Natural Computing

, Volume 12, Issue 2, pp 223–234 | Cite as

Graph-theoretic formalization of hybridization in DNA sticker complexes

  • Robert Brijder
  • Joris J. M. GillisEmail author
  • Jan Van den Bussche


Sticker complexes are a formal graph-based data model for a restricted class of DNA complexes, motivated by potential applications to databases. This data model allows for a purely declarative definition of hybridization. We introduce the notion of terminating hybridization, which intuitively means that only a finite number of different products can be generated. We characterize this notion in purely graph-theoretic terms. Under a finite alphabet, each product is shown to be of polynomial size. Yet, terminating hybridization can still produce results of exponential size, in that there may be exponentially many different (nonisomorphic) finished products. We indicate a class of complexes where hybridization is guaranteed to be polynomially bounded.


DNA Hybridization Graph-theory Complexity 



We thank the program committee for referring us to the work of Jonoska et al. (2011).


  1. Abiteboul S, Hull R, Vianu V (1995) Foundations of databases. Addison-Wesley, ReadingzbMATHGoogle Scholar
  2. Adleman L (1994) Molecular computation of solutions to combinatorial problems. Science 226:1021–1024CrossRefGoogle Scholar
  3. Amos M (2005) Theoretical and experimental DNA computation. Springer, BerlinzbMATHGoogle Scholar
  4. Arita M, Hagiya M, Suyama A, Joining and rotating data with molecules. In: Proceedings of 1997 IEEE international conference on evolutionary computation. pp 243–248Google Scholar
  5. Benenson Y, Gil B, Ben-Dor U, Adar R, Shapiro E (2004) An autonomous molecular computer for logical control of gene expression. Nature 429:423–429CrossRefGoogle Scholar
  6. Boneh D, Dunworth C, Lipton R, Sgall J (1996) On the computational power of DNA. Discr Appl Math 71:79–94MathSciNetzbMATHCrossRefGoogle Scholar
  7. Brijder R, Gillis JJM, Van den Bussche J, A Comparison of Graph-Theoretic DNA Hybridization models. Theoretical Computer Science (in print). doi: 10.1016/j.tcs.2011.12.023
  8. Brijder R, Gillis JJM, Van den Bussche J (2011) Graph-theoretic formalization of hybridization in DNA sticker complexes. 17th international conference on DNA computing and molecular programming. Lecture Notes in Computer Science, vol. 6937, Springer, Berlin, pp 49–63Google Scholar
  9. Cardelli L (2005) Abstract machines in systems biology. In: Transactions on computational systems biology III, Lecture Notes in Computer Science, vol. 3737, Springer, Berlin, pp 145–178Google Scholar
  10. Cardelli L (2009) Strand algebras for DNA computing. In: Deaton R, Suyama A (eds), vol.14, Springer, Heidelberg, pp 12–24Google Scholar
  11. Chen HL, Kao MY (2010) Optimizing tile concentrations to minimize errors and time for DNA tile self-assembly systems. In: Sakakibara Y, Mi Y, vol. 31, pp. 13–24Google Scholar
  12. Chen J, Deaton R, Wang YZ (2005) A DNA-based memory with in vitro learning and associative recall. Nat Comput 4(2):83–101MathSciNetCrossRefGoogle Scholar
  13. Condon A, Corn R, Marathe A (2001) On combinatorial DNA word design. J Comput Biol 8(3):201–220CrossRefGoogle Scholar
  14. Deaton R, Suyama A (eds.) (2009) Proceedings 15th international meeting on DNA computing and molecular programming, Lecture Notes in Computer Science, vol. 5877. Springer, BerlinGoogle Scholar
  15. Dimitrov R, Zuker M (2004) Prediction of hybridization and melting for double-stranded nucleic acids. Biophys J 87:215–226CrossRefGoogle Scholar
  16. Dirks R, Pierce N (2004) Triggered amplification by hybridization chain reaction. Proc Natl Acad Sci 101(43):15275–15278CrossRefGoogle Scholar
  17. Garcia-Molina H, Ullman J, Widom J (2009) Database Systems: The Complete Book. Prentice Hall, Upper Saddle RiverGoogle Scholar
