrane based molecular compartments on the early Earth.