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Programmable disorder in random DNA tilings

Abstract

Scaling up the complexity and diversity of synthetic molecular structures will require strategies that exploit the inherent stochasticity of molecular systems in a controlled fashion. Here we demonstrate a framework for programming random DNA tilings and show how to control the properties of global patterns through simple, local rules. We constructed three general forms of planar network—random loops, mazes and trees—on the surface of self-assembled DNA origami arrays on the micrometre scale with nanometre resolution. Using simple molecular building blocks and robust experimental conditions, we demonstrate control of a wide range of properties of the random networks, including the branching rules, the growth directions, the proximity between adjacent networks and the size distribution. Much as combinatorial approaches for generating random one-dimensional chains of polymers have been used to revolutionize chemical synthesis and the selection of functional nucleic acids, our strategy extends these principles to random two-dimensional networks of molecules and creates new opportunities for fabricating more complex molecular devices that are organized by DNA nanostructures.

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Figure 1: Summary of programmable disorder in random DNA tilings.
Figure 2: Implementation of Truchet arrays.
Figure 3: Programming the tile.
Figure 4: Programming the grid.
Figure 5: Programming the random choice.
Figure 6: Programming a finite grid.

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References

  1. Rao, C. V., Wolf, D. M. & Arkin, A. P. Control, exploitation and tolerance of intracellular noise. Nature 420, 231–237 (2002).

    Article  CAS  Google Scholar 

  2. Kærn, M., Elston, T. C., Blake, W. J. & Collins, J. J. Stochasticity in gene expression: from theories to phenotypes. Nat. Rev. Genet. 6, 451–464 (2005).

    Article  Google Scholar 

  3. Eldar, A. & Elowitz, M. B. Functional roles for noise in genetic circuits. Nature 467, 167–173 (2010).

    Article  CAS  Google Scholar 

  4. Losick, R. & Desplan, C. Stochasticity and cell fate. Science 320, 65–68 (2008).

    Article  CAS  Google Scholar 

  5. Zipursky, S. L. & Sanes, J. R. Chemoaffinity revisited: dscams, protocadherins, and neural circuit assembly. Cell 143, 343–353 (2010).

    Article  CAS  Google Scholar 

  6. Livet, J. et al. Transgenic strategies for combinatorial expression of fluorescent proteins in the nervous system. Nature 450, 56–62 (2007).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  10. Rinker, S., Ke, Y., Liu, Y., Chhabra, R. & Yan, H. Self-assembled DNA nanostructures for distance-dependent multivalent ligand–protein binding. Nat. Nanotech. 3, 418–422 (2008).

    Article  CAS  Google Scholar 

  11. Schreiber, R. et al. Hierarchical assembly of metal nanoparticles, quantum dots and organic dyes using DNA origami scaffolds. Nat. Nanotech. 9, 74–78 (2014).

    Article  CAS  Google Scholar 

  12. Pal, S., Deng, Z., Ding, B., Yan, H. & Liu, Y. DNA-origami-directed self-assembly of discrete silver-nanoparticle architectures. Angew. Chem. 122, 2760–2764 (2010).

    Article  Google Scholar 

  13. Pal, S. et al. DNA directed self-assembly of anisotropic plasmonic nanostructures. J. Am. Chem. Soc. 133, 17606–17609 (2011).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  15. Pinheiro, A. V., Han, D., Shih, W. M. & Yan, H. Challenges and opportunities for structural DNA nanotechnology. Nat. Nanotech. 6, 763–772 (2011).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  17. Yan, H., Park, S. H., Finkelstein, G., Reif, J. H. & LaBean, T. H. DNA-templated self-assembly of protein arrays and highly conductive nanowires. Science 301, 1882–1884 (2003).

    Article  CAS  Google Scholar 

  18. Malo, J. et al. Engineering a 2D protein–DNA crystal. Angew. Chem. Int. Ed. 44, 3057–3061 (2005).

    Article  CAS  Google Scholar 

  19. Zheng, J. et al. Two-dimensional nanoparticle arrays show the organizational power of robust DNA motifs. Nano Letters 6, 1502–1504 (2006).

    Article  CAS  Google Scholar 

  20. Zheng, J. et al. From molecular to macroscopic via the rational design of a self-assembled 3D DNA crystal. Nature 461, 74–77 (2009).

    Article  CAS  Google Scholar 

  21. Liu, W., Zhong, H., Wang, R. & Seeman, N. C. Crystalline two-dimensional DNA-origami arrays. Angew. Chem. 123, 278–281 (2011).

    Article  Google Scholar 

  22. Woo, S. & Rothemund, P. W. K. Self-assembly of two-dimensional DNA origami lattices using cation-controlled surface diffusion. Nat. Commun. 5, 4889 (2014).

    Article  CAS  Google Scholar 

  23. Aghebat Rafat, A., Pirzer, T. & Scheible, M. B., Kostina, A. & Simmel, F. C. Surface-assisted large-scale ordering of DNA origami tiles. Angew. Chem. Int. Ed. 53, 7665–7668 (2014).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  25. 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).

    Article  CAS  Google Scholar 

  26. 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).

    Article  CAS  Google Scholar 

  27. Woo, S. & Rothemund, P. W. K. Programmable molecular recognition based on the geometry of DNA nanostructures. Nat. Chem. 3, 620–627 (2011).

    Article  CAS  Google Scholar 

  28. Gerling, T., Wagenbauer, K. F., Neuner, A. M. & Dietz, H. Dynamic DNA devices and assemblies formed by shape-complementary, non–base pairing 3D components. Science 347, 1446–1452 (2015).

