We study the equilibrium shapes of vesicles, with an in-plane nematic order, using a Monte-Carlo scheme and show that highly curved shapes, like tubes and discs, with a striking similarity to the structures engendered by certain curvature sensing peripheral membrane proteins, can be spontaneously generated by anisotropic directional curvature with nematic disclinations playing an important role. We show that the coupling between nematic order and local curvature could lead to like defects moving towards each other and unlike defects moving away, in turn leading to tube formation. Thermally induced defect pair production lead to branched tubular structures. It is also shown that a helical arrangement of the membrane tubes, with nematic field spiraling around it, is the dominant soft mode of the system.
Ramakrishnan, N., Ipsen, J. H., & Kumar, P. B. S. (2012). Role of disclinations in determining the morphology of deformable fluid interfaces. Soft Matter, 8(11), 3058-3061. https://doi.org/10.1039/c2sm07384f