Skip to main content

Thank you for visiting 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.

DNA rendering of polyhedral meshes at the nanoscale


It was suggested1 more than thirty years ago that Watson–Crick base pairing might be used for the rational design of nanometre-scale structures from nucleic acids. Since then, and especially since the introduction of the origami technique2, DNA nanotechnology has enabled increasingly more complex structures3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18. But although general approaches for creating DNA origami polygonal meshes and design software are available14,16,17,19,20,21, there are still important constraints arising from DNA geometry and sense/antisense pairing, necessitating some manual adjustment during the design process. Here we present a general method of folding arbitrary polygonal digital meshes in DNA that readily produces structures that would be very difficult to realize using previous approaches. The design process is highly automated, using a routeing algorithm based on graph theory and a relaxation simulation that traces scaffold strands through the target structures. Moreover, unlike conventional origami designs built from close-packed helices, our structures have a more open conformation with one helix per edge and are therefore stable under the ionic conditions usually used in biological assays.

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

Access options

Rent or buy this article

Prices vary by article type



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

Figure 1: Design paradigm and automated workflow for scaffold-routeing sequence design of origami 3D meshes.
Figure 2: 3D meshes rendered in DNA.
Figure 3: Cryo-electron microscopy reveals the hollow characteristics and details of polyhedral meshes.
Figure 4: Mesh origami folds in and is fully stable in physiological buffers.


  1. Seeman, N. C. Nucleic-acid junctions and lattices. J. Theor. Biol. 99, 237–247 (1982)

    Article  CAS  Google Scholar 

  2. Rothemund, P. W. K. Folding DNA to create nanoscale shapes and patterns. Nature 440, 297–302 (2006)

    Article  CAS  ADS  Google Scholar 

  3. Chen, J. H. & Seeman, N. C. Synthesis from DNA of a molecule with the connectivity of a cube. Nature 350, 631–633 (1991)

    Article  CAS  ADS  Google Scholar 

  4. Rothemund, P. W. K., Papadakis, N. & Winfree, E. Algorithmic self-assembly of DNA Sierpinski triangles. PLoS Biol. 2, e424 (2004)

    Article  Google Scholar 

  5. He, Y., Tian, Y., Ribbe, A. E. & Mao, C. Highly connected two-dimensional crystals of DNA six-point-stars. J. Am. Chem. Soc. 128, 15978–15979 (2006)

    Article  CAS  Google Scholar 

  6. Shih, W. M., Quispe, J. D. & Joyce, G. F. A 1.7-kilobase single-stranded DNA that folds into a nanoscale octahedron. Nature 427, 618–621 (2004)

    Article  CAS  ADS  Google Scholar 

  7. Goodman, R. P. et al. Rapid chiral assembly of rigid DNA building blocks for molecular nanofabrication. Science 310, 1661–1665 (2005)

    Article  CAS  ADS  Google Scholar 

  8. Bhatia, D. et al. Icosahedral DNA nanocapsules by modular assembly. Angew. Chem. Int. Edn Engl. 48, 4134–4137 (2009)

    Article  CAS  Google Scholar 

  9. Geary, C., Rothemund, P. W. K. & Andersen, E. S. A single-stranded architecture for cotranscriptional folding of RNA nanostructures. Science 345, 799–804 (2014)

    Article  CAS  ADS  Google Scholar 

  10. List, J., Weber, M. & Simmel, F. C. Hydrophobic actuation of a DNA origami bilayer structure. Angew. Chem. Int. Edn Engl. 53, 4236–4239 (2014)

    Article  CAS  Google Scholar 

  11. Andersen, E. S. et al. Self-assembly of a nanoscale DNA box with a controllable lid. Nature 459, 73–76 (2009)

    Article  CAS  ADS  Google Scholar 

  12. Marchi, A. N., Saaem, I., Vogen, B. N., Brown, S. & LaBean, T. H. Toward larger DNA origami. Nano Lett. 14, 5740–5747 (2014)

