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. 2022 Jun 27;13:3697. doi: 10.1038/s41467-022-31286-4

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© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2022

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Fig. 7 — a Drawing for modeling two forces underlying the membrane shape transformations: a point-pulling force $(f_{p u l l})$ converts the flat membrane to Λ-shape, whereas a constriction force reduces the Λ-shape base radius ( $r_{b}$ ), which transforms Λ- to Ω-shape. $H$ is the height; $r_{p}$ is the pore radius. b Lower: computed shape diagram – membrane shape (Λ-, Ω- or tube-shape) depends on H and $r_{b}$ , both normalized to the internal length scale $r_{i} (= \sqrt{\frac{κ}{2 γ}})$ . Upper: examples of computed $Λ$ shape I, $(H = 3.0 \cdot r_{i})$ , $(r_{b} = 3 \cdot r_{i})$ , $Ω$ shape with a large pore II, $H = 3.9 \cdot r_{i}$ , $r_{b} = 0.81 \cdot r_{i}$ , and $Ω$ shape with a narrow pore III, $H = 3.8 \cdot r_{i}$ , $r_{b} = 0.46 \cdot r_{i}$ . c Computed Flat→ $Λ$ transition. An increase of $f_{p u l l}$ raises Λ-shape height H (normalized to $r_{i} (= \sqrt{\frac{κ}{2 γ_{0}}})$ ) upon a constant base radius $r_{b} (= 2.5 \cdot r_{i})$ . $f_{p u l l}$ is normalized to the intrinsic force $f_{i}$ $= \sqrt{2 κ γ_{0}}$ . Circles represent Λ-profiles shown on the top (applies to panels c and d). d Computed Λ→Ω transition. Constriction of the base radius, $r_{b}$ (normalized to $r_{i} (= \sqrt{\frac{κ}{2 γ_{0}}})$ ), upon keeping the force $(f_{p u l l} = 7.2 \cdot f_{i})$ and membrane area constant converts Λ to Ω shape and reduces the radius of the Ω-shape pore, $r_{p}$ (normalized to $r_{i}$ ). e Upper: $f_{p u l l}$ increased during an experimentally observed Flat→Λ-shape transition (each point from a frame in Supplementary Movie S7). Lower: sampled Λ-shape observed (green) and computed (red) that matches the observed one. $f_{p u l l}$ (upper) was obtained from computed Λ-shape (see Methods). Sticks indicate the time at which the sampled images were taken (also applies to panel F). f Upper: the endo-site base radius $r_{b}$ decreased in the course of an experimentally observed Λ→Ω endo-site base radius transition (each point from a frame in Supplementary Movie S8). Lower: examples of the observed Λ and Ω (green) and their computational fittings (red). $r_{b}$ (upper) was obtained from the fitting. g Schematic summary: actin filaments and dynamin generate a pulling force to mediate Flat→Λ transition; dynamin helix forms rings to surround and constrict Λ’s base and Ω’s pore, mediating Λ→Ω→O shape transition. Source data are provided as a Source Data file.