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.

Diverse and robust molecular algorithms using reprogrammable DNA self-assembly

Nature volume 567, pages366–372(2019)Cite this article

Subjects

An Author Correction to this article was published on 02 August 2019

This article has been updated

Abstract

Molecular biology provides an inspiring proof-of-principle that chemical systems can store and process information to direct molecular activities such as the fabrication of complex structures from molecular components. To develop information-based chemistry as a technology for programming matter to function in ways not seen in biological systems, it is necessary to understand how molecular interactions can encode and execute algorithms. The self-assembly of relatively simple units into complex products1 is particularly well suited for such investigations. Theory that combines mathematical tiling and statistical–mechanical models of molecular crystallization has shown that algorithmic behaviour can be embedded within molecular self-assembly processes2,3, and this has been experimentally demonstrated using DNA nanotechnology4 with up to 22 tile types5,6,7,8,9,10,11. However, many information technologies exhibit a complexity threshold—such as the minimum transistor count needed for a general-purpose computer—beyond which the power of a reprogrammable system increases qualitatively, and it has been unclear whether the biophysics of DNA self-assembly allows that threshold to be exceeded. Here we report the design and experimental validation of a DNA tile set that contains 355 single-stranded tiles and can, through simple tile selection, be reprogrammed to implement a wide variety of 6-bit algorithms. We use this set to construct 21 circuits that execute algorithms including copying, sorting, recognizing palindromes and multiples of 3, random walking, obtaining an unbiased choice from a biased random source, electing a leader, simulating cellular automata, generating deterministic and randomized patterns, and counting to 63, with an overall per-tile error rate of less than 1 in 3,000. These findings suggest that molecular self-assembly could be a reliable algorithmic component within programmable chemical systems. The development of molecular machines that are reprogrammable—at a high level of abstraction and thus without requiring knowledge of the underlying physics—will establish a creative space in which molecular programmers can flourish.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

Rent or Buy

All prices are NET prices.

Fig. 1: Abstraction hierarchy for design and implementation of the complete 6-bit IBC tile set.
Fig. 2: Experimental protocol and implementation of the Sorting circuit.
Fig. 3: Reprogramming IBCs.
Fig. 4: Testing of the complete 6-bit IBC tile set.

Data availability

The AFM data generated and analysed here are available from the authors’ website (http://www.dna.caltech.edu/SupplementaryMaterial/Algorithmic_SST/), as is the Python code for data analysis and DNA sequence design.

Change history

  • 02 August 2019

    An Amendment to this paper has been published and can be accessed via a link at the top of the paper.

References

  1. 1.

    Whitesides, G. M. & Grzybowski, B. Self-assembly at all scales. Science 295, 2418–2421 (2002).

    CAS  ADS  PubMed  PubMed Central  Google Scholar 

  2. 2.

    Winfree, E. Simulations of Computing by Self-Assembly. Technical Report CaltechCSTR:1998.22 (California Institute of Technology, 1998).

  3. 3.

    Doty, D. Theory of algorithmic self-assembly. Commun. ACM 55, 78–88 (2012).

    Article  Google Scholar 

  4. 4.

    Seeman, N. C. & Sleiman, H. F. DNA nanotechnology. Nat. Rev. Mater. 3, 17068 (2017).

    ADS  Article  Google Scholar 

  5. 5.

    Mao, C., LaBean, T. H., Reif, J. H. & Seeman, N. C. Logical computation using algorithmic self-assembly of DNA triple-crossover molecules. Nature 407, 493–496 (2000); erratum 408, 750 (2000).

    CAS  ADS  Article  Google Scholar 

  6. 6.

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

    Article  Google Scholar 

  7. 7.

    Schulman, R. & Winfree, E. Synthesis of crystals with a programmable kinetic barrier to nucleation. Proc. Natl Acad. Sci. USA 104, 15236–15241 (2007).

    CAS  ADS  Article  Google Scholar 

  8. 8.

    Barish, R. D., Schulman, R., Rothemund, P. W. K. & Winfree, E. An information-bearing seed for nucleating algorithmic self-assembly. Proc. Natl Acad. Sci. USA 106, 6054–6059 (2009).

    CAS  ADS  Article  Google Scholar 

  9. 9.

    Schulman, R., Yurke, B. & Winfree, E. Robust self-replication of combinatorial information via crystal growth and scission. Proc. Natl Acad. Sci. USA 109, 6405–6410 (2012).

    CAS  ADS  Article  Google Scholar 

  10. 10.

