Shape equations and curvature bifurcations induced by inhomogeneous rigidities in cell membranes

This article aims at two objectives: one is the shape equation for the equilibrium configurations of biomembranes with heterogeneous rigidities; another is the possible mechanism for curvature bifurcations in various biomembranes such as human red blood cells (RBC). The shape equation is established by treating the inhomogeneous biomembrane as a lipid bilayer vesicle containing inclusions or impurities. After careful investigation of the equation, the rigidity gradient is found to be an initial "driving force" that may destabilize the biomembrane and stimulate shape transitions, and the concept (or mechanism) termed "curvature bifurcations induced by rigidity gradients" is suggested. Various post-bifurcation modes recording the new equilibrium configurations are disclosed. A few post-bifurcation modes are found to coincide well with some practical shape transitions in cells such as the cup-like shape (stomatocyte) transition and spiculated shape (echinocyte) transition in RBC.