Elastic and flexoelectic aspects of out-of-plane fluctuations in biological and model membranes

Biomolecular transport and separation in nanotubular networks.

“…27 Another important membrane property that correlates with nanotube formation is membrane bending rigidity (). 28 A compilation of  values from the literature is shown in Table 1. 29,30,31,32 (It should be noted that these values tend to be somewhat variable depending on the measuring technique and conditions.)…”

Stability of growing vesicles

“…Whilst it is possible to directly calculate a perturbative form for ξ 1 -by substituting (33) and (34) into (32) and (30) and integrating-here, a change of variable is introduced to simplify the manipulations slightly. Motivated by the form of (30) introduce variables R(θ) and Θ(θ) such that ρ ′ = R cos Θ, and k ′ = R sin Θ,…”

“…Note also that the factor of M comes from the fact that ψ is a specific, or per unit mass, quantity. Here, in order to be consistent with membrane model literature (see for example the early sections of [1] or [33]), the previously defined "bar averaging" taken over the boundary to the membrane has been replaced by an average over a surface bisecting the two layers of lipids, A m , the so-called neutral surface [33]. Furthermore, this approach is extended to all thermodynamic variables: an average taken over the exterior of the membrane is the same as an average taken over the neutral surface.…”

“…Consider the surface area A = 2π π 0 √ gdθ, this will serve as a template for calculating V , ξ 1 and ξ 2 : the details of which are confined to Appendix B. Substituting (33) and (34) into (24) and (30) gives…”

“…it is intensive). In the above the membrane is taken to be of constant thickness l, where the factor preceding the integral comes from the fact that the Canham-Helfrich-Evans model is an integral over energy per unit area [33]. Note also that the factor of M comes from the fact that ψ is a specific, or per unit mass, quantity.…”