= Solution
A <lipid bilayer> self-assembles from <amphiphiles>: hydrophilic head groups face the surrounding <water>, while hydrocarbon tails form a hydrophobic interior. In a fluid membrane, molecules diffuse laterally within each <membrane leaflet>. Closing the bilayer into a vesicle avoids an exposed edge. The interior is a substantial barrier to isolated ions and many polar solutes; membrane proteins provide selective transport pathways in a <cell membrane>.
The <Helfrich energy> describes long-wavelength bending:
$$
F_b=\int\left[\frac{\kappa_b}{2}(2H-C_0)^2+\bar\kappa K\right]dA+\sigma A.
$$
Here $H=(c_1+c_2)/2$ and $K=c_1c_2$ are <mean curvature> and <Gaussian curvature>, $C_0$ is spontaneous curvature, $\kappa_b$ the bending modulus, $\bar\kappa$ the Gaussian-curvature coefficient and $\sigma$ the membrane tension. Bending is comparatively inexpensive, whereas stretching the molecular area strongly is costly. Leaflet asymmetry can favor a nonzero spontaneous curvature.
In <micropipette aspiration>, controlled suction draws part of a large vesicle into a narrow pipette. Pressure and geometry determine membrane tension, and the aspirated length measures apparent area change. At low tension, smoothing thermal undulations supplies much of that area; stronger tension probes actual stretching. Tracking vesicle shape fluctuations provides a complementary estimate of the bending modulus.
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