Fluctuation Spectrum of Fluid Membranes Coupled to an Elastic Meshwork: Jump of the Effective Surface Tension at the Mesh Size

We identify a class of composite membranes: fluid bilayers coupled to an elastic meshwork that are such that the meshwork’s energy is a function $F_{\mathrm{e}\mathrm{l}}[A_{\xi }]$ not of the real microscopic membrane area $A$, but of a smoothed membrane’s area $A_{\xi }$, which corresponds to the area of the membrane coarse grained at the mesh size $\xi$. We show that the meshwork modifies the membrane tension $\sigma$ both below and above the scale $\xi$, inducing a steep crossover of amplitude $\Delta \sigma =d{F}_{\mathrm{e}\mathrm{l}}/d{A}_{\xi }$. The predictions of our model account for the fluctuation spectrum of red blood cell membranes coupled to their cytoskeleton. Our results indicate that the cytoskeleton might be under extensional stress, which would provide a means to regulate available membrane areas. We also predict an observable tension jump for membranes decorated with polymer “brushes.”