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Graph-theoretic formalization of hybridization in DNA sticker complexes

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Abstract

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.

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Notes

  1. Of course, it remains to be seen, either experimentally or by numeric simulation, to what extent all structures that can be described as sticker complexes are realizable in practice.

  2. Note that in our theory only nodes with perfectly complementary labels may anneal. Of course, in pratice, node labels would be implemented as DNA codeword domains. With increasing number of codewords, the probability of imperfect hybridizations increases. Indeed, error analysis, and experimental and numerical validation of our model are important topics for future research.

References

  • Abiteboul S, Hull R, Vianu V (1995) Foundations of databases. Addison-Wesley, Reading

    MATH  Google Scholar 

  • Adleman L (1994) Molecular computation of solutions to combinatorial problems. Science 226:1021–1024

    Article  Google Scholar 

  • Amos M (2005) Theoretical and experimental DNA computation. Springer, Berlin

    MATH  Google Scholar 

  • Arita M, Hagiya M, Suyama A, Joining and rotating data with molecules. In: Proceedings of 1997 IEEE international conference on evolutionary computation. pp 243–248

  • Benenson Y, Gil B, Ben-Dor U, Adar R, Shapiro E (2004) An autonomous molecular computer for logical control of gene expression. Nature 429:423–429

    Article  Google Scholar 

  • Boneh D, Dunworth C, Lipton R, Sgall J (1996) On the computational power of DNA. Discr Appl Math 71:79–94

    Article  MathSciNet  MATH  Google Scholar 

  • 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

  • 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 49–63

  • 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 145–178

  • Cardelli L (2009) Strand algebras for DNA computing. In: Deaton R, Suyama A (eds), vol.14, Springer, Heidelberg, pp 12–24

  • 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. 13–24

  • Chen J, Deaton R, Wang YZ (2005) A DNA-based memory with in vitro learning and associative recall. Nat Comput 4(2):83–101

    Article  MathSciNet  Google Scholar 

  • Condon A, Corn R, Marathe A (2001) On combinatorial DNA word design. J Comput Biol 8(3):201–220

    Article  Google Scholar 

  • Deaton R, Suyama A (eds.) (2009) Proceedings 15th international meeting on DNA computing and molecular programming, Lecture Notes in Computer Science, vol. 5877. Springer, Berlin

  • Dimitrov R, Zuker M (2004) Prediction of hybridization and melting for double-stranded nucleic acids. Biophys J 87:215–226

    Article  Google Scholar 

  • Dirks R, Pierce N (2004) Triggered amplification by hybridization chain reaction. Proc Natl Acad Sci 101(43):15275–15278

    Article  Google Scholar 

  • Garcia-Molina H, Ullman J, Widom J (2009) Database Systems: The Complete Book. Prentice Hall, Upper Saddle River

    Google Scholar 

  • 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 http://alpha.uhasselt.be/~vdbuss/dnaql.pdf

  • Hartmanis J (1995) On the weight of computations. Bull EATCS 55:136–138

    MATH  Google Scholar 

  • Hopcroft J, Ullman J (1979) Introduction to automata theory, languages, and computation. Addison-Wesley, Reading

    MATH  Google Scholar 

  • Jonoska N, McColm G, Staninska A (2011) On stoichiometry for the assembly of flexible tile DNA complexes. Nat Comput 10(3):1121–1141

    Article  MathSciNet  MATH  Google Scholar 

  • Jonoska N, McColm G (2009) Complexity classes for self-assembling flexible tiles. Theor Comput Sci 410(4-5):332–346

    Article  MathSciNet  MATH  Google Scholar 

  • Majumder U, Reif J (2009) Design of a biomolecular device that executes process algebra. In: Deaton R, Suyama A (eds), vol. 14, pp. 97–105

  • Paun G, Rozenberg G, Salomaa A (1998) DNA Computing. Springer, Berlin

    Book  MATH  Google Scholar 

  • Qian L, Soloveichik D, Winfree E (2011) Efficient Turing-universal computation with DNA polymers. In: Sakakibara Y, Mi, Y. (eds), vol. 31., pp. 123–140

  • Reif J (1999) Parallel biomolecular computation: models and simulations. Algorithmica 25(2–3):142–175

    Article  MathSciNet  MATH  Google Scholar 

  • 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 231–247

  • 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 75–120

  • 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):615–629

    Article  Google Scholar 

  • 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 275–289

  • Sakakibara Y, Mi Y (eds.) (2011) Proceedings 16th International Conference on DNA Computing and Molecular Programming, Lecture Notes in Computer Science, vol. 6518. Springer

  • Sakamoto K et al (1999) State transitions by molecules. Biosystems 52:81–91

    Article  Google Scholar 

  • Seelig G, Soloveichik D, Zhang D, Winfree E (2006) Enzyme-free nucleic acid logic circuits. Science 315(5805):1585–1588

    Article  Google Scholar 

  • Shortreed M et al (2005) A thermodynamic approach to designing structure-free combinatorial DNA word sets. Nucl Acids Res 33(15):4965–4977

    Article  Google Scholar 

  • Soloveichik D, Seelig G, Winfree E (2010) DNA as a universal substrate for chemical kinetics. PNAS 107(12):5393–5398

    Google Scholar 

  • Soloveichik D, Winfree E (2005) The computational power of Benenson automata. Theor Comput Sci 244(2–3):279–297

    Article  MathSciNet  Google Scholar 

  • 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 191–213

  • 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 418–427

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Acknowledgment

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

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Authors and Affiliations

  1. Hasselt University and transnational University of Limburg, Diepenbeek, Belgium

    Robert Brijder, Joris J. M. Gillis & Jan Van den Bussche

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  1. Robert Brijder
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  2. Joris J. M. Gillis
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  3. Jan Van den Bussche
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Correspondence to Joris J. M. Gillis.

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Joris Gillis is a Ph.D. Fellow of the Research Foundation Flanders (FWO).

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Brijder, R., Gillis, J.J.M. & Van den Bussche, J. Graph-theoretic formalization of hybridization in DNA sticker complexes. Nat Comput 12, 223–234 (2013). https://doi.org/10.1007/s11047-013-9361-1

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