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.

Solving mazes with single-molecule DNA navigators


Molecular devices with information-processing capabilities hold great promise for developing intelligent nanorobotics. Here we demonstrate a DNA navigator system that can perform single-molecule parallel depth-first search on a ten-vertex rooted tree defined on a two-dimensional DNA origami platform. Pathfinding by the DNA navigators exploits a localized strand exchange cascade, which is initiated at a unique trigger site on the origami with subsequent automatic progression along paths defined by DNA hairpins containing a universal traversal sequence. Each single-molecule navigator autonomously explores one of the possible paths through the tree. A specific solution path connecting a given pair of start and end vertices can then be easily extracted from the set of all paths taken by the navigators collectively. The solution path laid out on origami is illustrated with single-molecule imaging. Our approach points towards the realization of molecular materials with embedded computational functions operating at the single-molecule level.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Physical implementation of the single-molecule DNA navigator.
Fig. 2: Single-molecule characterization of kinetics of PSEC.
Fig. 3: PSEC-driven graph traversal on a maze.
Fig. 4: Single-molecule DNA navigators for maze-solving.

Data availability

All the data that support the findings of this study are available within the paper and its Supplementary Information files, and from the corresponding authors upon reasonable request. 


  1. 1.

    Kudernac, T. et al. Electrically driven directional motion of a four-wheeled molecule on a metal surface. Nature 479, 208–211 (2011).

    CAS  Article  Google Scholar 

  2. 2.

    Hagiya, M., Konagaya, A., Kobayashi, S., Saito, H. & Murata, S. Molecular robots with sensors and intelligence. Acc. Chem. Res. 47, 1681–1690 (2014).

    CAS  Article  Google Scholar 

  3. 3.

    Kassem, S. et al. Artificial molecular motors. Chem. Soc. Rev. 46, 2592–2621 (2017).

    CAS  Article  Google Scholar 

  4. 4.

    Yin, P., Yan, H., Daniell, X. G., Turberfield, A. J. & Reif, J. H. A unidirectional DNA walker that moves autonomously along a track. Angew. Chem. Int. Ed. 43, 4906–4911 (2004).

    CAS  Article  Google Scholar 

  5. 5.

    Shin, J.-S. & Pierce, N. A. A synthetic DNA walker for molecular transport. J. Am. Chem. Soc. 126, 10834–10835 (2004).

    CAS  Article  Google Scholar 

  6. 6.

    Tian, Y., He, Y., Chen, Y., Yin, P. & Mao, C. A DNAzyme that walks processively and autonomously along a one-dimensional track. Angew. Chem. Int. Ed. 44, 4355–4358 (2005).

    CAS  Article  Google Scholar 

  7. 7.

    Gu, H., Chao, J., Xiao, S.-J. & Seeman, N. C. A proximity-based programmable DNA nanoscale assembly line. Nature 465, 202–205 (2010).

    CAS  Article  Google Scholar 

  8. 8.

    Lund, K. et al. Molecular robots guided by prescriptive landscapes. Nature 465, 206–210 (2010).

    CAS  Article  Google Scholar 

  9. 9.

    Wickham, S. F. J. et al. A DNA-based molecular motor that can navigate a network of tracks. Nat. Nanotech. 7, 169–173 (2012).

    CAS  Article  Google Scholar 

  10. 10.

    Tomov, T. E. et al. Rational design of DNA motors: Fuel optimization through single-molecule fluorescence. J. Am. Chem. Soc. 135, 11935–11941 (2013).

    CAS  Article  Google Scholar 

  11. 11.

    Cha, T.-G. et al. A synthetic DNA motor that transports nanoparticles along carbon nanotubes. Nat. Nanotech. 9, 39–43 (2014).

    CAS  Article  Google Scholar 

  12. 12.

    Kopperger, E., Pirzer, T. & Simmel, F. C. Diffusive transport of molecular cargo tethered to a DNA origami platform. Nano. Lett. 15, 2693–2699 (2015).

    CAS  Article  Google Scholar 

  13. 13.

    Yang, Y. et al. Direct visualization of walking motions of photocontrolled nanomachine on the DNA nanostructure. Nano. Lett. 15, 6672–6676 (2015).

