Cracking donuts and sorting lipids: geometry controls archaeal membrane stability and lipid organization

Abstract

Cells are defined by lipid membranes that differ in their structure across the tree of life. While the membranes of most bacteria and eukaryotes consist of single-headed bilayer lipids, the membranes of archaea are composed of mixtures of single-headed bilayer lipids and double-headed bolalipids. Archaeal bolalipids can adopt straight or u-shaped conformations, enabling them - together with bilayer lipids - to control whether membranes form bilayer or monolayer structures. Yet, the physical principles governing archaeal membranes remain largely unexplored, especially how membrane structure couples to externally imposed curvature during membrane remodeling. Here, we perform coarse-grained molecular dynamics simulations of toroidal vesicles to systematically probe the effects of all relevant combinations of mean and Gaussian curvatures on shape stability and lipid organization. We find that soft bilayer membranes can sustain all curvatures induced, whereas rigid bolalipid monolayer membranes either transition to different vesicle shapes or rupture. Bilayer-mimicking u-shaped bolalipids and bilayer lipids are spatially accumulated in regions of high mean membrane curvature independent of Gaussian curvature. Our work identifies curvature-composition coupling as a physical signature of archaeal membrane remodeling.

Figures (12)

• Figure 1: Computational model, toroidal vesicle geometry and curvature distribution on toroidal vesicles. (A, left) Bacterial or eukaryotic bilayer membrane. (right) Archaeal monolayer membrane. (B, left) A bilayer lipid consisting of 1 head bead (gray) and 2 tail beads (cyan). The molecular stiffness is controlled via $k_0$. (right) An archaeal bolalipid consisting of 2 head beads (gray) and 4 tail beads (pink). The molecular stiffness is controlled via $k_0$ and $k_\mathrm{bola}$. Bilayer and bolalipid tail beads attract each other, with $\omega$ and $\epsilon_\mathrm{p}$ controlling the range and strength of the hydrophobic interaction along lipid tail beads. (C) Bolalipids adopt two dominating conformations: u-shaped (orange) and straight shape (pink). (D) Torus geometry with ring radius $R_\mathrm{ring}$ and cross section radius $r_\mathrm{cross}$. The toroidal angle $\vartheta$ parametrizes the cross-sectional tube of the torus. (E) At any point on the surface two principle curvatures $C_1$ and $C_2$ parametrize the shape that can be combined into the mean curvature $H$ and Gaussian curvature $K$. (F) Normalized squared mean curvature on the Clifford torus, which has a toroidal aspect ratio of $\rho=R_\mathrm{ring}/r_\mathrm{cross}=\sqrt{2}$. (G) Normalized Gaussian curvature on the Clifford torus. (H) Toroidal vesicles for pure bolalipid membranes at $k_\mathrm{bola}=\unit[0]{}k_\mathrm{B}T$ (top), at $k_\mathrm{bola}=\unit[1]{}k_\mathrm{B}T$ (center) and a mixture membrane with bilayer content of $f_\mathrm{bi}=0.7$ and bolalipids at $k_\mathrm{bola}=\unit[2]{}k_\mathrm{B}T$.
• Figure 2: Bolalipid rigidity controls stability of toroidal vesicles composed of bolalipids. (A) Shape diagram of pure bolalipid membranes as a function of the bolalipid rigidity $k_\mathrm{bola}$. For $k_\mathrm{bola}=\unit[0]{}k_\mathrm{B}T$, we observe toroidal vesicle shapes. With increasing values of $k_\mathrm{bola}$, we observe spherical vesicles ($k_\mathrm{bola}=\unit[1]{}k_\mathrm{B}T$), flat membrane sheets or truncated wedges (ratio 2:2 for $k_\mathrm{bola}=\unit[2]{}k_\mathrm{B}T$) and flat membrane sheets ($k_\mathrm{bola} > \unit[2]{}k_\mathrm{B}T$). Membrane pores can only be observed for $k_\mathrm{bola}\ge \unit[2]{}k_\mathrm{B}T$. (B) Reduced volume $\nu$ along the simulation trajectory for different values of the bolalipid rigidity $k_\mathrm{bola}$. (C) Number of handles or pores in the membrane along the simulation trajectory for different values of the bolalipid rigidity $k_\mathrm{bola}$. (D) Global u-shaped bolalipid fraction $u_\mathrm{f}$ as a function of the bolalipid rigidity $k_\mathrm{bola}$. Dashed gray line shows $u_\mathrm{f}(k_\mathrm{bola})$, fitted for a flat membrane. (B-D) Each data point shows an average over $N_\mathrm{seeds}=4$ random initial seeds.
