Shape deformation of lipid membranes by banana-shaped protein rods: Comparison with isotropic inclusions and membrane rupture

Abstract

The assembly of curved protein rods on fluid membranes is studied using implicit-solvent meshless membrane simulations. As the rod curvature increases, the rods on a membrane tube assemble along the azimuthal direction first and subsequently along the longitudinal direction. Here, we show that both transition curvatures decrease with increasing rod stiffness. For comparison, curvature-inducing isotropic inclusions are also simulated. When the isotropic inclusions have the same bending rigidity as the other membrane regions, the inclusions are uniformly distributed on the membrane tubes and vesicles even for large spontaneous curvature of the inclusions. However, the isotropic inclusions with much larger bending rigidity induce shape deformation and are concentrated on the region of a preferred curvature. For high rod density, high rod stiffness, and/or low line tension of the membrane edge, the rod assembly induces vesicle rupture, resulting in the formation of a high-genus vesicle. A gradual change in the curvature suppresses this rupture. Hence, large stress, compared to the edge tension, induced by the rod assembly is the key factor determining rupture. For rod curvature with the opposite sign to the vesicle curvature, membrane rupture induces inversion of the membrane, leading to division into multiple vesicles as well as formation of a high-genus vesicle.

Acceleration and suppression of banana-shaped-protein-induced tubulation by addition of small membrane inclusions of isotropic spontaneous curvatures

“…Molecular dynamics with a Langevin thermostat is employed [63,64]. In the following, the results are displayed with the rod length r rod = 10σ for the length unit, k B T for the energy unit, and τ = r 2 rod /D for the time unit, where D is the diffusion coefficient of the membrane particles in the tensionless membrane [57].…”

“…Since the stiffness of the BAR domains is not known, the protein rods in our simulations may be more flexible or stiffer than the real value. Stiffer rod has a greater bending force and the phase boundaries are shifted to lower curvatures [57]. Thus, greater rod stiffness can be interpreted as an effectively higher curvature.…”

“…Further, tubular formation via membrane protrusion was simulated using a dynamically triangulated membrane model [51,52] and meshless membrane models [53,54]. Membrane rupture leads to the formation of a tubular membrane network [55][56][57] and membrane inversion [57]. The protein assembly produces polygonal membrane tubes and polyhedral vesicles at a high protein density [58].…”

Membrane structure formation induced by two types of banana-shaped proteins

“…The scaffold formation [38] and linear assembly [39] of BAR domains have been demonstrated. To investigate large-scale membrane deformations, a dynamically triangulated membrane model [41,42] and meshless membrane models [43][44][45][46][47] have been employed; consequently, various (meta)stable vesicle shapes [41][42][43][44] and the tubule formation dynamics [45] have been reported. However, the relation with the large-scale picture of the theory of point-like anisotropic inclusions [30][31][32] is not well investigated.…”

“…In our simulations an implicit-solvent meshless membrane model [43][44][45][46][48][49][50] is used to represent a fluid membrane. Banana-shaped proteins, assumed to be strongly adsorbed onto the membrane, are modelled together with the membrane region below them as linear strings of particles with a bending stiffness and a preferred curvature.…”