We develop equilibrium fluctuation formulae for the isothermal elastic moduli of discrete biomembrane models at different scales. We account for the coupling of large stretching and bending strains of triangulated network models endowed with harmonic and dihedral angle potentials, on the basis of the discrete-continuum approach presented in Schmidt and Fraternali (J Mech Phys Solids 60:172–180, 2012). We test the proposed equilibrium fluctuation formulae with reference to a coarse-grained molecular dynamics model of the red blood cell (RBC) membrane (Marcelli et al. in Biophys J 89:2473–2480, 2005; Hale et al. in Soft Matter 5:3603–3606, 2009), employing a local maximum-entropy regularization of the fluctuating configurations (Fraternali et al. in J Comput Phys 231:528–540, 2012). We obtain information about membrane stiffening/softening due to stretching, curvature, and microscopic undulations of the RBC model. We detect local dependence of the elastic moduli over the RBC membrane, establishing comparisons between the present theory and different approaches available in the literature
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