Fluctuations and stability of polymerized vesicles

The shape fluctuations and the stability of polymerized vesicles are investigated within the framework of shell theory. The intrinsic curvature of the vesicle leads to an enhanced coupling between bending and stretching modes which acts to suppress the shape fluctuations on large scales. This effect is explicitly calculated for a cylindrical shape of the vesicle. For a cylinder with radius $r_0$, the shape fluctuations exhibit the crossover scale $L^*\simeq (r_0^2\kappa /Y)^{1/4}$, where $\kappa$ and $Y$ are the bending rigidity and the (2–dimensional) Young modulus of the polymerized membrane. For $L\ll L^*$, the fluctuations are fluid-like but are strongly suppressed for $L\gg L^*$. In addition, the stability of the cylinder with respect to an external pressure is studied, and a sequence of critical pressure values is determined at which the cylinder becomes unstable