Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

A cost–benefit analysis of the physical mechanisms of membrane curvature

Nature Cell Biology volume 15, pages 1019–1027 (2013)Cite this article

Subjects

Abstract

Many cellular membrane-bound structures exhibit distinct curvature that is driven by the physical properties of their lipid and protein constituents. Here we review how cells manipulate and control this curvature in the context of dynamic events such as vesicle-mediated membrane traffic. Lipids and cargo proteins each contribute energy barriers that must be overcome during vesicle formation. In contrast, protein coats and their associated accessory proteins drive membrane bending using a variety of interdependent physical mechanisms. We survey the energy costs and drivers involved in membrane curvature, and draw a contrast between the stochastic contributions of molecular crowding and the deterministic assembly of protein coats. These basic principles also apply to other cellular examples of membrane bending events, including important disease-related problems such as viral egress.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Cellular sites of membrane curvature.
Figure 2: Steric effects during membrane curvature.
Figure 3: Energetics of coated vesicle formation.

Similar content being viewed by others

References

  1. McMahon, H. T. & Gallop, J. L. Membrane curvature and mechanisms of dynamic cell membrane remodelling. Nature 438, 590–596 (2005).

    CAS  PubMed  Google Scholar 

  2. Bigay, J. & Antonny, B. Curvature, lipid packing, and electrostatics of membrane organelles: defining cellular territories in determining specificity. Dev. Cell 23, 886–895 (2012).

    CAS  PubMed  Google Scholar 

  3. Zimmerberg, J. & Kozlov, M. M. How proteins produce cellular membrane curvature. Nat. Rev. Mol. Cell Biol. 7, 9–19 (2006).

    CAS  PubMed  Google Scholar 

  4. Canham, P. B. The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. J. Theoret. Biol. 26, 61–81 (1970).

    CAS  Google Scholar 

  5. Helfrich, W. Elastic properties of lipid bilayers: theory and possible experiments. Biochem. Biophys. Biol. Virol. 28, 693–703 (1973).

    CAS  Google Scholar 

  6. Aghamohammadzadeh, S. & Ayscough, K. R. Differential requirements for actin during yeast and mammalian endocytosis. Nat. Cell Biol. 11, 1039–1042 (2009).

    CAS  PubMed  Google Scholar 

  7. Boulant, S., Kural, C., Zeeh, J. C., Ubelmann, F. & Kirchhausen, T. Actin dynamics counteract membrane tension during clathrin-mediated endocytosis. Nat. Cell Biol. 13, 1124–1131 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  8. Svetina, S. & Zeks, B. Membrane bending energy and shape determination of phospholipid vesicles and red blood cells. Eur. Biophys. J. 17, 101–111 (1989).

    CAS  PubMed  Google Scholar 

  9. Fuller, N. & Rand, R. P. The influence of lysolipids on the spontaneous curvature and bending elasticity of phospholipid membranes. Biophys. J. 81, 243–254 (2001).

    CAS  PubMed  PubMed Central  Google Scholar 

  10. Takamori, S. et al. Molecular anatomy of a trafficking organelle. Cell 127, 831–846 (2006).

    CAS  PubMed  Google Scholar 

  11. Fujita, M. & Kinoshita, T. GPI-anchor remodeling: potential functions of GPI-anchors in intracellular trafficking and membrane dynamics. Biochim. Biophys. Acta 1821, 1050–1058 (2012).

    CAS  PubMed  Google Scholar 

  12. Sheetz, M. P. & Singer, S. J. Biological membranes as bilayer couples. A molecular mechanism of drug-erythrocyte interactions. Proc. Natl Acad. Sci. USA 71, 4457–4461 (1974).

    CAS  PubMed  PubMed Central  Google Scholar 

  13. Decher, G. et al. Interaction of amphiphilic polymers with model membranes. Angew. Makromol. Chem. 166, 71–80 (1989).