    Article  CAS  ADS  Google Scholar 

  13. Ke, Y. et al. Scaffolded DNA origami of a DNA tetrahedron molecular container. Nano Lett. 9, 2445–2447 (2009)

    Article  CAS  ADS  Google Scholar 

  14. Douglas, S. M. et al. Self-assembly of DNA into nanoscale three-dimensional shapes. Nature 459, 414–418 (2009)

    Article  CAS  ADS  Google Scholar 

  15. Dietz, H., Douglas, S. & Shih, W. M. Folding DNA into twisted and curved nanoscale shapes. Science 325, 725 (2009)

    Article  CAS  ADS  Google Scholar 

  16. Han, D. et al. DNA gridiron nanostructures based on four-arm junctions. Science 339, 1412–1415 (2013)

    Article  CAS  ADS  Google Scholar 

  17. Iinuma, R. et al. Polyhedra self-assembled from DNA tripods and characterized with 3D DNA-PAINT. Science 344, 65–69 (2014)

    Article  CAS  ADS  Google Scholar 

  18. Liedl, T., Högberg, B., Tytell, J., Ingber, D. E. & Shih, W. M. Self-assembly of three-dimensional prestressed tensegrity structures from DNA. Nature Nanotechnol. 5, 520–524 (2010)

    Article  CAS  ADS  Google Scholar 

  19. Rothemund, P. W. K. in Nanotechnology: Science and Computation (eds Chen, J., Jonoska, N. & Rozenberg, G. ) 3–21 (Springer, 2006)

    Book  Google Scholar 

  20. Ellis-Monaghan, J. A., McDowell, A., Moffatt, I. & Pangborn, G. DNA origami and the complexity of Eulerian circuits with turning costs. Natural Comput. (2014)

  21. Douglas, S. M. et al. Rapid prototyping of 3D DNA-origami shapes with caDNAno. Nucleic Acids Res. 37, 5001–5006 (2009)

    Article  CAS  Google Scholar 

  22. Edmonds, J. & Johnson, E. L. Matching, Euler tours and the Chinese postman. Math. Program. 5, 88–124 (1973)

    Article  MathSciNet  Google Scholar 

  23. Døvling Andersen, L. & Fleischner, H. The NP-completeness of finding A-trails in Eulerian graphs and of finding spanning trees in hypergraphs. Discrete Appl. Math. 59, 203–214 (1995)

    Article  MathSciNet  Google Scholar 

  24. Martin, T. G. & Dietz, H. Magnesium-free self-assembly of multi-layer DNA objects. Nature Commun. 3, 1103 (2012)

    Article  ADS  Google Scholar 

  25. Hahn, J., Wickham, S. F. J., Shih, W. M. & Perrault, S. D. Addressing the instability of DNA nanostructures in tissue culture. ACS Nano 8, 8765–8775 (2014)

    Article  CAS  Google Scholar 

  26. Gradišar, H. et al. Design of a single-chain polypeptide tetrahedron assembled from coiled-coil segments. Nature Chem. Biol. 9, 362–366 (2013)

    Article  Google Scholar 

  27. Ducani, C., Kaul, C., Moche, M., Shih, W. M. & Högberg, B. Enzymatic production of ‘monoclonal stoichiometric’ single-stranded DNA oligonucleotides. Nature Methods 10, 647–652 (2013)

    Article  CAS  Google Scholar 

  28. Shaw, A. et al. Spatial control of membrane receptor function using ligand nanocalipers. Nature Methods 11, 841–846 (2014)

    Article  CAS  Google Scholar 

  29. Douglas, S. M., Bachelet, I. & Church, G. M. A logic-gated nanorobot for targeted transport of molecular payloads. Science 335, 831–834 (2012)

