A Gaussian model for the membrane of red blood cells with cytoskeletal defects

We study a Gaussian model of the membrane of red blood cells: a "phantom" triangular network of springs attached at its vertices to a fluid bilayer with curvature elasticity and tension. We calculate its fluctuation spectrum and we discuss the different regimes and non-monotonic features, including the precise crossover at the mesh size between the already known limits with two different tensions and the renormalisation of the bending rigidity at low wavevectors. We also show that the non-diagonal correlations reveal, in "dark field", the cytoskeletal defects. As a first step toward a non-invasive defect spectroscopy, the specific case of lacking bonds is studied numerically and analytically.