    Google Scholar 

  14. Stachowiak, J. C., Hayden, C. C. & Sasaki, D. Y. Steric confinement of proteins on lipid membranes can drive curvature and tubulation. Proc. Natl Acad. Sci. USA 107, 7781–7786 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  15. Copic, A., Latham, C. F., Horlbeck, M. A., D'Arcangelo, J. G. & Miller, E. A. ER cargo properties specify a requirement for COPII coat rigidity mediated by Sec13p. Science 335, 1359–1362 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  16. Sharpe, H. J., Stevens, T. J. & Munro, S. A comprehensive comparison of transmembrane domains reveals organelle-specific properties. Cell 142, 158–169 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  17. Roth, T. F. & Porter, K. R. Yolk protein uptake in the oocyte of the mosquito Aedes aegypti L. J. Cell Biol. 20, 313–332 (1964).

    CAS  PubMed  PubMed Central  Google Scholar 

  18. Pearse, B. M. & Crowther, R. A. Structure and assembly of coated vesicles. Annu. Rev. Biophys. Biophys. Chem. 16, 49–68 (1987).

    CAS  PubMed  Google Scholar 

  19. Thomas, P. D. & Poznansky, M. J. Curvature and composition-dependent lipid asymmetry in phosphatidylcholine vesicles containing phosphatidylethanolamine and gangliosides. Biochim. Biophys. Acta 978, 85–90 (1989).

    CAS  PubMed  Google Scholar 

  20. Goni, F. M. & Alonso, A. Biophysics of sphingolipids, I. Membrane properties of sphingosine, ceramides and other simple sphingolipids. Biochim. Biophys. Acta 1758, 1902–1921 (2006).

    CAS  PubMed  Google Scholar 

  21. Hailey, D. W. et al. Mitochondria supply membranes for autophagosome biogenesis during starvation. Cell 141, 656–667 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  22. Yang, J. S. et al. A role for phosphatidic acid in COPI vesicle fission yields insights into Golgi maintenance. Nat. Cell Biol. 10, 1146–1153 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  23. Gall, W. E. et al. Drs2p-dependent formation of exocytic clathrin-coated vesicles in vivo. Curr. Biol. 12, 1623–1627 (2002).

    CAS  PubMed  Google Scholar 

  24. Zha, X. et al. Sphingomyelinase treatment induces ATP-independent endocytosis. J. Cell Biol. 140, 39–47 (1998).

    CAS  PubMed  PubMed Central  Google Scholar 

  25. Leibler, S. Curvature instability in membranes. J. Phys. 47, 507–516 (1986).

    CAS  Google Scholar 

  26. Ford, M. G. et al. Curvature of clathrin-coated pits driven by epsin. Nature 419, 361–366 (2002).

    CAS  PubMed  Google Scholar 

  27. Lee, M. C. S. et al. Sar1p N-terminal helix initiates membrane curvature and completes the fission of a COPII vesicle. Cell 122, 605–617 (2005).

    CAS  PubMed  Google Scholar 

  28. Lundmark, R., Doherty, G. J., Vallis, Y., Peter, B. J. & McMahon, H. T. Arf family GTP loading is activated by, and generates, positive membrane curvature. Biochem. J. 414, 189–194 (2008).

    CAS  PubMed  Google Scholar 

  29. Krauss, M. et al. Arf1-GTP-induced tubule formation suggests a function of Arf family proteins in curvature acquisition at sites of vesicle budding. J. Biol. Chem. 283, 27717–27723 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  30. Campelo, F., McMahon, H. T. & Kozlov, M. M. The hydrophobic insertion mechanism of membrane curvature generation by proteins. Biophys. J. 95, 2325–2339 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  31. Stachowiak, J. C. et al. Membrane bending by protein-protein crowding. Nat. Cell Biol. 14, 944–949 (2012).

