Rupture of a biomembrane under dynamic surface tension

How long will a fluid membrane vesicle stressed with a steady ramp of micropipette last before rupture? Or conversely, how high should the surface tension be to rupture such a membrane? To answer these challenging questions we developed a theoretical framework that allows for the description and reproduction of dynamic tension spectroscopy (DTS) observations. The kinetics of the membrane rupture under ramps of surface tension is described as a succession of an initial pore formation followed by the Brownian process of the pore radius crossing the time-dependent energy barrier. We present the formalism and a derive (formal) analytical expression of the survival probability describing the fate of the membrane under DTS conditions. Using numerical simulations for the membrane prepared in an initial state with a given distribution of times for pore nucleation, we study the membrane lifetime (or inverse of rupture rate) and distribution of membrane surface tension at rupture as a function of membrane characteristics like pore nucleation rate, the energy barrier to failure, and tension loading rate. It is found that simulations reproduce the main features of DTS experiments, particularly the pore nucleation and pore-size diffusion-controlled limits of membrane rupture dynamics. This approach can be adapted and applied to processes of permeation and pore opening in membranes (electroporation, membrane disruption by antimicrobial peptides, vesicle fusion).