    Evans, C. G. Crystals that Count! Physical Principles and Experimental Investigations of DNA Tile Self-Assembly. PhD thesis, Caltech (2014).

  11. 11.

    Schulman, R., Wright, C. & Winfree, E. Increasing redundancy exponentially reduces error rates during algorithmic self-assembly. ACS Nano 9, 5760–5771 (2015).

    CAS  Article  Google Scholar 

  12. 12.

    Winfree, E., Liu, F., Wenzler, L. A. & Seeman, N. C. Design and self-assembly of two-dimensional DNA crystals. Nature 394, 539–544 (1998).

    CAS  ADS  Article  Google Scholar 

  13. 13.

    Yin, P. et al. Programming DNA tube circumferences. Science 321, 824–826 (2008).

    CAS  ADS  Article  Google Scholar 

  14. 14.

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

    CAS  ADS  Article  Google Scholar 

  15. 15.

    Wei, B., Dai, M. & Yin, P. Complex shapes self-assembled from single-stranded DNA tiles. Nature 485, 623–626 (2012).

    CAS  ADS  Article  Google Scholar 

  16. 16.

    Wang, W. et al. Self-assembly of fully addressable DNA nanostructures from double crossover tiles. Nucleic Acids Res. 44, 7989–7996 (2016).

    CAS  Article  Google Scholar 

  17. 17.

    Ong, L. L. et al. Programmable self-assembly of three-dimensional nanostructures from 10,000 unique components. Nature 552, 72–77 (2017).

    CAS  ADS  Article  Google Scholar 

  18. 18.

    Rothemund, P. W. K. & Winfree, E. The program-size complexity of self-assembled squares. In STOC: Proceedings of the 32nd Annual ACM Symposium on Theory of Computing (eds Yao, F. & Luks, E.) 459–468 (Association for Computing Machinery, 2000).

  19. 19.

    Soloveichik, D. & Winfree, E. Complexity of self-assembled shapes. SIAM J. Comput. 36, 1544–1569 (2007).

    MathSciNet  Article  Google Scholar 

  20. 20.

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

  21. 21.

    Cook, M. Universality in elementary cellular automata. Complex Syst. 15, 1–40 (2004).

    MathSciNet  MATH  Google Scholar 

  22. 22.

    Neary, T. & Woods, D. P-completeness of cellular automaton Rule 110. In ICALP 2006: International Colloquium on Automata, Languages, and Programming (eds Bugliesi, M., Preneel, B., Sassone, V. & Wegener, I.) 132–143 (Springer, 2006).

  23. 23.

    Schulman, R. & Winfree, E. Programmable control of nucleation for algorithmic self-assembly. SIAM J. Comput. 39, 1581–1616 (2009).

    MathSciNet  Article  Google Scholar 

  24. 24.

    Evans, C. G. & Winfree, E. Physical principles for DNA tile self-assembly. Chem. Soc. Rev. 46, 3808–3829 (2017).

    CAS  Article  Google Scholar 

  25. 25.

    Winfree, E. & Bekbolatov, R. Proofreading tile sets: error correction for algorithmic self-assembly. In DNA9: Proceedings of the 9th International Conference on DNA Computing (eds Chen, J. & Reif, J.) 126–144 (Springer, 2004).

  26. 26.

    Mohammed, A. M. & Schulman, R. Directing self-assembly of DNA nanotubes using programmable seeds. Nano Lett. 13, 4006–4013 (2013).

    CAS  ADS  Article  Google Scholar 

  27. 27.

    Evans, C. G. & Winfree, E. DNA sticky end design and assignment for robust algorithmic self-assembly. In DNA19: Proceedings of the 19th International Conference on DNA Computing and Molecular Programming (Eds Soloveichik, D. & Yurke, B.) 61–75 (Springer, 2013).

  28. 28.

    Zadeh, J. N. et al. NUPACK: analysis and design of nucleic acid systems. J. Comput. Chem. 32, 170–173 (2011).

    CAS  Article  Google Scholar 

  29. 29.

    Lorenz, R. et al. ViennaRNA Package 2.0. Algorithms Mol. Biol. 6, 26 (2011).

    Article  Google Scholar 

  30. 30.

    Wei, B., Luvena, L. L., Ong, J., Jaffe, A. S. & Yin, P. Complex reconfiguration of DNA nanostructures. Angew. Chem. Int. Ed. 126, 7605–7609 (2014).

    Article  Google Scholar 

  31. 31.