    Article  CAS  ADS  Google Scholar 

  30. Amir, Y. et al. Universal computing by DNA origami robots in a living animal. Nature Nanotechnol. 9, 353–357 (2014)

    Article  CAS  ADS  Google Scholar 

  31. Cromwell, P. R. Polyhedra 476 (Cambridge Univ. Press, 1999)

    MATH  Google Scholar 

  32. Jungnickel, D. Graphs, Networks and Algorithms Vol. 8, 695 (Springer, 2012)

    Google Scholar 

  33. Boyer, J. M. & Myrvold, W. J. On the cutting edge: simplified O(n) planarity by edge addition. J. Graph Algorithms Appl. 8, 241–273 (2004)

    Article  MathSciNet  Google Scholar 

  34. Ziegler, G. M. Lectures on Polytopes 370 (Springer, 1995)

    Book  Google Scholar 

  35. Fleischner, J. & Fleischner, H. Eulerian Graphs and Related Topics Part 1, Vol. 1, 407 (Elsevier, 1990)

    MATH  Google Scholar 

  36. Andersen, L. D., Fleischner, H. & Regner, S. Algorithms and outerplanar conditions for A-trails in plane Eulerian graphs. Discrete Appl. Math. 85, 99–112 (1998)

    Article  MathSciNet  Google Scholar 

  37. Bent, S. W. & Manber, U. On non-intersecting Eulerian circuits. Discrete Appl. Math. 18, 87–94 (1987)

    Article  MathSciNet  Google Scholar 

  38. Tsai, M.-T. & West, D. B. A new proof of 3-colorability of Eulerian triangulations. Ars Math. Contemp. 4, 1 (2011)

    Article  MathSciNet  Google Scholar 

  39. Ortiz-Lombardia, M. et al. Crystal structure of a DNA Holliday junction. Nature Struct. Biol. 6, 913–917 (1999)

    Article  CAS  Google Scholar 

  40. Kremer, J. R., Mastronarde, D. N. & McIntosh, J. R. Computer visualization of three-dimensional image data using IMOD. J. Struct. Biol. 116, 71–76 (1996)

    Article  CAS  Google Scholar 

  41. Cherepanova, A. et al. Immunochemical assay for deoxyribonuclease activity in body fluids. J. Immunol. Methods 325, 96–103 (2007)

    Article  CAS  Google Scholar 

Download references


This work was funded through grants from the Swedish Research Council (grants 2010-5060 and 2013-5883 to B.H.), the Swedish Foundation for Strategic Research (grant FFL12-0219 to B.H.) and the Knut and Alice Wallenberg foundation (Academy Fellow grant KAW2014.0241 to B.H.). E.B. was also funded by a Wallenberg Scholars grant to O. Inganäs. The work of A.M. was supported by the Helsinki Doctoral Education Network on Information and Communications Technology. We acknowledge the computational resources provided by the Aalto Science-IT project and the use of the Facility for EM Tomography at the Karolinska Institutet. A.M., E.C. and P.O. thank G. García Pérez for help in implementing early variants of the scaffold routing software. We thank P. Kumar Areddy (Karolinska Institutet) and A.-L. Bank Kodal and K. Gothelf (Aarhus University) for help with early experimental testing.

Author information

Authors and Affiliations



B.H. conceived and designed the study. P.O., E.C. and A.M. performed the theoretical work. E.B. performed the experimental work. A.M. performed most of the algorithm implementation. J.G. collaborated on the algorithm implementation and implemented the relaxation method and the vHelix plug-in. S.M. performed the cryo-electron tomography and tomography with help from E.B. All authors contributed to the writing of the manuscript.