    CAS  PubMed  Google Scholar 

  32. Dannhauser, P. N. & Ungewickell, E. J. Reconstitution of clathrin-coated bud and vesicle formation with minimal components. Nat. Cell Biol. 14, 634–639 (2012).

    CAS  PubMed  Google Scholar 

  33. Settles, E. I., Loftus, A. F., McKeown, A. N. & Parthasarathy, R. The vesicle trafficking protein Sar1 lowers lipid membrane rigidity. Biophys. J. 99, 1539–1545 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  34. Bigay, J., Gounon, P., Robineau, S. & Antonny, B. Lipid packing sensed by ArfGAP1 couples COPI coat disassembly to membrane bilayer curvature. Nature 426, 563–566 (2003).

    CAS  PubMed  Google Scholar 

  35. Tsafrir, I., Caspi, Y., Guedeau-Boudeville, M. A., Arzi, T. & Stavans, J. Budding and tubulation in highly oblate vesicles by anchored amphiphilic molecules. Phys. Rev. Lett. 91, 138102 (2003).

    PubMed  Google Scholar 

  36. Lipowsky, R. Bending of membranes by anchored polymers. Europhys. Lett. 30, 197–202 (1995).

    CAS  Google Scholar 

  37. Kim, Y. W. & Sung, W. Y. Membrane curvature induced by polymer adsorption. Phys. Rev. E 63, 041910 (2001).

    CAS  Google Scholar 

  38. Imjeti, N. S. et al. N-Glycosylation instead of cholesterol mediates oligomerization and apical sorting of GPI-APs in FRT cells. Mol. Biol. Cell 22, 4621–4634 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  39. Tooze, S. A., Martens, G. J. & Huttner, W. B. Secretory granule biogenesis: rafting to the SNARE. Trends Cell Biol. 11, 116–122 (2001).

    CAS  PubMed  Google Scholar 

  40. Vennema, H. et al. Nucleocapsid-independent assembly of coronavirus-like particles by co-expression of viral envelope protein genes. EMBO J. 15, 2020–2028 (1996).

    CAS  PubMed  PubMed Central  Google Scholar 

  41. Wang, C. W., Hamamoto, S., Orci, L. & Schekman, R. Exomer: A coat complex for transport of select membrane proteins from the trans-Golgi network to the plasma membrane in yeast. J. Cell Biol. 174, 973–983 (2006).

    CAS  PubMed  PubMed Central  Google Scholar 

  42. Shibata, Y. et al. The reticulon and DP1/Yop1p proteins form immobile oligomers in the tubular endoplasmic reticulum. J. Biol. Chem. 283, 18892–18904 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  43. Walser, P. J. et al. Constitutive formation of caveolae in a bacterium. Cell 150, 752–763 (2012).

    CAS  PubMed  Google Scholar 

  44. Hu, J. et al. Membrane proteins of the endoplasmic reticulum induce high-curvature tubules. Science 319, 1247–1250 (2008).

    CAS  PubMed  Google Scholar 

  45. Stagg, S. M. et al. Structure of the Sec13/31 COPII coat cage. Nature 439, 234–238 (2006).

    CAS  PubMed  Google Scholar 

  46. Faini, M. et al. The structures of COPI-coated vesicles reveal alternate coatomer conformations and interactions. Science 336, 1451–1454 (2012).

    CAS  PubMed  Google Scholar 

  47. Darsow, T., Katzmann, D. J., Cowles, C. R. & Emr, S. D. Vps41p function in the alkaline phosphatase pathway requires homo-oligomerization and interaction with AP-3 through two distinct domains. Mol. Biol. Cell 12, 37–51 (2001).

    CAS  PubMed  PubMed Central  Google Scholar 

  48. Bielli, A. et al. Regulation of Sar1 NH2 terminus by GTP binding and hydrolysis promotes membrane deformation to control COPII vesicle fission. J. Cell Biol. 171, 919–924 (2005).