    Article  CAS  Google Scholar 

  29. Truchet, S. Mémoire sur les combinaisons. Mém. Acad. R. Sci. 1704, 363–372 (1704).

    Google Scholar 

  30. Smith, C. S. & Boucher, P. The tiling patterns of Sebastien Truchet and the topology of structural hierarchy. Leonardo 20, 373–385 (1987).

    Article  Google Scholar 

  31. Murphy, C. J. et al. Structure and energetics of hydrogen-bonded networks of methanol on close packed transition metal surfaces. J. Chem. Phys. 141, 014701 (2014).

    Article  Google Scholar 

  32. Less, J. R., Skalak, T. C., Sevick, E. M. & Jain, R. K. Microvascular architecture in a mammary carcinoma: branching patterns and vessel dimensions. Cancer Res. 51, 265–273 (1991).

    CAS  Google Scholar 

  33. Portmann, O., Vaterlaus, A. & Pescia, D. An inverse transition of magnetic domain patterns in ultrathin films. Nature 422, 701–704 (2003).

    Article  CAS  Google Scholar 

  34. Blagodatski, A., Sergeev, A., Kryuchkov, M., Lopatina, Y. & Katanaev, V. L. Diverse set of Turing nanopatterns coat corneae across insect lineages. Proc. Natl Acad. Sci. USA 112, 10750–10755 (2015).

    Article  CAS  Google Scholar 

  35. Metzger, R. J., Klein, O. D., Martin, G. R. & Krasnow, M. A. The branching programme of mouse lung development. Nature 453, 745–750 (2008).

    Article  CAS  Google Scholar 

  36. Lefebvre, J. L., Kostadinov, D., Chen, W. V., Maniatis, T. & Sanes, J. R. Protocadherins mediate dendritic self-avoidance in the mammalian nervous system. Nature 488, 517–521 (2012).

    Article  CAS  Google Scholar 

  37. Svitkina, T. M. & Borisy, G. G. Arp2/3 complex and actin depolymerizing factor/cofilin in dendritic organization and treadmilling of actin filament array in lamellipodia. J. Cell Biol. 145, 1009–1026 (1999).

    Article  CAS  Google Scholar 

  38. Temperley, H. N. V. & Lieb, E. H. Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem. Proc. R. Soc. Lond. A 322, 251–280 (1971).

    Article  CAS  Google Scholar 

  39. Blöte, H. W. J. & Nienhuis, B. Fully packed loop model on the honeycomb lattice. Phys. Rev. Lett. 72, 1372–1375 (1994).

    Article  Google Scholar 

  40. Nahum, A., Chalker, J. T., Serna, P., Ortuño, M. & Somoza, A. M. 3D loop models and the CP(n−1) sigma model. Phys. Rev. Lett. 107, 110601 (2011).

    Article  Google Scholar 

  41. Rothemund, P. W. K. & Winfree, E. The program-size complexity of self-assembled squares. In Proc. 32nd Annual ACM Symp. Theory Computing 459–468 (Association for Computing Machinery, 2000).

    Google Scholar 

  42. Rajendran, A., Endo, M., Katsuda, Y., Hidaka, K. & Sugiyama, H. Programmed two-dimensional self-assembly of multiple DNA origami jigsaw pieces. ACS Nano 5, 665–671 (2011).

    Article  CAS  Google Scholar 

  43. Zhao, Z., Liu, Y. & Yan, H. Organizing DNA origami tiles into larger structures using preformed scaffold frames. Nano Letters 11, 2997–3002 (2011).

    Article  CAS  Google Scholar 

  44. Browne, C. Truchet curves and surfaces. Comput. Graph. 32, 268–281 (2008).

    Article  Google Scholar 

  45. 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  Google Scholar 

  46. Hirokawa, N. Kinesin and dynein superfamily proteins and the mechanism of organelle transport. Science 279, 519–526 (1998).

    Article  CAS  Google Scholar 

  47. Vale, R. D. The molecular motor toolbox for intracellular transport. Cell 112, 467–480 (2003).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  51. Maune, H. T. et al. Self-assembly of carbon nanotubes into two-dimensional geometries using DNA origami templates. Nat. Nanotech. 5, 61–66 (2010).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  53. Gordon, E. M., Barrett, R. W., Dower, W. J., Fodor, S. P. A. & Gallop, M. A. Applications of combinatorial technologies to drug discovery. 2. Combinatorial organic synthesis, library screening strategies, and future directions. J. Med. Chem. 37, 1385–1401 (1994).

    Article  CAS  Google Scholar 

  54. Ellington, A. D. & Szostak, J. W. In vitro selection of RNA molecules that bind specific ligands. Nature 346, 818–822 (1990).

    Article  CAS  Google Scholar 

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Acknowledgements

We thank S. Wang for designing the fish and gear tile (Supplementary Fig. 38) and J. Parkin, A. Karan and S. Wang for designing and creating a heart shape that is self-assembled from square DNA origami tiles (Supplementary Fig. 68). We thank E. Winfree, P. Rothemund, D. Soloveichik and A. Condon for critique on the manuscript. G.T. was supported by an NSF grant (1317694). P.P. was supported by a NIH/NRSA training grant (5 T32 GM07616). L.Q. was supported by a Career Award at the Scientific Interface from the Burroughs Wellcome Fund (1010684) and a Faculty Early Career Development Award from the NSF (1351081).

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G.T. and P.P. performed the experiments and analysed the data. P.P. performed the simulations and developed the software tools. G.T., P.P. and L.Q. designed the systems and wrote the manuscript. L.Q. initiated and guided the project.

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Correspondence to Lulu Qian.

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The authors declare no competing financial interests.

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Tikhomirov, G., Petersen, P. & Qian, L. Programmable disorder in random DNA tilings. Nature Nanotech 12, 251–259 (2017). https://doi.org/10.1038/nnano.2016.256

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