Effects of orientational order on modulated cylindrical interfaces

Abstract

Cylindrical interfaces occur in sheared or deformed emulsions and as biological or technological lipid monolayer or bilayer tubules. Like the corresponding spherical droplets and vesicles, these cylinder-like surfaces may host orientaional order with n-fold rotational symmetry, for example in the positions of lipid molecules or of spherical nanoparticles. We examine how that order interacts with and induces shape modulations of cylindrical interfaces. While on spherical droplets 2n topological defects necessarily exist and can induce icosahedral droplet shapes, the cylindrical topology is compatible with a defect-free patterning. Nevertheless, once a modulation is introduced by a mechanism such as spontaneous curvature, nontrivial patterns of order, including ones with excess defects, emerge and have nonlinear effects on the shape of the tube. Examining the equilibrium energetics of the system analytically and with a lattice-based Markov chain Monte Carlo simulation, we predict low-temperature morphologies of modulated cylindrical interfaces hosting orientational order. A shape modulation induces a banded pattern of alternatingly isotropic and ordered interfacial material. Furthermore cylindrical systems can be divided into Type I, without defects, and Type II, which go through a spectrum of defect states with up to 4n excess defects.The character of the curvature-induced shape transition from unmodulated to modulated cylinders is continuous or discontinuous accordingly.

Non-Classical Euler Buckling and Brazier Instability in Cylindrical Liquid Droplets

“…First, the small-r cylindrical shapes have a lower surface area. Thus, the number of structural defects (coupled to possible fluctuations of Gaussian curvature 41 ) and surfaceadsorbed impurities is smaller, so that the structure of the interfacial crystal is closer to being perfect and its Y 2D is higher. Another possibility is that the unscreened electrostatic fields due to the charged head groups of the interfacial surfactants penetrate through the bulk oil of the small-r droplets, 42 so that the ensuing electrostatic contribution modifies the elastic moduli.…”

Stability of a biomembrane tube covered with proteins

“…Examples include the effects of different types of lipids [21–30] polymers [31–35] nanoparticles [36–40] phospholipid-surfactant mixtures [41], protein pumps [20, 42], adsorbed BAR proteins [43–48] inter-calated curvature-inducing proteins [49–51] and crowds of sterically-repelling proteins [52–56] (see also reviews in [57–59] Generally speaking, the total free energy of such systems contains, besides the Helfrich free energy, the free energy of the particles and a term accounting for the interaction of the membrane with the particles. Expressions for the free energy of the particles often contain terms penalising phase boundaries [22, 41, 43, 49, 60] and terms accounting for interactions between the particles and for entropy, either through a Flory-Huggins theory for a mixture of occupied and unoccupied sites [21, 27, 33, 41, 43], or a Ginzburg-Landau expansion thereof [22, 49, 61]. To describe the interaction of particles with a vesicle, most authors [21, 22, 33, 35, 41, 43, 46, 49–51, 60, 62, 63] considered a linear coupling ∝ Λ Hϕ of the mean curvature H to the areal particle density ϕ with a coupling parameter Λ. Leibler showed that such interaction between proteins and a flat membrane sheet changes its effective bending rigidity to κ− Λ 2 /a , with a setting the strength of mutual protein interactions [49].…”