    CAS  PubMed  PubMed Central  Google Scholar 

  49. Brodsky, F. M. Diversity of clathrin function: new tricks for an old protein. Annu. Rev. Cell Dev. Biol. 28, 309–336 (2012).

    CAS  PubMed  Google Scholar 

  50. Luo, Y., Zhan, Y. & Keen, J. H. Arf6 regulation of gyrating-clathrin. Traffic 14, 97–106 (2012).

    PubMed  PubMed Central  Google Scholar 

  51. Wakeham, D. E., Chen, C. Y., Greene, B., Hwang, P. K. & Brodsky, F. M. Clathrin self-assembly involves coordinated weak interactions favorable for cellular regulation. EMBO J. 22, 4980–4990 (2003).

    CAS  PubMed  PubMed Central  Google Scholar 

  52. Den Otter, W. K. & Briels, W. J. The generation of curved clathrin coats from flat plaques. Traffic 12, 1407–1416 (2011).

    CAS  PubMed  Google Scholar 

  53. Nossal, R. Energetics of clathrin basket assembly. Traffic 2, 138–147 (2001).

    CAS  PubMed  Google Scholar 

  54. Antonny, B., Madden, D., Hamamoto, S., Orci, L. & Schekman, R. Dynamics of the COPII coat with GTP and stable analogues. Nat. Cell Biol. 3, 531–537 (2001).

    CAS  PubMed  Google Scholar 

  55. Townley, A. K. et al. Efficient coupling of Sec23–Sec24 to Sec13–Sec31 drives COPII-dependent collagen secretion and is essential for normal craniofacial development. J. Cell Sci. 121, 3025–3034 (2008).

    CAS  PubMed  Google Scholar 

  56. Malhotra, V. & Erlmann, P. Protein export at the ER: loading big collagens into COPII carriers. EMBO J. 30, 3475–3480 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  57. Huang, F. & Sorkin, A. Growth factor receptor binding protein 2-mediated recruitment of the RING domain of Cbl to the epidermal growth factor receptor is essential and sufficient to support receptor endocytosis. Mol. Biol. Cell 16, 1268–1281 (2005).

    CAS  PubMed  PubMed Central  Google Scholar 

  58. Ferreira, F. et al. Endocytosis of G protein-coupled receptors is regulated by clathrin light chain phosphorylation. Curr. Biol. 22, 1361–1370 (2012).

    CAS  PubMed  Google Scholar 

  59. Kukulski, W., Schorb, M., Kaksonen, M. & Briggs, J. A. G. Plasma membrane reshaping during endocytosis is revealed by time-resolved electron tomography. Cell 150, 508–520 (2012).

    CAS  PubMed  Google Scholar 

  60. Collins, A., Warrington, A., Taylor, K. A. & Svitkina, T. Structural organization of the actin cytoskeleton at sites of clathrin-mediated endocytosis. Curr. Biol. 21, 1167–1175 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  61. Idrissi, F. Z., Blasco, A., Espinal, A. & Geli, M. I. Ultrastructural dynamics of proteins involved in endocytic budding. Proc. Natl Acad. Sci. USA 109, E2587–2594 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  62. Fujimoto, L. M., Roth, R., Heuser, J. E. & Schmid, S. L. Actin assembly plays a variable, but not obligatory role in receptor-mediated endocytosis in mammalian cells. Traffic 1, 161–171 (2000).

    CAS  PubMed  Google Scholar 

  63. Saffarian, S., Cocucci, E. & Kirchhausen, T. Distinct dynamics of endocytic clathrin-coated pits and coated plaques. PLoS Biol. 7, e1000191 (2009).

    PubMed  PubMed Central  Google Scholar 

  64. Bonazzi, M. et al. Clathrin phosphorylation is required for actin recruitment at sites of bacterial adhesion and internalization. J. Cell Biol. 195, 525–536 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  65. Cureton, D. K., Massol, R. H., Whelan, S. P. & Kirchhausen, T. The length of vesicular stomatitis virus particles dictates a need for actin assembly during clathrin-dependent endocytosis. PLoS Pathog. 6, e1001127 (2010).

