Bending elasticity and thermal fluctuations of lipid membranes. Theoretical and experimental requirements

Thermal fluctuations of giant lipid vesicles have been investigated both theoretically and experimentally. At the theoretical level, the model developed here takes explicitly into account the conservation of vesicle volume and membrane area. Under these conditions, the amplitude of thermal fluctuations depends critically not only on the bending elasticity of the bilayer, but also on the membrane tension and/or hydrostatic pressure difference between the interior and exterior of the vesicle. At the experimental level, the determination of the bending modulus kc first requires the analysis of a large number (several hundred) of vesicle contours to obtain a significant statistics. Secondly, the contribution of the experimental error on the contour coordinates, which results in a white noise on the Fourier amplitudes, must be eliminated, and this can be done by using the angular autocorrelation function of the fluctuations. Finally, the amplitudes of harmonics having short correlation times must be corrected from the effect of the integration time (40 ms) of the video camera, which otherwise leads to an overestimation of kc. All these theoretical and experimental requirements have been considered in the analysis of the thermal fluctuations of 42 giant vesicles composed of egg phosphatidylcholine. The behaviour of this population of vesicles can be accounted for with a bending modulus kc equal to 0.4 - 0.5 x 10-19 J, and extremely low membrane tensions, ranging below 15 × 10-5 mN/m.