What is the surface tension of a lipid bilayer membrane?

In a recent paper in this journal, Chiu et al. (1995) presented a molecular dynamics study of a planar lipid bilayer membrane in water with the explicit incorporation of a surface tension. Parallel to the membrane plane, a negative pressure of-100 atmospheres was applied, derived from the measured surface tension of a monolayer at an air/water interface. The same approach was put forward by Feller et al. (1995). The question as to what is the surface tension of a bilayer membrane goes far back in the literature. To my knowledge, it was first raised by de Gennes and Papoular in 1969 and taken up again in a paper by Brochard et al. (1976). The answer was that bilayer membranes of vesicles or cells (without concentration gradients across the membrane) have zero surface tension, because the free energy should be minimal with respect to the surface area of the membrane. This explained the great fluctuations in the shape of red cell membranes. Independently, the same argument was put forward by Tanford (1979), for membranes without high curvature, and by Israelachvili et al. (1977). The latter authors used this argument to develop a theory for the self-assembly of lipids in micelles or bilayers, either planar or vesicular, which proved to be very useful. Likewise, a theory for the exchange of lipid molecules between a bilayer and a monolayer at the air/water interface was worked out based on the assumption that the surface tension of a bilayer is zero, whereas that of a monolayer is finite (Jaihnig, 1984). The predictions of this theory were in good agreement with experimental results on the equilibrium surface pressure of a monolayer in exchange with vesicle bilayers in the sub-phase (Schindler, 1980). Hence, although the surface tension of a bilayer membrane is not accessible directly, indirect measurements support the notion that it is zero. White (1980) pointed out that the surface area is not necessarily the only variable that may change when a membrane tries to minimize its free energy. The volume of the membrane may also change, so that the free energy must not be minimal with respect to the area, i.e., the surface tension must not vanish. This implies a coupling between the area and the volume, which is weak, however, because a lipid molecule may expand laterally and shrink vertically while keeping the volume constant. In essence, this happens at the lipid phase transition, …