    PubMed  PubMed Central  Google Scholar 

  66. Hansen, C. G. & Nichols, B. J. Exploring the caves: cavins, caveolins and caveolae. Trends Cell Biol. 20, 177–186 (2010).

    CAS  PubMed  Google Scholar 

  67. Karpova, T. S. et al. Role of actin and Myo2p in polarized secretion and growth of Saccharomyces cerevisiae. Mol. Biol. Cell 11, 1727–1737 (2000).

    CAS  PubMed  PubMed Central  Google Scholar 

  68. Zech, T., Calaminus, S. D. & Machesky, L. M. Actin on trafficking: Could actin guide directed receptor transport? Cell Adh. Migr. 6, 476–481 (2012).

    PubMed  PubMed Central  Google Scholar 

  69. Campelo, F. & Malhotra, V. Membrane fission: the biogenesis of transport carriers. Annu. Rev. Biochem. 81, 407–427 (2012).

    CAS  PubMed  Google Scholar 

  70. Ferguson, S. M. & De Camilli, P. Dynamin, a membrane-remodelling GTPase. Nat. Rev. Mol. Cell Biol. 13, 75–88 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  71. Schmid, S. L. & Frolov, V. A. Dynamin: functional design of a membrane fission catalyst. Annu. Rev. Cell Dev. Biol. 27, 79–105 (2011).

    CAS  PubMed  Google Scholar 

  72. Boucrot, E. et al. Membrane fission is promoted by insertion of amphipathic helices and is restricted by crescent BAR domains. Cell 149, 124–136 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  73. Rawicz, W., Olbrich, K. C., McIntosh, T., Needham, D. & Evans, E. Effect of chain length and unsaturation on elasticity of lipid bilayers. Biophys. J. 79, 328–339 (2000).

    CAS  PubMed  PubMed Central  Google Scholar 

  74. Evans, E. & Rawicz, W. Entropy-driven tension and bending elasticity in condensed-fluid membranes. Phys. Rev. Lett. 64, 2094–2097 (1990).

    CAS  PubMed  Google Scholar 

  75. Van Meer, G., Voelker, D. R. & Feigenson, G. W. Membrane lipids: where they are and how they behave. Nat. Rev. Mol. Cell Biol. 9, 112–124 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  76. Hochmuth, F. M., Shao, J. Y., Dai, J. & Sheetz, M. P. Deformation and flow of membrane into tethers extracted from neuronal growth cones. Biophys. J. 70, 358–369 (1996).

    CAS  PubMed  PubMed Central  Google Scholar 

  77. Liu, J., Kaksonen, M., Drubin, D. G. & Oster, G. Endocytic vesicle scission by lipid phase boundary forces. Proc. Natl Acad. Sci. USA 103, 10277–10282 (2006).

    CAS  PubMed  PubMed Central  Google Scholar 

  78. Sankaranarayanan, S., Atluri, P. P. & Ryan, T. A. Actin has a molecular scaffolding, not propulsive, role in presynaptic function. Nat. Neurosci. 6, 127–135 (2003).

    CAS  PubMed  Google Scholar 

  79. Cocucci, E., Aguet, F., Boulant, S. & Kirchhausen, T. The first five seconds in the life of a clathrin-coated pit. Cell 150, 495–507 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  80. Mehlert, A., Wormald, M. R. & Ferguson, M. A. Modeling of the N-glycosylated transferrin receptor suggests how transferrin binding can occur within the surface coat of Trypanosoma brucei. PLoS Pathog. 8, e1002618 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  81. Zhang, F., Zang, T., Wilson, S. J., Johnson, M. C. & Bieniasz, P. D. Clathrin facilitates the morphogenesis of retrovirus particles. PLoS Pathog. 7, e1002119 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  82. Johnson, D. C. & Baines, J. D. Herpesviruses remodel host membranes for virus egress. Nat. Rev. Microbiol. 9, 382–394 (2011).

