Curvature of double-membrane organelles generated by changes in membrane size and composition

Abstract

Transient double-membrane organelles are key players in cellular processes such as autophagy, reproduction, and viral infection. These organelles are formed by the bending and closure of flat, double-membrane sheets. Proteins are believed to be important in these morphological transitions but the underlying mechanism of curvature generation is poorly understood. Here, we describe a novel mechanism for this curvature generation which depends primarily on three membrane properties: the lateral size of the double-membrane sheets, the molecular composition of their highly curved rims, and a possible asymmetry between the two flat faces of the sheets. This mechanism is evolutionary advantageous since it does not require active processes and is readily available even when resources within the cell are restricted as during starvation, which can induce autophagy and sporulation. We identify pathways for protein-assisted regulation of curvature generation, organelle size, direction of bending, and morphology. Our theory also provides a mechanism for the stabilization of large double-membrane sheet-like structures found in the endoplasmic reticulum and in the Golgi cisternae.

Figure 1. Growth and fate of cup-shaped vesicles in cells.

Double-membrane sheets can be built by fusing small vesicles. The sheets grow to a critical size, bend and eventually close to form a double-membrane organelle, for intermediate states see Fig. 2. In the autophagosomal pathway, autophagosomes fuse with lysosomes. In the resulting autolysosome, the cytosolic content of the autophagosome becomes degraded together with the inner vesicle membrane. In the yeast sporulation pathway, a spore wall is synthesized between both membranes to build the prespore. The completed spore has only one membrane, because during spore wall assembly the outer membrane disintegrates.

Figure 2. Cellular double-membrane organelles at different stages of their genesis.

(A–D) electron microscopy micrographs, (E) schematic illustration of the sequence of shape changes, and (F) schematic cross section of the sheet with possible bending directions. (A) A growing double-membrane sheet during spore formation in Schizosaccharomyces pombe, . (B) A cup-shaped phagophore with immunogold label (black spots) for the mammalian Atg8 homologue GATE16 . (C) A closed autophagosome with the double membrane clearly visible . (D) A freeze-fracture electron micrograph showing the smooth autophagosomal membrane. In the upper right corner a small, particle-rich endosome had fused with the autophagosome ; the smooth surface of the autophagosome away from the fusion area suggests the absence of a protein coat. All scale bars correspond to 0.5 µm. The electron microscopy images were adapted with permissions of the J. Cell Sci. and Elsevier. (E) Schematic illustrations of the shape transition from a double-membrane sheet to a double-membrane vesicle (cross sections shown). The solid line represents one bilayer. Geometrical parameters used in the main text are indicated in the first cartoon. The transition between the flat sheet and the vesicle can be reversible. The final step of generating the double-membrane vesicle requires irreversible fission. (F) Schematic cross sections of the sheet and cup-shape morphologies. Three different segments of the shapes are distinguished: lower segment (1, dashed blue), upper segment (2, solid green), and highly curved rim (3, solid red). The sheet (middle) is characterized by zero mean curvatures of the upper and lower segments, M ₁ = M ₂ = 0. When the sheet bends downwards (left), the mean curvature of the lower segment is negative, M ₁<0, and that of the upper segment is positive, M ₂>0. The situation is reversed when the sheet bends upwards (right).

Figure 3. Reduced bending energy of double-membrane shapes,

, as a function of the reduced curvature r_sheetM ₁. The results are calculated for vanishing preferred or spontaneous curvatures m ₁ = m ₂ = m ₃ = 0 and vanishing curvature asymmetry m ₁₂ = 0; see Equation 8 in Text S1 for the definition of . The reduced curvature r_sheetM ₁ of the cup shapes can be positive or negative, which distinguishes between upward and downward bending of the sheet as schematically illustrated in the top row of the figure. For r_sheet/r_rim<5.1 the sheet represents the shape of minimal energy. At r_sheet/r_rim = 5.1 the flat sheet and the closed double-membrane vesicle are local minima with the same energy, but separated by a considerable energy barrier preventing the shape transition. Increasing the effective size of the vesicle decreases the barrier continuously. At the critical size, r_sheet/r_rim = 10.2, the energy barrier disappears and the sheet becomes unstable with respect to arbitrarily small perturbations, which transforms the sheet into a closed vesicle. Energy landscapes of asymmetric sheets with nonzero curvature asymmetry m ₁₂ are displayed in Fig. S3.

Figure 4. Stability diagram of double-membrane sheets as a function of preferred or spontaneous rim curvature m ₃ and sheet size r_sheet.

Both the rim curvature and sheet size are given in units of the rim curvature radius r_rim. The sheets are (almost) symmetric in the sense that their two faces have similar preferred curvatures, m ₁≅m ₂ and the curvature asymmetry m ₁₂ is small compared to 1/r_rim. The regime of stable sheets (gray area) is bounded by an instability line corresponding to the critical sheet size as described by Equation 10 in Text S1. The instability line has two branches for m₃r_rim<1/2 and m₃r_rim>1/2. For nonzero m ₁₂ the two branches meet at the maximal critical disk size as given by 2/|m₁₂|. The latter size diverges for vanishing curvature asymmetry m₁₂ = 0, i.e., in this case, an arbitrarily large sheet remains stable. If the sheet reaches the instability line by lateral growth, protein adsorption and/or desorption at its rim (long arrows), it closes into a double-membrane vesicle. Sheets above the instability line are unstable and close into such vesicles as well. The broken horizontal line with r_sheet/r_rim≅45 corresponds to the autophagosome in Fig. 2C with diameter r ⁰ _sheet≅900 nm and r_rim≅20 nm. The intersection of the broken line with the two branches of the instability line determines the preferred or spontaneous rim curvature m ₃≅1/(76 nm) or 1/(28 nm) (arrowheads) of the unstable sheet that preceded the autophagosome in Fig. 2C.