Fluctuations of coupled fluid and solid membranes with application to red blood cells

The fluctuation spectra and the intermembrane interaction of two membranes at a fixed average distance are investigated. Each membrane can either be a fluid or a solid membrane, and in isolation, its fluctuations are described by a bare or a wave-vector-dependent bending modulus, respectively. The membranes interact via their excluded-volume interaction; the average distance is maintained by an external, homogeneous pressure. For strong coupling, the fluctuations can be described by a single, effective membrane that combines the elastic properties. For weak coupling, the fluctuations of the individual, noninteracting membranes are recovered. The case of a composite membrane consisting of one fluid and one solid membrane can serve as a microscopic model for the plasma membrane and cytoskeleton of the red blood cell. We find that, despite the complex microstructure of bilayers and cytoskeletons in a real cell, the fluctuations with wavelengths lambda greater than or similar to 400 nm are well described by the fluctuations of a single, polymerized membrane (provided that there are no inhomogeneities of the microstructure). The model is applied to the fluctuation data of discocytes (normal red blood cells), a stomatocyte, and an echinocyte. The elastic parameters of the membrane and an effective temperature that quantifies active, metabolically driven fluctuations are extracted from the experiments.