    CAS  PubMed  Google Scholar 

  83. Fotin, A. et al. Molecular model for a complete clathrin lattice from electron cryomicroscopy. Nature 432, 573–579 (2004).

    CAS  PubMed  Google Scholar 

  84. Hierro, A. et al. Functional architecture of the retromer cargo-recognition complex. Nature 449, 1063–1067 (2007).

    CAS  PubMed  PubMed Central  Google Scholar 

  85. Tanaka-Takiguchi, Y., Kinoshita, M. & Takiguchi, K. Septin-mediated uniform bracing of phospholipid membranes. Curr. Biol. 19, 140–145 (2009).

    CAS  PubMed  Google Scholar 

  86. Effantin, G. et al. ESCRT-III CHMP2A and CHMP3 form variable helical polymers in vitro and act synergistically during HIV-1 budding. Cell. Microbiol. 15, 213–226 (2013).

    CAS  PubMed  Google Scholar 

  87. Carnahan, N. F. & Starling, K. E. Equation of state for nonattracting rigid spheres. J. Chem. Phys. 51, 635 (1969).

    CAS  Google Scholar 

  88. Song, Y. H., Mason, E. A. & Stratt, R. M. Why does the Carnahan-Starling equation work so well. J. Phys Chem 93, 6916–6919 (1989).

    CAS  Google Scholar 

  89. Scheve, C. S., Gonzales, P. A., Momin, N. & Stachowiak, J. C. Steric pressure between membrane-bound proteins opposes lipid phase separation. J. Am. Chem. Soc. 135, 1185–1188 (2013).

    CAS  PubMed  Google Scholar 

  90. Blondeau, F. et al. Tandem MS analysis of brain clathrin-coated vesicles reveals their critical involvement in synaptic vesicle recycling. Proc. Natl Acad. Sci. USA 101, 3833–3838 (2004).

    CAS  PubMed  PubMed Central  Google Scholar 

Download references

Acknowledgements

J.C.S. acknowledges funding from the University of Texas Austin Cockrell School of Engineering and the Texas 4000 Cancer Seed Grant Program. F.M.B. and E.A.M. acknowledge support from the National Institute of General Medical Science of the National Institutes of Health under award numbers R01GM038093 (F.M.B.), R01GM078186 (E.A.M.) and R01GM085089 (E.A.M.). We thank M. C. S. Lee (Columbia University), E. Schmid (University of California, Berkeley), C. Hayden (Sandia National Laboratories) and E. Lafer (University of Texas Health Science Center) for thoughtful discussions and comments on the manuscript.

Author information

Authors and Affiliations

  1. Jeanne C. Stachowiak is in the Department of Biomedical Engineering, Institute for Cellular and Molecular Biology, University of Texas at Austin, Austin, Texas 78712, USA,

    Jeanne C. Stachowiak

  2. Frances M. Brodsky is in the Departments of Bioengineering and Therapeutic Sciences, Pharmaceutical Chemistry and Microbiology and Immunology, The G.W. Hooper Foundation, University of California, San Francisco, California 94143, USA,

    Frances M. Brodsky

  3. Elizabeth A. Miller is in the Department of Biological Sciences, Columbia University, New York, New York 10027, USA,

    Elizabeth A. Miller

Authors
  1. Jeanne C. Stachowiak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Frances M. Brodsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Elizabeth A. Miller
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Elizabeth A. Miller.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stachowiak, J., Brodsky, F. & Miller, E. A cost–benefit analysis of the physical mechanisms of membrane curvature. Nat Cell Biol 15, 1019–1027 (2013). https://doi.org/10.1038/ncb2832

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/ncb2832

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing