Pulling long tubes from firmly adhered vesicles

We used optical tweezers to measure the force-extension curve for the elongation of nanotubes from adhered giant vesicles. We show that the force increases significantly with the length of the tube, which is drastically different from what is observed when the membrane tension is kept constant, e.g. by pipette aspiration. The absence of any force plateau is quantitatively analysed in the framework of the material model of membranes. In particular, we rationalize a counter-intuitive weaker force rise for long tubes and demonstrate that the measured force-length trace allows us to probe both the entropic regime (characterised by the bending rigidity) and the elastic regime (characterised by the area expansion modulus) of the lipid membrane.