Corresponding author

Correspondence to Björn Högberg.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Comparison with previous strategy for polygonal DNA origami.

a, Previous strategies for folding polygonal DNA origami have relied on folding the circular single-stranded DNA into a tree-like shape, where each branch is composed of an even number of helices (two in this illustration), these branches are then connected using helper joins as in b, where staple strands (in blue) bridge the gap between the distant parts of the scaffold, to yield the final polyhedral structure: the tetrahedron to the right in this example. c, The target shape and its flattened Schlegel representation. d, Previous methods have introduced helper joins in N − 1 of the edges, where N is the number of faces in the structure. Notably, the structures presented in this work would require on the order of 100 helper joins. A large number of helper joins is commonly believed to increase aggregation problems owing to the sticky ends produced as intermediates during folding. e, The strategy presented in this work. The goal is to route the entire scaffold through all the edges of the mesh, without crossing and with preferably only one traverse per edge. *It turns out that one helix per edge is not possible for all meshes (as described in the main text, Fig. 1 and in Supplementary Note 1). Odd-degree vertices require some edges to be traversed twice by the scaffold routeing.

Extended Data Figure 2 An overview of vHelix.

To be able to work with non-canonical origami designs, we implemented software that would allow free-form manipulation of helices directly in 3D space. The software was implemented as a plug-in for Autodesk Maya (several versions) and is available at The associated source code can be found at a, The interface in vHelix when viewing the design of the ball structure. b The ‘Helix’ menu provides most of the functionality, such as the ability to create new helices, disconnect and connect bases. c, Close-up of a connected vertex. Selecting a base shows its associated connectivity by highlighting all connected bases and displaying the associated sequence if a sequence has been applied. d, Using the “apply sequence” command to one of the strands (the scaffold), the plug-in calculates the sequence of all paired bases (on the staple strands) and subsequently the command “export strands” generates a spreadsheet file containing the staple-strand sequences. The physical dimensions of the DNA model follows what is usually used in DNA nanotechnology design processes (that is, a 2-nm helical radius, a 0.334-nm rise, a 34.286° pitch and a 155° minor groove). e, Overlaying the model with crystallography data from the literature39 shows that the model fits natural DNA well.

Extended Data Figure 3 Design pipeline overview.

a, We started the designs in Autodesk Maya, importing or modelling our own 3D polygon mesh object. b, The triangulation step is not mandatory because the scaffold routeing and further processing is not limited to triangulated meshes, but it is used for all structures reported here to achieve extra rigidity by triangulation. Steps ce are implemented as a series of scripts that process the mesh exported from the 3D design software. c, All odd-degree vertices are joined by helper edges using a minimum weight perfect matching algorithm (see Supplementary Note 1). d, The re-conditioned mesh is fed to a script implementing the A-trails routeing algorithm (see Supplementary Note 1). e, After scaffold routeing, the physical relaxation model reads the routed path. Up until now, the mesh has been treated as an abstract graph; in the relaxation step, however, an input is required to set the physical size of the desired DNA rendering, that is, the user sets a scaling value to fit the mesh to the scaffold available for the folding. The relaxation simulation and length-modification scheme (described in more detail in Supplementary Note 2) will rotate and shorten/lengthen some edges to find an overall best fit to the desired 3D shape while accounting for strain between nucleotides in the vertices. The output of the relaxation/length modification optimization is a file readable by vHelix, a plug-in for Autodesk Maya. f, As the file is imported into vHelix, the user has the option of automatically positioning staple-strand break-points by stating parameters for maximum staple length and the minimum length of edges with breakpoints. Alternatively, the staple-strand breakpoints can be edited manually in vHelix after importing. g, The DNA sequences of all staple strands given a scaffold input is calculated and exported to a spreadsheet by vHelix. h, The mixing of staple strands and scaffold is done by hand but a pipetting robot could conceivably also make this last step highly automated.

Supplementary information

Supplementary Information

This file contains Supplementary Notes 1–2, Supplementary Figures 1–26 and Supplementary Tables 1–8. (PDF 18428 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Benson, E., Mohammed, A., Gardell, J. et al. DNA rendering of polyhedral meshes at the nanoscale. Nature 523, 441–444 (2015).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


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