MONTE CARLO CALCULATION OF GIANT VESICLE SHAPE FLUCTUATIONS
F. Sevšek1 and G. Gomišček2
Giant phospholipid vesicles form spontaneously in water when a thin film of amphiphilic phospholipid molecules closes due to hydrophobic effect. Their shapes are mainly controlled by the bending elasticity of the membrane. This can be studied experimentally by recording the shape fluctuations of flaccid vesicles. For that purpose a reliable theoretical description of shape fluctuations is essential.
Monte Carlo method was used to determine the thermal shape fluctuations of nearly spherical vesicles. Membrane elastic energy was calculated using spherical harmonics expansion of the vesicle shape deviations from a sphere and retaining only the second order terms. The constraints of constant volume and surface area were treated in two ways: (i) strictly, by considering only the phase space of the allowed shapes and (ii) by adding the appropriate elastic term to the energy. By the Metropolis Monte Carlo method the mean square values of the expansion coefficients were calculated as a function of elastic constants and the number of spherical harmonics terms (lmax).
As expected, for large values of elastic constants, the results of the two approaches were essentially the same. They also agreed well with the predictions of the effective tension approximation and the importance of the value of lmax was demonstrated. The "elastic approach" allowed us to determine the transition from the free fluctuation regime to the constrained one.
The results were used to analyse the experimental data of vesicle shape fluctuations in laminar flow. Here, giant vesicles were attached to a glass substrate and the surrounding liquid was forced to move by hydrostatic pressure difference. The flow velocity served to control the membrane tension. Vesicle shape fluctuations were studied by recording large number of microscope images and analysing the vesicle contours in terms of Fourier coefficients.
1University College of Health Studies, University of Ljubljana, Slovenia
2Institute of Biophysics, Medical Faculty, University of Ljubljana,Slovenia