Shape transformation transitions of a tethered surface model

A surface model of Nambu and Goto is studied statistical mechanically by using the canonical Monte Carlo simulation technique on a spherical meshwork. The model is defined by the area energy term and a one-dimensional bending energy term in the Hamiltonian. We find that the model has a large variety of phases; the spherical phase, the planar phase, the long linear phase, the short linear phase, the wormlike phase, and the collapsed phase. Almost all two neighboring phases are separated by discontinuous transitions. It is also remarkable that no surface fluctuation can be seen in the surfaces both in the spherical phase and in the planar phase.Comment: 7 pages with 8 figure

Polyhedral vesicles

Polyhedral vesicles with a large bending modulus of the membrane such as the gel phase lipid membrane were studied using a Brownian dynamics simulation. The vesicles exhibit various polyhedral morphologies such as tetrahedron and cube shapes. We clarified two types of line defects on the edges of the polyhedrons: cracks of both monolayers at the spontaneous curvature of monolayer $C_{\text {0}}<0$, and a crack of the inner monolayer at $C_{\text {0}}\ge0$. Around the latter defect, the inner monolayer curves positively. Our results suggested that the polyhedral morphology is controlled by $C_{\text {0}}$.Comment: 4 pages, 5 figure

Morphology of axisymmetric vesicles with encapsulated filaments and impurities

The shape deformation of a three-dimensional axisymmetric vesicle with encapsulated filaments or impurities is analyzed by integrating a dissipation dynamics. This method can incorporate systematically the constraint of a fixed surface area and/or a fixed volume. The filament encapsulated in a vesicle is assumed to take a form of a rod or a ring so as to imitate cytoskeletons. In both cases, results of the shape transition of the vesicle are summarized in phase diagrams in the phase space of the vesicular volume and a rod length or a ring radius. We also study the dynamics of a vesicle with impurities coupled to the membrane curvature. The phase separation and the associated shape deformation in the early stage of the dynamical evolution can well be explained by the linear stability analysis. Long runs of simulation demonstrate the nonlinear coarsening of the wavy deformation of the vesicle in the late stage.Comment: 9 pages, 9 figure

Shape Changes of Self-Assembled Actin Bilayer Composite Membranes

We report the self-assembly of thin actin shells beneath the membranes of giant vesicles. Ion-carrier mediated influx of Mg2+ induces actin polymerization in the initially spherical vesicles. Buckling of the vesicles and the formation of blisters after thermally induced bilayer expansion is demonstrated. Bilayer flickering is dominated by tension generated by its coupling to the actin cortex. Quantitative flicker analysis suggests the bilayer and the actin cortex are separated by 0.4 \mum to 0.5 \mum due to undulation forces.Comment: pdf-file, has been accepted by PR

Twirling and Whirling: Viscous Dynamics of Rotating Elastica

Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by a novel pair of coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two dynamical regimes separated by a Hopf bifurcation: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. The consequences of these phenomena for self-propulsion are investigated, and experimental tests proposed.Comment: To be published in Physical Review Letter

Numerical observation of non-axisymmetric vesicles in fluid membranes

By means of Surface Evolver (Exp. Math,1,141 1992), a software package of brute-force energy minimization over a triangulated surface developed by the geometry center of University of Minnesota, we have numerically searched the non-axisymmetric shapes under the Helfrich spontaneous curvature (SC) energy model. We show for the first time there are abundant mechanically stable non-axisymmetric vesicles in SC model, including regular ones with intrinsic geometric symmetry and complex irregular ones. We report in this paper several interesting shapes including a corniculate shape with six corns, a quadri-concave shape, a shape resembling sickle cells, and a shape resembling acanthocytes. As far as we know, these shapes have not been theoretically obtained by any curvature model before. In addition, the role of the spontaneous curvature in the formation of irregular crenated vesicles has been studied. The results shows a positive spontaneous curvature may be a necessary condition to keep an irregular crenated shape being mechanically stable.Comment: RevTex, 14 pages. A hard copy of 8 figures is available on reques

Motor-Driven Bacterial Flagella and Buckling Instabilities

Many types of bacteria swim by rotating a bundle of helical filaments also called flagella. Each filament is driven by a rotary motor and a very flexible hook transmits the motor torque to the filament. We model it by discretizing Kirchhoff's elastic-rod theory and develop a coarse-grained approach for driving the helical filament by a motor torque. A rotating flagellum generates a thrust force, which pushes the cell body forward and which increases with the motor torque. We fix the rotating flagellum in space and show that it buckles under the thrust force at a critical motor torque. Buckling becomes visible as a supercritical Hopf bifurcation in the thrust force. A second buckling transition occurs at an even higher motor torque. We attach the flagellum to a spherical cell body and also observe the first buckling transition during locomotion. By changing the size of the cell body, we vary the necessary thrust force and thereby obtain a characteristic relation between the critical thrust force and motor torque. We present a sophisticated analytical model for the buckling transition based on a helical rod which quantitatively reproduces the critical force-torque relation. Real values for motor torque, cell body size, and the geometry of the helical filament suggest that buckling should occur in single bacterial flagella. We also find that the orientation of pulling flagella along the driving torque is not stable and comment on the biological relevance for marine bacteria.Comment: 15 pages, 11 figure