© 2005 Nature Publishing Group *Laboratory of Cellular and Molecular Biophysics, National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892-1855, USA.‡Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, 69978 Tel Aviv, Israel.e-mails: [email protected]; [email protected]:10.1038/nrm1784Published online15 November 2005The extraordinarily beautiful and complex shapes of cells and cell organelles are fashioned by the physical forces that operate on their membranes (FIG. 1). A fundamental problem of molecular cell biology in conjunction with physics and mathematics is to understand the evolution-ary, developmental and functional rationale for these shapes, as well as the mechanisms that are used by cells to produce them.Each shape evolved for specific physiological reasons1–3. Cells without internal membranes, such as prokaryotic cells and erythrocytes, can take on an array of shapes for their purposes. The corkscrew shape of spirochetes, which are long and slender bacte-ria (FIG. 1), might favour their penetration and packing into host cells, and the biconcave disc-like shape of erythrocytes guarantees the optimal surface-to-vol-ume ratio that is necessary for fast oxygen exchange between haemoglobin and the outside medium. Moreover, the ability of erythrocytes to change their shape easily in the hydrodynamic flow allows them to navigate within various blood vessels with varying flow rates. The plasma membranes of cells that have internal membranes undergo radical shape transfor-mations when they develop intercellular contacts, or spread and move on a substrate4. Even more complex shapes can be achieved by endothelial cells, the plasma membranes of which can develop internal tubes that span the cell volume5,6. In mathematical terms, the for-mation of each of these tubes changes the membrane topology7, progressively moving the surface to higher levels of shape complexity.Intracellular membranes are even more dynamic and varied in their shapes. For example, the endoplasmic reticulum (ER) and the Golgi apparatus are complex systems of interconnected tubules, cylinders and discs (FIG. 1), and intracellular transport intermediates have a broad range of shapes from small (~50 nm) spheres and narrow tubes to tubular–saccular carriers8–11.There are many questions about this dazzling array of shapes for which we do not know the answers. For example, why do the ER and Golgi have distinctly different shapes (FIG. 1), with the Golgi being much more saccular and fenestrated and the ER being more tubular with small cisternae? Both shapes maximize the surface area while keeping the internal volume low, which allows efficient and fast protein traffick-ing in and out of these organelles. But why are they different? Is it related to the fact that the Golgi sorts specific proteins for export to specific organelles and sites on the plasma membrane? Are there domains of lipids and proteins that form in the Golgi, but not in the ER, and that stabilize the strange fenestrated and interconnected Golgi stacks?To intelligently investigate such questions, which abound in cell biology, we must recognize that membrane curvature is generated as a result of a complex interplay between membrane proteins, lipids and physical forces that are applied to the membrane surface. Moreover, to control membrane curvature, cells must have sensors that feed back to the curvature-producing molecules. As the physical principles that underlie shape creation and sensing must be universal for all cells, the aim of this review is to describe these principles and consider their realization in one biological instance — intracellular membrane trafficking. Physical principles underlying membrane shapeThe surface of a cell, or cell organelle, is formed by a biological membrane. Therefore, the shape of a cell, or cell organelle, is determined by the membrane shape, How proteins produce cellular membrane curvatureJoshua Zimmerberg* and Michael M. Kozlov‡Abstract | Biological membranes exhibit various function-related shapes, and the mechanism by which these shapes are created is largely unclear. Here, we classify possible curvature-generating mechanisms that are provided by lipids that constitute the membrane bilayer and by proteins that interact with, or are embedded in, the membrane. We describe membrane elastic properties in order to formulate the structural and energetic requirements of proteins and lipids that would enable them to work together to generate the membrane shapes seen during intracellular trafficking.Nature Reviews Molecular Cell Biology | AOP, published online 15 November 2005; doi:10.1038/nrm1784REVIEWSNATURE REVIEWS | MOLECULAR CELL BIOLOGY ADVANCE ONLINE PUBLICATION | 1© 2005 Nature Publishing Group Golgi ribbonEndoplasmic reticulumGolgi bypassTra ns-GolgiRodsCocci A spirocheteabCoatomer proteinsCoat proteins that cover the cytoplasmic surfaces of coated vesicles that are involved in intracellular membrane trafficking at the endoplasmic reticulum and Golgi apparatus.DynaminA large, 100-kDa GTPase that has been shown to form helical oligomers on membrane surfaces and to tubulate membranes. Dynamin is thought to mediate the pinching off of clathrin-coated and other vesicles during endocytosis.Figure 1 | The beautiful and complex shapes of cells and cell organelles. a | These panels show the prokaryotic shapes of cocci, rods and a spirochete. These images are reproduced from REF. 88. b | The large image shows the stained endoplasmic reticulum of a 3T3 fibroblast cell as recorded by confocal microscopy. This image is reproduced with permission from REF. 89 © (1986) the Rockefeller University Press. From top to bottom, the three smaller images show a part of a tubular–saccular Golgi ribbon, an intracisternal connection of the Golgi (labelled Golgi bypass) and fenestrated Golgi forms (labelled trans-Golgi). These images were taken from an electron-micrograph tomography series. The Golgi ribbon image is reproduced with permission from REF. 90 © (2002) Macmillan Magazines Ltd, the Golgi bypass image is reproduced with permission from REF. 91© (2004) the National Academy of Sciences, and the tr ans-Golgi image is reproduced with permission from REF. 92 © (2004) Blackwell Publishing. and understanding the mechanisms that control cellu-lar shapes requires the geometrical and physics tools of membrane