  How long a fluid membrane vesicle stressed with a steady ramp of micropipette
last before rupture? Or conversely, how high the surface tension should be to
rupture a membrane? To answer these challenging questions we have developed a
theoretical framework that allows description and reproduction of Dynamic
Tension Spectroscopy (DTS) observations. The kinetics of the membrane rupture
under ramps of surface tension is described as a combination of initial pore
formation followed by Brownian process of the pore radius crossing the
time-dependent energy barrier. We present the formalism and 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 have studied 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 main
features of the experimental data, particularly, the pore nucleation and pore
size diffusion controlled limits of membrane rupture dynamics. This approach
can also be applied to processes of permeation and pore opening in membranes
(electroporation, membrane disruption by antimicrobial peptides, vesicle
fusion).
