  We theoretically investigate the membrane fluctuations of red blood cells
with focus laid on the role of the cytoskeleton, viewing the system as a
membrane coupled to sparse spring network. This model is exactly solvable and
enables us to examine the coupling strength dependence of the membrane
undulation. We find that the coupling modifies the fluctuation spectrum at
wavelengths longer than the mesh size of the network, while leaving the
fluid-like behavior of the membrane intact at shorter wavelengths. The
fluctuation spectra can be markedly different, depending on not only the
relative amplitude of the bilayer bending energy with respect to the
cytoskeleton deformation energy but also the bilayer-cytoskelton coupling
strength.
