Colloidal membranes, self assembled monolayers of aligned rod like molecules, offer a template for designing membranes with definite shapes and curvature, and possibly new functionalities in the future. Often the...
Chiral, rod-like molecules can self-assemble into cylindrical membrane tubules and helical ribbons. They have been successfully modeled using the theory of chiral nematics. Models have also predicted the role of...
Chiral, rod-like molecules can self-assemble into cylindrical membrane tubules and helical ribbons. They have been successfully modeled using the theory of chiral nematics. Models have also predicted the role of chiral lipids in forming nanometer-sized membrane buds in the cell. However, in most theoretical studies, the membrane shapes are considered fixed (cylinder, sphere, saddle, etc.), and their optimum radius of curvatures are found variationally by minimizing the energy of the composite system consisting of membrane and chiral nematics. Numerical simulations have only recently started to consider membrane deformation and chiral orientation simultaneously. Here we examine how deformable, closed membrane vesicles and chiral nematic rods mutually influence each other's shape and orientation, respectively, using Monte-Carlo (MC) simulation on a closed triangulated surface. For this, we adopt a discrete form of chiral interaction between rods, originally proposed by Van der Meer et al. (1976) for off-lattice simulations. In our simulation, both conical and short cylindrical tubules emerge, depending on the strength of the chiral interaction and the intrinsic chirality of the molecules. We show that the Helfrich-Prost term, which couple nematic tilt with local membrane curvature in continuum models, can account for most of the observations in the simulation. At higher chirality, our theory also predicts chiral tweed phase on cones, with varying bandwidths.
Colloidal membranes, self assembled monolayers of aligned rod like molecules, offer a template for designing membranes with definite shapes and curvature, and possibly new functionalities in the future. Often the constituent rods, due to their molecular chirality, are tilted with respect to the membrane normal. Spatial patterns of this tilt on curved membranes result from a competition among depletion forces, nematic interaction, molecular chirality and boundary effects. We present a covariant theory for the tilt pattern on minimal surfaces, like helicoids and catenoids, which have been generated in the laboratory only recently. We predict several non-uniform tilt patterns, some of which are consistent with experimental observations and some, which are yet to be discovered.
Exocytosis is a common transport mechanism via which cells transport out non-essential macromolecules (cargo) into the extra cellular space. ESCRT-III proteins are known to help in this. They polymerize into a conical spring like structure and help deform the cell membrane locally into a bud which wrapps the outgoing cargo. we model this process using a continuum energy functional. It consists of elastic energies of the membrane and the semi-rigid ESCRT-III filament, favorable adhesion energy between the cargo and the membrane, and affinity among the ESCRT-III filaments. We take the free energy minimization route to identify the sequence of composite structures which form during the process. We show that membrane adhesion of the cargo is the driving force for this budding process and not the buckling of ESCRT-III filaments from flat spiral to conical spring shape. However ESCRT-III stabilizes the bud once it forms. Further we conclude that a nonequilibrium process is needed to pinch off/separate the stable bud (containing the cargo) from the cell body.
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