Computational model and phase space of bilayer and bolalipid membranes.

(A) Structure of the diether bilayer lipid archaeol (left) and the tetraether bolalipid caldarchaeol including four cyclopentane rings (right), both present in the membrane of Sulfolobus acidocaldarius, a common archaeal model system that lives at high temperatures and low pH [5]. (B) Schematics for a bilayer lipid, a bolalipid and its two in-membrane conformations, membranes made of bilayer molecules only, bolalipid molecules only, and a mixture of the two (left to right). (C) Bilayer lipid (left) is described with one head bead and two tail beads straightened by an angular potential of strength k0. Tail beads of different lipids attract with the strength ϵp and the range ω. Bolalipids (right) consist of two bilayer lipids connected by a bond and straightened by an angular potential of strength kbola. (D) Snapshots of bolalipids self-assembling into a flat membrane (kbola = 0.3 kBT). (E) Cross-section of self-assembled membrane (right), with bolalipids colored according to their conformation: straight lipids in crimson and U-shaped lipids in orange. (F) Membrane phase behavior: liquid, gel and gas regions as a function of the effective temperature Teff and tail interaction range ω for bilayer (top left) and membranes made of flexible kbola = 0 (top right) and stiff kbola = 5 kBT (bottom left) bolalipid molecules. Overlays of all liquid regions (bottom right) show that stiffer lipids exhibit fluid membrane region at higher temperatures. The dashed line marks ω = 1.5o-, the value we used in the rest of the work.

Mechanics of pure bolalipid membranes.

(A) Liquid region as a function of temperature and bolalipid rigidity for pure bolalipid membranes (gray). The dashed line shows the bolalipid membranes of approximately same fluidities. (B) Fraction of bolalipids in the U-shape conformation (θ = 0), fitted to uf(kbola) = 1/(1 + exp(β (-0.16 + 3kbola))) (gray dashed line) according to a two-state model. Insets: simulation snapshots with bolalipids colored according to their conformations. (C) Bending modulus as a function of bolalipid molecule rigidity kbola. Inset: Tilt modulus as a function of bolalipid rigidity kbola. (D) Snapshots of bolalipid membranes at the range of explored curvatures for kbola = 1kBT. (E) Fraction of bolalipid molecules in the U-shaped conformation as a function of the mean membrane curvature H = 1/(2R) for membranes made of flexible (kbola = 0) and semi-flexible (kbola = 1kBT) bolalipid molecules. (F) Bending modulus as a function of curvature. For the flat membrane (H ∼ 0), the corresponding bending rigidity from (C) is marked by the vertical line and empty circles.

Fluidity and rigidity of mixed bilayer/bolalipid membranes.

(A) Single lipid diffusion constant for each species as a function of bilayer fraction f bi (kbola = 2kBT, Teff = 1.3). For f bi ≥0.1, the resulting mixture becomes liquid. Top: Diffusion trajectories of a bolalipid (blue) and a bilayer lipid (red) in a mixture membrane at f bi = 0.5. (B) Bending rigidity κ and (Inset) tilt modulus κθ as a function of the fraction of bilayer molecules f bi. Top: Snapshots show bilayer lipids (blue) in mixed membranes at two different values of f bi.

Reshaping of pure bolalipid membranes.

(A) Simulation snapshots of the membrane wrapping a cargo bead adsorbing onto it. Above the onset adsorption energy ,the cargo is fully wrapped by the membrane and buds off the mother membrane. (B) Onset energy as function of the bolalipid molecule rigidity kbola (for the parameters defined by the line in Fig. 2A). (C) Bottom: Fraction of bolalipids in the U-shape conformation uf in the outer and inner layers of the membrane bud, and in the flat mother membrane, as function of the bolalipid molecule rigidity kbola. Top: Snapshots and cross-sections of the membrane around the cargo bud. At high bolalipid rigidity the pores form around the cargo, and are lined with bolalipid molecules lying flat around the pore in a straight conformation, with both heads in the outer layer (colored in white). The rest of bolalipids colored according to their head-to-head angle as before. (D) Bottom: Average diameter of transient pores in the membrane bud and the mother membrane as function of the bolalipid molecule rigidity kbola. Pores are defined as membrane openings through which a sphere of diameter 1o-can cross. Top: Snapshots of the membrane surface with outer and inner leaflet surface colored in purple and orange, respectively, intersecting at the rim of the pore (gray).

Curving of the mixed membranes, made of bilayer and bolalipid molecules.

(A) Onset energy required to form the membrane bud, ,as function of bilayer head fraction (for the parameters defined in Fig. 3.) (B and C) Fraction of U-shaped bolalipid molecules uf (B) and bilayer molecules (C) in the outer and inner layers of the membrane bud and in the flat mother membrane as a function of the bilayer head fraction .Top panels show the respective snapshots of membrane surface around cargo, where bilayer lipids are shown in light blue as in Fig. 4. (D) Average diameter of transient pores in the membrane bud and the mother membrane as function of bilayer head fraction and respective snapshots of membrane leaflet surfaces surrounding the bud (Top panel).