Bending elasticity and dynamical fluctuations of giant lipidic vesicles

Abstract

perimental data [10]. The static analysis of a large number of egg-yolk phosphatidylcholine vesicles led to a bending elastic modulus kc = (0.4-0.5) x 10 -19 J, the corresponding membrane tensions being very low, in every case smaller than 15 x 10 -5 mN/m. We also studied the dynamics of the thermal fluctuations of giant vesicles, following earlier studies [5, 11] and showed [12] that a rigourous and complete analysis of the dynamics of the fluctuations can be performed. Indeed, the space-time autocorrelation function can be expressed as a series of Legendre polynomials whose coefficients are directly related to the time correlation functions of the spherical harmonics derived by Milner and Safran [13]. The experimental space-time autocorrelation function was calculated using about ten thousand contours of a single vesicle. Owing to this very large number of contours which considerably increases the accuracy, the time dependence of the Legendre polynomials coefficients could be evaluated up to the 8 th mode. Furthermore, a mono-exponential decrease was observed versus time with correlation times ranging from 2 to 0.18 s. Finally, these data led to values of the bending modulus and of the membrane tension practically identical to those derived from the static analysis. The time correlation functions of the Fourier amplitudes of the contours were also determined. In this case, as expected, the time dependence was not truly mono-exponential. However, the correlation times of a given mode q could also be extracted, by using a linear combination of the correlation functions of the different Fourier amplitudes. The obtained values were then in very good agreement with those derived from the space-time autocorrelation function. These results clearly demonstrate the validity of the theoretical model of Milner and Safran [13] for the dynamics of fluctuations, which strongly supports their hypothesis that the effect of convective and inertial terms can be neglected to describe the hydrodynamic behaviour of the lipid bilayer.