Adhesion dynamics of confined membranes

Abstract

We report on the modeling of the dynamics of confined lipid membranes. We derive a thin film model in the lubrication limit which describes an inextensible liquid membrane with bending rigidity confined between two adhesive walls. The resulting equations share similarities with the Swift-Hohenberg model. However, inextensibility is enforced by a time-dependent nonlocal tension. Depending on the excess membrane area available in the system, three different dynamical regimes, denoted as A, B and C, are found from the numerical solution of the model. In regime A, membranes with small excess area form flat adhesion domains and freeze. Such freezing is interpreted by means of an effective model for curvature-driven domain wall motion. The nonlocal membrane tension tends to a negative value corresponding to the linear stability threshold of flat domain walls in the Swift-Hohenberg equation. In regime B, membranes with intermediate excess areas exhibit endless coarsening with coexistence of flat adhesion domains and wrinkle domains. The tension tends to the nonlinear stability threshold of flat domain walls in the Swift-Hohenberg equation. The fraction of the system covered by the wrinkle phase increases linearly with the excess area in regime B. In regime C, membranes with large excess area are completely covered by a frozen labyrinthine pattern of wrinkles. As the excess area is increased, the tension increases and the wavelength of the wrinkles decreases. For large membrane area, there is a crossover to a regime where the extrema of the wrinkles are in contact with the walls. In all regimes after an initial transient, robust localised structures form, leading to an exact conservation of the number of adhesion domains. arXiv:1808.00316v1 [cond-mat.soft] 1 Aug 2018

Undulation of a moving fluid membrane pushed by filament growth

“…The initial suppression of the membrane undulation induces this overshoot buckling, because the lowest mode can evolve the fastest. Such buckling could share similarities with the buckling induced by a negative surface tension [39] as well as wrinkles forming when a membrane is confined between two walls [40], which are also be suppressed by tension [41].…”

Shear dynamics of confined membranes

“…For example in the absence of shear, coarsening of adhesion domains coexisting with wrinkles can be observed with double-well potentials as discussed in Ref. [12], while only frozen labyrinthine wrinkle patterns can be seen with single-well potentials, as discussed below.…”

“…The opposite limit of impermeable wallsν 1 is suitable to describe, e.g., substrates covered by other lipid membranes as discussed in Ref. [12]. Models which account for finite permeabilityν ∼ 1 have also been reported in Ref.…”

“…The second ingredient is the balance between two dissipation mechanisms, controlled by the viscosity of the liquid and the permeability of the walls. The relative roles of the liquid flow through the walls and along the walls is characterized by a dimensionless number [12]…”

“…We use a numerical scheme described in Ref. [12] which preserves precisely the membrane area, and random initial conditions as described in Appendix C. Fig. 3 shows topviews of the membrane height profile for several membrane excess area.…”