Europhys. Lett., 71 (6), pp. 1015–1021 (2005) DOI: 10.1209/epl/i2005-10173-4 EUROPHYSICS LETTERS 15 September 2005 Pulling long tubes from firmly adhered vesicles D. Cuvelier, N. Chiaruttini, P. Bassereau and P. Nassoy( * ) Laboratoire de Physico-Chimie Curie, UMR 168 (CNRS) Institut Curie - F-75005 Paris, France received 18 March 2005; accepted in final form 15 July 2005 published online 10 August 2005 PACS. 87.14.Cc – Lipids. PACS. 87.15.La – Mechanical properties. PACS. 87.16.Dg – Membranes, bilayers, and vesicles. Abstract. – 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 quantita- tively analysed in the framework of the material model of membranes. In particular, we rational- ize 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. Introduction. – A large variety of cellular processes (such as membranous tails left by migrating cells [1], intracellular trafficking pathway [2], intercellular organelle transport [3]) in- volve the formation of thin tubular structures, known as tethers. Formation of these nanotubes either results from global cell motion in culture dish or is triggered by membrane-anchored molecular motors, which slide along cytoskeletal filaments. Tethers can also be extracted from living cells or synthetic vesicles by the application of an external force to a bead using hydrodynamics flows [4], micropipettes [5], magnetic tweezers [6] or optical traps [7]. Most experimental studies have focused on the static tether force, f 0 , which was first surprisingly observed to be independent of the tube elongation. From a theoretical point of view, the origin of tubular membranes is well understood and the finding of a static force f 0 can be rationalized as follows [8,9]. The free energy of a tube of length L and radius r t , pulled with a force f is the sum of a surface tension term, which acts to reduce the surface area of the tube, a bending rigidity term, which tends to increase the radius of the tube, and the negative mechanical work of the external force. Minimization of the free energy with respect to L and r t yields the equilibrium tether radius and force: r 0 =(κ/2σ) 1/2 , (1) f 0 =2π(2κσ) 1/2 . (2) This dependence of r 0 and f 0 upon σ has been experimentally verified by others [5,6]. Whereas r 0 is usually in the 10–100nm range, and thus too small to be measured optically, f 0 , typically ( * ) E-mail: pierre.nassoy@curie.fr c  EDP Sciences Article published by EDP Sciences and available at http://www.edpsciences.org/epl or http://dx.doi.org/10.1209/epl/i2005-10173-4