  18. Gillis J, Van den Bussche J (2012) A formal model of databases in DNA. In: Horimoto, K., Nakatsui, M., Popov, N. (eds.) Algebraic and numeric biology 2010. Lecture Notes in Computer Science, vol. 6479. Springer. For a preprint see
  19. Hartmanis J (1995) On the weight of computations. Bull EATCS 55:136–138zbMATHGoogle Scholar
  20. Hopcroft J, Ullman J (1979) Introduction to automata theory, languages, and computation. Addison-Wesley, ReadingzbMATHGoogle Scholar
  21. Jonoska N, McColm G, Staninska A (2011) On stoichiometry for the assembly of flexible tile DNA complexes. Nat Comput 10(3):1121–1141MathSciNetzbMATHCrossRefGoogle Scholar
  22. Jonoska N, McColm G (2009) Complexity classes for self-assembling flexible tiles. Theor Comput Sci 410(4-5):332–346MathSciNetzbMATHCrossRefGoogle Scholar
  23. Majumder U, Reif J (2009) Design of a biomolecular device that executes process algebra. In: Deaton R, Suyama A (eds), vol. 14, pp. 97–105Google Scholar
  24. Paun G, Rozenberg G, Salomaa A (1998) DNA Computing. Springer, BerlinzbMATHCrossRefGoogle Scholar
  25. Qian L, Soloveichik D, Winfree E (2011) Efficient Turing-universal computation with DNA polymers. In: Sakakibara Y, Mi, Y. (eds), vol. 31., pp. 123–140Google Scholar
  26. Reif J (1999) Parallel biomolecular computation: models and simulations. Algorithmica 25(2–3):142–175MathSciNetzbMATHCrossRefGoogle Scholar
  27. Reif J et al. (2002) Experimental construction of very large scale DNA databases with associative search capability. In: Jonoska N, Seeman N (eds.) Proceedings 7th international meeting on DNA computing. Lecture Notes in Computer Science, vol. 2340. Springer, Heidelberg, pp 231–247Google Scholar
  28. Rothemund P (1996) A DNA and restriction enzyme implementation of turing machines. In: Lipton R, Baum E. (eds) DNA based computers: DIMACS workshop, April 4. American Mathematical Society, Providence, pp 75–120Google Scholar
  29. Roweis S, Winfree E, Burgoyne R, Chelyapov N, Goodman M, Rothemund P, Adleman L (1998) A sticker-based model for DNA computation. J Comput Biol 5(4):615–629CrossRefGoogle Scholar
  30. Sager J, Stefanovic D (2006) Designing nucleotide sequences for computation: a survey of constraints. In: Carbone A, Pierce N (eds) Proceedings 11th international meeting on DNA computing. Lecture Notes in Computer Science, vol. 3892, Springer, Berlin, pp 275–289Google Scholar
  31. Sakakibara Y, Mi Y (eds.) (2011) Proceedings 16th International Conference on DNA Computing and Molecular Programming, Lecture Notes in Computer Science, vol. 6518. SpringerGoogle Scholar
  32. Sakamoto K et al (1999) State transitions by molecules. Biosystems 52:81–91CrossRefGoogle Scholar
  33. Seelig G, Soloveichik D, Zhang D, Winfree E (2006) Enzyme-free nucleic acid logic circuits. Science 315(5805):1585–1588CrossRefGoogle Scholar
  34. Shortreed M et al (2005) A thermodynamic approach to designing structure-free combinatorial DNA word sets. Nucl Acids Res 33(15):4965–4977CrossRefGoogle Scholar
  35. Soloveichik D, Seelig G, Winfree E (2010) DNA as a universal substrate for chemical kinetics. PNAS 107(12):5393–5398Google Scholar
  36. Soloveichik D, Winfree E (2005) The computational power of Benenson automata. Theor Comput Sci 244(2–3):279–297MathSciNetCrossRefGoogle Scholar
  37. Winfree E, Yang X, Seeman N (1998) Universal computation via self-assembly of DNA: Some theory and experiments. In: Landweber L, Baum E (eds) DNA based computers II: DIMACS workshop, June 10–12, 1996. American Mathematical Society, Providence, pp 191–213Google Scholar
  38. Yamamoto M et al. (2006) Development of DNA relational databases and data manipulation experiments. In: Mao C, Yokomori T (eds) Proceedings 12th international meeting on DNA computing. Lecture Notes in Computer Science, vol. 4287. Springer, Berlin, pp 418–427Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Robert Brijder
    • 1
  • Joris J. M. Gillis
    • 1
    Email author
  • Jan Van den Bussche
    • 1
  1. 1.Hasselt University and transnational University of LimburgDiepenbeekBelgium

Personalised recommendations