Axisymmetric membranes with edges under external force: buckling, minimal surfaces, and tethers

Stationary shapes of axisymmetric vesicles beyond lowest-energy configurations

We conduct a systematic exploration of the energy landscape of vesicle morphologies within the framework of the Helfrich model. Vesicle shapes are determined by minimizing the elastic energy subject to constraints of constant area and volume. The results show that pressurized vesicles can adopt higher-energy spindle-like configurations that require the action of point forces at the poles. If the internal pressure is lower than the external one, multilobed shapes are predicted. We utilize our results to rationalize experimentally observed spindle shapes of giant vesicles in a uniform AC electric field.

Three membrane fusion pore families determine the pathway to pore dilation

During exocytosis secretory vesicles fuse with a target membrane and release neurotransmitters, hormones, or other bioactive molecules through a membrane fusion pore. The initially small pore may subsequently dilate for full contents release, as commonly observed in amperometric traces. The size, shape, and evolution of the pore is critical to the course of contents release, but exact fusion pore solutions accounting for membrane tension and bending energy constraints have not been available. Here, we obtained exact solutions for fusion pores between two membranes. We find three families: a narrow pore, a wide pore, and an intermediate tether-like pore. For high tensions these are close to the catenoidal and tether solutions recently reported for freely hinged membrane boundaries. We suggest membrane fusion initially generates a stable narrow pore, and the dilation pathway is a transition to the stable wide pore family. The unstable intermediate pore is the transition state that sets the energy barrier for this dilation pathway. Pore dilation is mechanosensitive, as the energy barrier is lowered by increased membrane tension. Finally, we study fusion pores in nanodiscs, powerful systems for the study of individual pores. We show that nanodiscs stabilize fusion pores by locking them into the narrow pore family.

Geometry of catenoidal soap film collapse induced by boundary deformation

Experimental and theoretical work reported here on the collapse of catenoidal soap films of various viscosities reveal the existence of a robust geometric feature that appears not to have been analyzed previously; prior to the ultimate pinchoff event on the central axis, which is associated with the formation of a well-studied local double-cone structure folded back on itself, the film transiently consists of two acute-angle cones connected to the supporting rings, joined by a central quasicylindrical region. As the cylindrical region becomes unstable and pinches, the opening angle of those cones is found to be universal, independent of film viscosity. Moreover, that same opening angle at pinching is found when the transition occurs in a hemicatenoid bounded by a surface. The approach to the conical structure is found to obey classical Keller-Miksis scaling of the minimum radius as a function of time, down to very small but finite radii. While there is a large body of work on the detailed structure of the singularities associated with ultimate pinchoff events, these large-scale features have not been addressed. Here we study these geometrical aspects of film collapse by several distinct approaches, including a systematic analysis of the linear and weakly nonlinear dynamics in the neighborhood of the saddle node bifurcation leading to collapse, both within mean curvature flow and the physically realistic Euler flow associated with the incompressible dynamics of the surrounding air. These analyses are used to show how much of the geometry of collapsing catenoids is accurately captured by a few active modes triggered by boundary deformation. A separate analysis based on a mathematical sequence of shapes progressing from the critical catenoid towards the Goldschmidt solution is shown to predict accurately the cone angle at pinching. We suggest that the approach to the conical structures can be viewed as passage close to an unstable fixed point of conical similarity solutions. The overall analysis provides the basis for the systematic study of more complex problems of surface instabilities triggered by deformations of the supporting boundaries.