    Chalk, C., Fu, B., Martinez, E., Schweller, R. & Wylie, T. Concentration independent random number generation in tile self-assembly. Theor. Comput. Sci. 667, 1–15 (2017).

    MathSciNet  Article  Google Scholar 

  32. 32.

    Jacobs, W. M., Reinhardt, A. & Frenkel, D. Rational design of self-assembly pathways for complex multicomponent structures. Proc. Natl Acad. Sci. USA 112, 6313–6318 (2015).

    CAS  ADS  Article  Google Scholar 

  33. 33.

    Hedges, L. O., Mannige, R. V. & Whitelam, S. Growth of equilibrium structures built from a large number of distinct component types. Soft Matter 10, 6404–6416 (2014).

    CAS  ADS  Article  Google Scholar 

  34. 34.

    Cairns-Smith, A. G. Genetic Takeover and the Mineral Origins of Life (Cambridge Univ. Press, Cambridge, 1982).

Download references

Acknowledgements

We thank C. Evans, A. Gopinath, B. Wei, C. Geary, R. Schulman, S. Woo, P. Rothemund and Y. Rondelez for experimental advice; R. Barish and R. Hariadi for contributing to preliminary designs for algorithmic self-assembly by SST; C. Moore, T. Stérin, C. Thachuk, P.-É. Meunier and C. Geary for discussions on theory; and L. Qian, G. Tikhomirov and P. Petersen for AFM usage. This work was supported by National Science Foundation (NSF) grants CCF-1162589 (to E.W., D.D. and D.W.), CCF-1162459 (to P.Y.), CCF-1219274 (to D.W. and D.D.), CCF-1619343 (to D.D.), CCF-0832824 and CCF-1317694 (Expeditions in Computing, to E.W.) and CCF-1317291 (Expeditions in Computing, to P.Y.), and by NASA grant NNX13AJ56G (to D.W.). C.M. was funded by the Fannie and John Hertz Foundation. F.Z. and J.H. received support from the Caltech Summer Undergraduate Research Fellowship program.

Author information

Author notes

  1. Damien Woods

    Present address: Maynooth University, Maynooth, Ireland

  2. These authors contributed equally: Damien Woods, David Doty

Affiliations

  1. California Institute of Technology, Pasadena, CA, USA

    Damien Woods, David Doty, Joy Hui, Felix Zhou & Erik Winfree

  2. Inria, Paris, France

    Damien Woods

  3. University of California, Davis, CA, USA

    David Doty

  4. Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston, MA, USA

    Cameron Myhrvold & Peng Yin

  5. Department of Systems Biology, Harvard University, Boston, MA, USA

    Cameron Myhrvold & Peng Yin

  6. Harvard University, Cambridge, MA, USA

    Joy Hui

  7. University of Oxford, Oxford, UK

    Felix Zhou

Authors
  1. Damien Woods
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Doty
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cameron Myhrvold
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Joy Hui
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Felix Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Peng Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Erik Winfree
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

D.W., D.D., E.W. and P.Y. conceived the study. D.W., D.D. and E.W. designed the circuits and wrote the manuscript. D.W. and D.D. carried out all data analysis and experiments reported except for the nanotube nucleation/melt experiments (which were performed by J.H. and D.W.) and the unzipping and other early experimental protocols (performed by F.Z., C.M. and D.D.).

Corresponding authors

Correspondence to Damien Woods or David Doty or Erik Winfree.

Ethics declarations

Competing interests

D.W., D.D., J.H., F.Z. and E.W. declare that they have no competing interests. P.Y. and C.M. declare competing interests: they are both listed as inventors on pending and issued patents on single-stranded tiles; and P.Y. is a co-founder of Ultivue Inc. and NuProbe Global.

Additional information

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

Supplementary information

Supplementary Information

This file contains Supplementary Information section A, which contains details about the IBC model, the abstract tile assembly model and proofreading, the SST binding domain schematics, DNA sequence design, data supporting design decisions, experimental methods, AFM image analysis, and the 21 implemented circuits

Supplementary Data

This file contains Supplementary Information section B, which contains sequences for the DNA systems explored in this paper

Supplementary Figures

This file contains Supplementary Information section C, four sample high-resolution AFM images of DNA nanostructures for several circuits

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Woods, D., Doty, D., Myhrvold, C. et al. Diverse and robust molecular algorithms using reprogrammable DNA self-assembly. Nature 567, 366–372 (2019). https://doi.org/10.1038/s41586-019-1014-9

Download citation

Further reading

Comments

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.

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