Natural Computing

, Volume 15, Issue 4, pp 611–634 | Cite as

Activatable tiles for compact robust programmable molecular assembly and other applications

  • Urmi Majumder
  • Sudhanshu Garg
  • Thomas H. LaBean
  • John H. ReifEmail author


Algorithmic DNA self-assembly is capable of forming complex patterns and shapes, that have been shown theoretically, and experimentally. Its experimental demonstrations, although improving over recent years, have been limited by significant assembly errors. Since 2003 there have been several designs of error-resilient tile sets but all of these existing error-resilient tile systems assumed directional growth of the tiling assembly. This is a very strong assumption because experiments show that tile self-assembly does not necessarily behave in such a fashion, since they may also grow in the reverse of the intended direction. The assumption of directional growth of the tiling assembly also underlies the growth model in theoretical assembly models such as the TAM. What is needed is a means for enforce this directionality constraint, which will allow us to reduce assembly errors. In this paper we describe a protection/deprotection strategy to strictly enforce the direction of tiling assembly growth so that the assembly process is robust against errors. Initially, we start with (1) a single “activated” tile with output pads that can bind with other tiles, along with (2) a set of “deactivated” tiles, meaning that the tile’s output pads are protected and cannot bind with other tiles. After other tiles bind to a “deactivated” tile’s input pads, the tile transitions to an active state and its output pads are exposed, allowing further growth. When these are activated in a desired order, we can enforce a directional assembly at the same scale as the original one. Such a system can be built with minimal modifications of existing DNA tile nanostructures. We propose a new type of tiles called activatable tiles and its role in compact proofreading. Activatable tiles can be thought of as a particular case of the more recent signal tile assembly model, where signals transmit binding/unbinding instructions across tiles on binding to one or more input sites. We describe abstract and kinetic models of activatable tile assembly and show that the error rate can be decreased significantly with respect to Winfree’s original kinetic tile assembly model without considerable decrease in assembly growth speed. We prove that an activatable tile set is an instance of a compact, error-resilient and self-healing tile-set. We describe a DNA design of activatable tiles and a mechanism of deprotection using DNA polymerization and strand displacement. We also perform detailed stepwise simulations using a DNA Tile simulator Xgrow, and show that the activatable tiles mechanism can reduce error rates in self assembly. We conclude with a brief discussion on some applications of activatable tiles beyond computational tiling, both as (1) a novel system for concentration of molecules, and (2) a catalyst in sequentially triggered chemical reactions .


DNA self-assembly Error correction Tile assembly model Strand displacement Programmable molecular machines Deprotection systems Concentration systems Reaction catalyzation 



Polymerase chain reaction


DeoxyriboNucleic acid


Double stranded DeoxyriboNucleic acid


Tile assembly model


Abstract tile assembly model


Kinetic tile assembly model


Abstract activatable tile assembly model


Kinetic activatable tile assembly model


Layered tile mechanism


Protected tile mechanism



The authors thank the anonymous referees, whose suggestions have had a noticeable improvement on the quality of the article, in helping us better articulate ideas and by giving attention to detail. The work was supported by NSF Grants CCF-1217457, CCF-1141847, CCF-0829797,  CCF-1320360.


