Cytoskeleton influence on normal and tangent fluctuation modes in the red blood cells

We argue that the paradoxal softness of the red blood cells (RBC) in fluctuation spectra experiments is apparent. We show that the effective surface shear modulus $\mu_s$ of the RBC obtained from fluctuation data and that measured in static deformation experiments have the same order of magnitude. A simple micromechanical model of the RBC developped for this purpose accounts for the influence of a finite-thickness cytoskeleton on the fluctuations of the composite membrane-cytoskeleton system. The spectrin network cytoskeleton with the bulk shear modulus estimated as $\mu\approx105\div 165$ Pa contributes to both normal and tangent fluctuations of the system and confines the fluctuations of the lipid membrane. The ratio of mean square amplitudes of the RBC normal and tangent fluctuations $<X_n^2> /< X_t^2>$ calculated in the frame of the model is 2-3 orders of magnitude smaller that it is in the free membrane with the same bending and shear moduli