Phase transition of compartmentalized surface models

Two types of surface models have been investigated by Monte Carlo simulations on triangulated spheres with compartmentalized domains. Both models are found to undergo a first-order collapsing transition and a first-order surface fluctuation transition. The first model is a fluid surface one. The vertices can freely diffuse only inside the compartments, and they are prohibited from the free diffusion over the surface due to the domain boundaries. The second is a skeleton model. The surface shape of the skeleton model is maintained only by the domain boundaries, which are linear chains with rigid junctions. Therefore, we can conclude that the first-order transitions occur independent of whether the shape of surface is mechanically maintained by the skeleton (= the domain boundary) or by the surface itself.Comment: 10 pages with 16 figure

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 $F_\mathrm{el}[A_\xi]$ \textit{not} of the real microscopic membrane area $A$, but of a \textit{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 tension-jump $\Delta\sigma=dF_\mathrm{el}/dA_\xi$. The predictions of our model account for the fluctuation spectrum of red blood cells 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 area. We also predict an observable tension jump for membranes decorated with polymer "brushes"

Phase transition of triangulated spherical surfaces with elastic skeletons

A first-order transition is numerically found in a spherical surface model with skeletons, which are linked to each other at junctions. The shape of the triangulated surfaces is maintained by skeletons, which have a one-dimensional bending elasticity characterized by the bending rigidity $b$, and the surfaces have no two-dimensional bending elasticity except at the junctions. The surfaces swell and become spherical at large $b$ and collapse and crumple at small $b$. These two phases are separated from each other by the first-order transition. Although both of the surfaces and the skeleton are allowed to self-intersect and, hence, phantom, our results indicate a possible phase transition in biological or artificial membranes whose shape is maintained by cytoskeletons.Comment: 15 pages with 10 figure