Stability of multicomponent biological membranes

Equilibrium equations and stability conditions are derived for a general class of multicomponent biological membranes. The analysis is based on a generalized Helfrich energy that accounts for geometry through the stretch and curvature, the composition, and the interaction between geometry and composition. The use of nonclassical differential operators and related integral theorems in conjunction with appropriate composition and mass conserving variations simplify the derivations. We show that instabilities of multicomponent membranes are significantly different from those in single component membranes, as well as those in systems undergoing spinodal decomposition in flat spaces. This is due to the intricate coupling between composition and shape as well as the nonuniform tension in the membrane. Specifically, critical modes have high frequencies unlike single component vesicles and stability depends on system size unlike in systems undergoing spinodal decomposition in flat space. An important implication is that small perturbations may nucleate localized but very large deformations. We show that the predictions of the analysis are in qualitative agreement with experimental observations.