Lattice of Passages Connecting Membranes

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Abstract
Lattices of passages connecting membranes are frequently observed in a variety of membranous systems. We study their elastic properties within the framework of the curvature energy. Our calculations apply to the vesicle case where the constraints of constant surface and volume determine the shape profile. We concentrate on the physically relevant case of periodic boundary conditions for each cell containing passages, where the lattice parameter is set by the Gaussian bending modulus. It is shown that lattices of passages lack in-plane shear rigidity and we propose this as the basic reason for the strong fluctuations which are observed in experiments. Other compression modes couple to the vesicle shape. Our calculations are based on a detailed analysis of the shape equation. Using the Abrikosov vortex solution we show the analogies between lattices of passages and topological defects.

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