The mechanical properties of biological membranes play an important role in the structure and the functioning of living organisms. One of the most widely used methods for determination of the bending elasticity modulus of the model lipid membranes (simplified models of the biomembranes with similar mechanical properties) is analysis of the shape fluctuations of the nearly spherical lipid vesicles. A theoretical basis of such an analysis is developed by Milner and Safran. In the present studies we analyze their results using an approach based on the Bogoljubov inequalities and the approximating Hamiltonian method. This approach is in accordance with the principles of statistical mechanics and is free of contradictions. Our considerations validate the results of Milner and Safran if the stretching elasticity K_s of the membrane tends to zero.
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