• Figure 3: Bilayer lipid fraction controls stability of toroidal vesicles of archaeal mixture membranes composed of bilayer and bolalipids. (A) Shape diagram of mixture membranes as a function of bilayer fraction $f_\mathrm{bi}$. For $f_\mathrm{bi}=0.1$, we observe spherical or cylindrical membrane shapes (ratio 3:1). With increasing values of $f_\mathrm{bi}$, we first observe spherical membrane shapes, followed by vesicles of torus shape. For $f_\mathrm{bi}=0.5$ and $f_\mathrm{bi}=0.6$, we observe either spherical or toroidal vesicles (ratio 2:2) as final state in independent simulation runs. For $f_\mathrm{bi}=0.1$, the transition from the initial toroidal membrane shape is accompanied by the appearance of transient membrane pores, which we do not observe otherwise. (B) Reduced volume $\nu$ along the simulation trajectory for different bilayer fractions $f_\mathrm{bi}$. (C) Number of handles or pores in the membrane along the simulation trajectory for different bilayer fractions $f_\mathrm{bi}$. (D) Global u-shaped bolalipid fraction $u_\mathrm{f}$ as a function of $f_\mathrm{bi}$ for mixture membranes of bilayer and bolalipids. (B-D) Each data point shows an average over $N_\mathrm{seeds}=4$ random initial seeds.
• Figure 4: Curvature controls lipid distribution in pure bolalipid and archaeal mixture membranes. (A) For $k_\mathrm{bola}=\unit[0]{}k_\mathrm{B}T$, we observe membrane vesicles of torus shape (left). For the torus shape, the u-shaped bolalipid fraction $u_\mathrm{f}$ is mapped on the cross-section circle (right), averaged and represented by the toroidal angle $\vartheta$ (bottom). (B) u-shaped bolalipid fraction $u_\mathrm{f}$ as a function of $\vartheta$ (solid black line) with standard error (gray area). Along with $u_\mathrm{f}$, the scaled squared mean curvature $\tilde{H^2}$ (solid red line) and the scaled Gaussian curvature $\tilde{K}$ (solid purple line) are plotted. The global value along the torus is shown by the solid orange line. (C) The u-shaped bolalipid fraction $u_\mathrm{f}$ as a function of the reduced squared mean curvature $H^2 \cdot r_\mathrm{cross}^2$ (red) and a linear fit to the data (solid black line). (B and C) Each data point shows an average over $N_\mathrm{seeds}=16$ random initial seeds. (D) For a bilayer fraction of $f_\mathrm{bi}=0.7$, we observe membrane vesicles of torus shape. The averaged bilayer fraction $f_\mathrm{bi}$ as a function of the toroidal angle $\vartheta$ (solid black line) with standard error (gray area). Along with $f_\mathrm{bi}$, the scaled squared mean curvature $\tilde{H^2}$ (solid red line) and the scaled Gaussian curvature $\tilde{K}$ (solid purple line) are plotted. (E) The bilayer fraction $f_\mathrm{bi}$ as a function of the reduced squared mean curvature $H^2 \cdot r_\mathrm{cross}^2$ (red) and a linear fit to the data (solid black line). (F) Bilayer heterogeneity (for definition see text) as a function of the bilayer lipid fraction $f_\mathrm{bi}$. A completely homogeneous membrane would show a bilayer heterogeneity of 0 (solid orange line). (D-E) Each data point shows an average over $N_\mathrm{seeds}=4$ random initial seeds.
• Figure S1: Fraction of u-shaped bolalipids as a function of time for increasing bolalipid rigidity $k_\mathrm{bola}$ (A-F). From fits to the data (see text), we determine the steady state value of the fraction of u-shaped bolalipids $u_\mathrm{f}^0$. We average the values of $u_\mathrm{f}^0$ for the different seeds and show the results in Fig. 2D. Data shown is based on $N_\mathrm{seeds}=4$ random initial seeds.