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

Abstract

We use theory and numerical computation to determine the shape of an axisymmetric fluid membrane with a resistance to bending and constant area. The membrane connects two rings in the...

Three membrane fusion pore families determine the pathway to pore dilation

“…1A, zero torque, or equivalently H = 0) at the boundary of the planar membranes. As shown previously (45, 53), there are three fusion pore solutions: two catenoids and one tether-like solution. We consider first equal membranes, .…”

“…Wide and thin catenoids. The freely hinged BCs allow for two catenoidal solutions (45,49). Consider first a fusion pore that is a minimal surface (54), locally minimizing the membrane area 𝐴 and the tension contribution to the free energy of Eq.…”

Stationary shapes of axisymmetric vesicles beyond lowest-energy configurations

“…Results for the axial force, F , shown in Fig. 3(b) are calculated using 56 F = 2π κη ,where η is a Lagrange multiplier determined from relations (2.7) and (2.14) in the ESI† using the numerical values of pressure, tension, the radial coordinate, and the principal curvatures evaluated at the equator ( i.e. , at s = L /2) where all quantities are well defined.…”

Three membrane fusion pore families determine the pathway to pore dilation

“…These studies identified a single family of narrow fusion pores, with minimum diameter < 10 nm. By contrast, an important recent study found exact solutions minimizing the Helfrich free energy corresponding to three fusion pore families, using freely hinged boundary conditions at the membrane edges (45). Membrane tethers are structures closely related to fusion pores, typically pulled from cells or artificial liposomes by optical tweezers that use the measured pulling force to infer membrane tension (46,47).…”

“…The study of ref. (45) showed that when bending energy features, the second thinner catenoid family can also be realized if the far field boundary conditions are freely hinged (45).…”