  1. Adleman L, Cheng Q, Goel A, Huang M-D (2001) Running time and program size for self-assembled squares. In: Symposium on theory of computing, 740–748Google Scholar
  2. Barish RD, Schulman R, Rothemund PWK, Winfree E (2009) An information-bearing seed for nucleating algorithmic self-assembly. Proc Natl Acad Sci 106(15):6054–6059CrossRefGoogle Scholar
  3. Chen H-L, Cheng Q, Goel A, Huang M-D, de Espanés PM (2004) Invadable self-assembly: combining robustness with efficiency. In: Proceedings of the fifteenth annual ACM-SIAM symposium on discrete algorithms (Philadelphia, PA, USA, 2004), SODA ’04, Society for Industrial and Applied Mathematics, pp 890–899Google Scholar
  4. Chen H-L, Doty D (2012) Parallelism and time in hierarchical self-assembly. In: Proceedings of the twenty-third annual ACM-SIAM symposium on discrete algorithms (2012), SODA ’12, SIAM, pp 1163–1182Google Scholar
  5. Chen H-L, Goel A (2004) Error free self-assembly using error prone tiles. In: Ferretti C, Mauri G, Sandro C (eds) Proceedings of the Tenth International Workshop on DNA Computing, Milan, LNCS, Vol 3384. Springer, Heidelberg, pp 62–75Google Scholar
  6. Demaine E, Demaine M, Fekete S, Ishaque M, Rafalin E, Schweller R, Souvaine D (2008) Staged self-assembly: nanomanufacture of arbitrary shapes with o(1) glues. Nat Comput 7(3):347–370MathSciNetCrossRefzbMATHGoogle Scholar
  7. Dirks R, Pierce N (2004) Triggered amplification by hybridization chain reaction. Proc Natl Acad Sci USA 101(43):15275–15278CrossRefGoogle Scholar
  8. Fujibayashi K, Hariadi R, Park SH, Winfree E, Murata S (2008) Toward reliable algorithmic self-assembly of DNA tiles: a fixed-width cellular automaton pattern. Nano Lett 8(7):1791–1797CrossRefGoogle Scholar
  9. Fujibayashi K, Murata S (2005) A method of error suppression for self-assembling DNA tiles. 10th International Workshop on DNA Computing, DNA10, vol 3384. Springer, Milan, pp 113–127Google Scholar
  10. Fujibayashi K, Zhang DY, Winfree E, Murata S (2009) Error suppression mechanisms for DNA tile self-assembly and their simulation, pp 589–612Google Scholar
  11. Garg S. Xgrow modified for activatable tiles. Available at
  12. Garg S, Chandran H, Gopalkrishnan N, LaBean TH, Reif J (2015) Directed enzymatic activation of 1-d DNA tiles. ACS Nano 9(2):1072–1079CrossRefGoogle Scholar
  13. Gautam V, Haddow P, Kuiper M (2013) Reliable self-assembly by self-triggered activation of enveloped DNA tiles. In: Dediu A-H, Martn-Vide C, Truthe C, Vega-Rodrguez M (eds) Theory and practice of natural computing, vol. 8273 of lecture notes in computer science. Springer, Berlin, pp 68–79Google Scholar
  14. Hendricks J, Padilla J, Patitz M, Rogers T (2013) Signal transmission across tile assemblies: 3d static tiles simulate active self-assembly by 2d signal-passing tiles. In: Soloveichik D, Yurke B (eds) DNA computing and molecular programming, vol. 8141 of lecture notes in computer science. Springer International Publishing, pp 90–104Google Scholar
  15. Jang B, Kim Y-B, Lombardi F (2007) Error rate reduction in DNA self-assembly by non-constant monomer concentrations and profiling. In: Design, automation test in Europe conference exhibition, 2007. DATE ’07, pp 1–6Google Scholar
  16. Jonoska N, Karpenko D (2014) Active tile self-assembly, part 1: universality at temperature 1. Int J Found Comput Sci 25(02):141–163MathSciNetCrossRefzbMATHGoogle Scholar
  17. Jonoska N, Karpenko D (2014) Active tile self-assembly, part 2: self-similar structures and structural recursion. Int J Found Comput Sci 25(02):165–194MathSciNetCrossRefzbMATHGoogle Scholar
  18. Kamtekar S, Berman AJ, Wang J, Lzaro JM, de Vega M, Blanco L, Salas M, Steitz TA (2004) Insights into strand displacement and processivity from the crystal structure of the protein-primed DNA polymerase of bacteriophage \(\varphi\)29. Mol Cell 16(4):609–618CrossRefGoogle Scholar
  19. Keenan A, Schweller R, Zhong X (2013) Exponential replication of patterns in the signal tile assembly model. In: Soloveichik D, Yurke B (eds) DNA Computing and molecular programming, vol. 8141 of lecture notes in computer science. Springer International Publishing, pp 118–132Google Scholar
  20. LaBean T, Yan H, Kopatsch J, Liu F, Winfree E, Reif J, Seeman N (2000) Construction, analysis, ligation, and self-assembly of DNA triple crossover complexes. J Am Chem Soc 122(9):1848–1860CrossRefGoogle Scholar
  21. Majumder U, Sahu S, LaBean T, Reif J (2006) Design and simulation of self-repairing DNA lattices. In: Mao C, Yokomori T, (eds) DNA computing, vol. 4287 of lecture notes in computer science. Springer, Berlin, pp 195–214Google Scholar
  22. Mao C, Labean T, Reif J, Seeman N (2000) Logical computation using algorithmic self-assembly of DNA triple-crossover molecules. Nature 407:493–496CrossRefGoogle Scholar