    CAS  Article  Google Scholar 

  14. 14.

    Thubagere, A. J. et al. A cargo-sorting DNA robot. Science 357, eaan6558 (2017).

    Article  Google Scholar 

  15. 15.

    Fan, C. & Pei, H. DNA nanotechnology. Chin. J. Chem. 34, 251 (2016).

    CAS  Article  Google Scholar 

  16. 16.

    Zhou, C., Duan, X. & Liu, N. A plasmonic nanorod that walks on DNA origami. Nat. Commun. 6, 8102 (2015).

    CAS  Article  Google Scholar 

  17. 17.

    Zhu, D. et al. A surface-confined proton-driven DNA pump using a dynamic 3D DNA scaffold. Adv. Mater. 28, 6860–6865 (2016).

    CAS  Article  Google Scholar 

  18. 18.

    Adleman, L. M. Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994).

    CAS  Article  Google Scholar 

  19. 19.

    Elbaz, J. et al. DNA computing circuits using libraries of DNAzyme subunits. Nat. Nanotech. 5, 417–422 (2010).

    CAS  Article  Google Scholar 

  20. 20.

    Pei, R., Matamoros, E., Liu, M., Stefanovic, D. & Stojanovic, M. N. Training a molecular automaton to play a game. Nat. Nanotech. 5, 773–777 (2010).

    CAS  Article  Google Scholar 

  21. 21.

    Macdonald, J. et al. Medium scale integration of molecular logic gates in an automaton. Nano. Lett. 6, 2598–2603 (2006).

    CAS  Article  Google Scholar 

  22. 22.

    Qian, L., Winfree, E. & Bruck, J. Neural network computation with DNA strand displacement cascades. Nature 475, 368–372 (2011).

    CAS  Article  Google Scholar 

  23. 23.

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

    CAS  Article  Google Scholar 

  24. 24.

    Han, D. et al. A cascade reaction network mimicking the basic functional steps of adaptive immune response. Nat. Chem. 7, 835–841 (2015).

    CAS  Article  Google Scholar 

  25. 25.

    Li, J., Green, A. A., Yan, H. & Fan, C. H. Engineering nucleic acid structures for programmable molecular circuitry and intracellular biocomputation. Nat. Chem. 9, 1056–1067 (2017).

    CAS  Article  Google Scholar 

  26. 26.

    Liu, H., Wang, J., Song, S., Fan, C. & Gothelf, K. V. A DNA-based system for selecting and displaying the combined result of two input variables. Nat. Commun. 6, 10089 (2015).

    CAS  Article  Google Scholar 

  27. 27.

    Boemo, M. A., Lucas, A. E., Turberfield, A. J. & Cardelli, L. The formal language and design principles of autonomous DNA walker circuits. ACS Synth. Biol. 5, 878–884 (2016).

    CAS  Article  Google Scholar 

  28. 28.

    Chatterjee, G., Dalchau, N., Muscat, R. A., Phillips, A. & Seelig, G. A spatially localized architecture for fast and modular DNA computing. Nat. Nanotech. 12, 920–927 (2017).

    CAS  Article  Google Scholar 

  29. 29.

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

    CAS  Article  Google Scholar 

  30. 30.

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

    CAS  Article  Google Scholar 

  31. 31.

    Voigt, N. V. et al. Single-molecule chemical reactions on DNA origami. Nat. Nanotech. 5, 200–203 (2010).

    CAS  Article  Google Scholar 

  32. 32.

    Lin, C. et al. Submicrometre geometrically encoded fluorescent barcodes self-assembled fromDNA. Nat. Chem. 4, 832–839 (2012).

    CAS  Article  Google Scholar 

  33. 33.

    Kuzyk, A. et al. DNA-based self-assembly of chiral plasmonic nanostructures with tailored optical response. Nature 483, 311–314 (2012).

    CAS  Article  Google Scholar 

  34. 34.

    Knudsen, J. B. et al. Routing of individual polymers in designed patterns. Nat. Nanotech. 10, 892–898 (2015).

    CAS  Article  Google Scholar 

  35. 35.

    Timm, C. & Niemeyer, C. M. Assembly and purification of enzyme-functionalized DNA origami structures. Angew. Chem. Int. Ed. 54, 6745–6750 (2015).

