Surface tension in bilayer membranes with fixed projected area.

We study the elastic response of bilayer membranes with fixed projected area to both the stretching and shape deformations. A surface tension is associated to each of these deformations. By using model amphiphilic membranes and computer simulations, we are able to observe both the types of deformation, and thus, both the surface tensions, related to each type of deformation, are measured for the same system. These surface tensions are found to assume different values in the same bilayer membrane, in particular, they vanish for different values of the projected area. We introduce a simple theory which relates the two quantities and successfully apply it to the data obtained with computer simulations.