  23. Murata S (2004) Self-assembling DNA tiles-mechanisms of error suppression. In: SICE 2004 annual conference, vol. 3, pp 2764–2767Google Scholar
  24. Padilla J, Liu W, Seeman N (2012) Hierarchical self assembly of patterns from the robinson tilings: DNA tile design in an enhanced tile assembly model. Nat Comput 11(2):323–338MathSciNetCrossRefzbMATHGoogle Scholar
  25. Padilla J, Patitz M, Pena R, Schweller R, Seeman N, Sheline R, Summers S, Zhong X (2013) Asynchronous signal passing for tile self-assembly Fuel efficient computation and efficient assembly: fuel efficient computation and efficient assembly of shapes. In: Mauri G, Dennunzio A, Manzoni L, Porreca A (eds) Unconventional computation and natural computation, vol. 7956 of lecture notes in computer science. Springer, Berlin, pp 174–185Google Scholar
  26. Reif J, Sahu S, Yin P (2004) Compact error-resilient computational DNA tiling assemblies. In: Ferretti C, Mauri G, Zandron C (eds) Tenth International Meeting on DNA Based Computers (DNA10), Milano, Italy, June 7-10, 2004. Lecture Notes in Computer Science, vol 3384. Springer-Verlag, New York, pp 293–307. Extended version appears as invited chapter in text Nanotechnology: Science and Computation (2006) In: Chen J, Jonoska N, Rozenberg G (eds) Natural Computing. Springer, Germany, pp 79–104Google Scholar
  27. Rosenbaum DM, Liu DR (2003) Efficient and sequence-specific DNA-templated polymerization of peptide nucleic acid aldehydes. J Am Chem Soc 125(46):13924–13925CrossRefGoogle Scholar
  28. Rothemund P (2006) Folding DNA to create nanoscale shapes and patterns. Nature 440:297–302CrossRefGoogle Scholar
  29. Rothemund P, Papadakis N, Winfree E (2004) Algorithmic self-assembly of DNA sierpinski triangles. PLoS Biol 2:424–436CrossRefGoogle Scholar
  30. Sahu S, Reif J (2006) Capabilities and limits of compact error resilience methods for algorithmic self-assembly in two and three dimensions. In: Mao C, Yokomori T (eds) DNA computing, vol. 4287 of lecture notes in computer science. Springer, Berlin, pp 223–238Google Scholar
  31. Saturno J, Blanco L, Salas M, Esteban JA (1995) A novel kinetic analysis to calculate nucleotide affinity of proofreading DNA polymerases: application to 29 DNA polymerase fidelity mutants. J Biol Chem 270(52):31235–31243CrossRefGoogle Scholar
  32. Schulman R, Winfree E (2009) Programmable control of nucleation for algorithmic self-assembly. SIAM J Comput 39(4):1581–1616MathSciNetCrossRefzbMATHGoogle Scholar
  33. Schulman R, Yurke B, Winfree E (2012) Robust self-replication of combinatorial information via crystal growth and scission. In: Proceedings of the national academy of sciencesGoogle Scholar
  34. Soloveichik D, Winfree E (2006) Complexity of compact proofreading for self-assembled patterns. In: Carbone A, Pierce N (eds) DNA computing, vol. 3892 of lecture notes in computer science. Springer, Berlin, pp 305–324Google Scholar
  35. Thompson BJ, Escarmis C, Parker B, Slater W, Doniger J, Tessman I, Warner RC (1975) Figure-8 configuration of dimers of s13 and \(\varphi \times 174\) replicative form DNA. J Mol Biol 91(4):409–419CrossRefGoogle Scholar
  36. Wang H (1961) Proving theorems by pattern recognition II. Bell Syst Tech J 40:1-41CrossRefGoogle Scholar
  37. Winfree E (1998) Algorithmic self-assembly of DNA. Ph.D. thesis, California Institute of TechnologyGoogle Scholar
  38. Winfree E (1998) Simulations of computing by self-assembly. California Institute of Technology technical reportGoogle Scholar
  39. Winfree E (2006) Self-healing tile sets. In: Chen J, Jonoska N, Rozenberg G (eds) Nanotechnology: science and computation, natural computing series. Springer, Berlin, pp 55–78CrossRefGoogle Scholar
  40. Winfree E, Bekbolatov R (2003) Proof reading tile sets: error correction for algorithmic self-assembly. In: Chen J, Reif J (eds) DNA Computing. Lecture Notes in Computer Science, vol 2943. Springer, Heidelberg, pp 126–144Google Scholar
  41. Yan H, Park SH, Finkelstein G, Reif J, LaBean T (2003) DNA-templated self-assembly of protein arrays and highly conductive nanowires. Science 301(5641):1882–1884CrossRefGoogle Scholar
  42. Zhang DY (2011) Cooperative hybridization of oligonucleotides. J Am Chem Soc 133(4):1077–1086CrossRefGoogle Scholar
  43. Zhang DY, Hariadi RF, Choi HM, Winfree E (2013) Integrating DNA strand-displacement circuitry with DNA tile self-assembly. Nat Commun 4:1965Google Scholar
  44. Zhang DY, Winfree E (2009) Control of DNA strand displacement kinetics using toehold exchange. J Am Chem Soc 131(48):17303–17314CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Urmi Majumder
    • 1
  • Sudhanshu Garg
    • 2
  • Thomas H. LaBean
    • 3
  • John H. Reif
    • 2
    Email author
  1. 1.Oracle CorporationWashingtonUSA
  2. 2.Department of Computer ScienceDuke UniversityDurhamUSA
  3. 3.Materials Science and Engineering Department at NC StateRaleighUSA

Personalised recommendations