    CAS  Article  Google Scholar 

  36. 36.

    Edwardson, T. G. W., Lau, K. L., Bousmail, D., Serpell, C. J. & Sleiman, H. F. Transfer of molecular recognition information from DNA nanostructures to gold nanoparticles. Nat. Chem. 8, 162–170 (2016).

    CAS  Article  Google Scholar 

  37. 37.

    Zhang, Y. et al. Transfer of two-dimensional oligonucleotide patterns onto stereocontrolled plasmonic nanostructures through DNA-origami-based nanoimprinting lithography. Angew. Chem. Int. Ed. 55, 8036–8040 (2016).

    CAS  Article  Google Scholar 

  38. 38.

    Zhang, Z., Yang, Y., Pincet, F., C. Llaguno, M. & Lin, C. Placing and shaping liposomes with reconfigurable DNA nanocages. Nat. Chem. 9, 653–659 (2017).

    CAS  Article  Google Scholar 

  39. 39.

    Rao, V. N. & Kumar, V. Parallel depth first search. Part I. implementation. Int. J. Parallel Prog. 16, 479–499 (1987).

    Article  Google Scholar 

  40. 40.

    Dirks, R. M. & Pierce, N. A. Triggered amplification by hybridization chain reaction. Proc. Natl Acad. Sci. USA 101, 15275–15278 (2004).

    CAS  Article  Google Scholar 

  41. 41.

    Lakin, M. R., Youssef, S., Polo, F., Emmott, S. & Phillips, A. Visual DSD: a design and analysis tool for DNA strand displacement systems. Bioinformatics 27, 3211–3213 (2011).

    CAS  Article  Google Scholar 

  42. 42.

    Moore, C. & Mertens, S. The Nature of Computation (Oxford Univ. Press, Oxford, 2011).

  43. 43.

    Scheible, M. B., Pardatscher, G., Kuzyk, A. & Simmel, F. C. Single molecule characterization of DNA binding and strand displacement reactions on lithographic DNA origami microarrays. Nano. Lett. 14, 1627–1633 (2014).

    CAS  Article  Google Scholar 

  44. 44.

    Jungmann, R. et al. Multiplexed 3D cellular super-resolution imaging with DNA-PAINT and Exchange-PAINT. Nat. Methods 11, 313–318 (2014).

    CAS  Article  Google Scholar 

  45. 45.

    Ovesný, M., Křížek, P., Borkovec, J., Švindrych, Z. & Hagen, G. M. ThunderSTORM: a comprehensive ImageJ plug-in for PALM and STORM data analysis and super-resolution imaging. Bioinformatics 30, 2389–2390 (2014).

    Article  Google Scholar 

Download references


We greatly appreciate financial support from the Ministry of Science and Technology of China (2016YFA0201200), National Science Foundation of China (21390414, 21473236, 21675167, 21505148, 21722310, 61771253), and the Chinese Academy of Sciences (QYZDJ-SSW-SLH031). We further acknowledge support by the Deutsche Forschungsgemeinschaft through SFB1032 Project A2 and by the Technical University Munich International Graduate School
of Science and Engineering.

Author information




C.F. directed the research. C.F., F.C.S., H.L. and J.C. conceived the project and designed the experiments. J.C., J.W., F.W., X.O. and E.K. designed the DNA sequences, constructed the navigator system and performed the single-molecule studies. F.W., Q.L. and J.S. carried out the theoretical simulation. J.C., J.W., F.W., E.K., H.L., Lihua W., J.H., Lianhui W., W.H. and F.C.S. analysed the data. All authors discussed the results and commented on the manuscript. C.F., F.C.S. and H.L. co-wrote the paper.

Corresponding authors

Correspondence to Huajie Liu, Friedrich C. Simmel or Chunhai Fan.

Ethics declarations

Competing Interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Notes 1–4, Supplementary Schemes 1–3, Supplementary Software, Supplementary Figures 1–26, Supplementary References 1–3

Reporting Summary

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chao, J., Wang, J., Wang, F. et al. Solving mazes with single-molecule DNA navigators. Nature Mater 18, 273–279 (2019).

Download citation

Further reading


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