Skip to main content
SpringerLink
Log in

Watson–Crick palindromes in DNA computing

  • Published:
Natural Computing Aims and scope Submit manuscript

Abstract

This paper provides an overview of existing approaches to encoding information on DNA strands for biocomputing, with a focus on the notion of Watson–Crick (WK) palindromes. We obtain a closed form for, as well as several properties of WK palindromes: The set of WK-palindromes is dense, context-free, but not regular, and is in general not closed under catenation and insertion. We obtain some properties that link the WK palindromes to classical notions such as that of primitive words. For example we show that the set of WK-palindromic words that cannot be written as the product of two nonempty WK-palindromes equals the set of primitive WK-palindromes. We also investigate various simultaneous Watson–Crick conjugate equations of words and show that the equations have, in most cases, only Watson–Crick palindromic solutions. Our results hold for more general functions, such as arbitrary morphic and antimorphic involutions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Adleman L (2000) Towards a mathematical theory of self-assembly. Technical Report 00-722, Department of Computer Science, University of Southern California

  • Daley M, McQuillan I (2006) On computational properties of template-guided DNA recombination. In: Carbone A, Pierce N (eds) Proceedings of the DNA computing 11. LNCS, vol 3892. Springer, Berlin, pp 27–37

  • de Luca A (2006) Pseudopalindrome closure operators in free monoids. Theor Comput Sci 362:282–300

    Article  MATH  Google Scholar 

  • Domaratzki M (2006) Hairpin structures defined by DNA trajectories. In: Mao C, Yokomori T (eds) Proceedings of the DNA computing 12. LNCS, vol 4287. Springer, Berlin, pp 182–194

  • Feldkamp U, Banzhaf W, Rauhe H (2000) A DNA sequence compiler. In: Condon A, Rozenberg G (eds) Pre-proceedings of the DNA-based computers 6. Leiden, Netherlands

  • Feldkamp U, Saghafi S, Banzhaf W, Rauhe H (2001) DNA sequence generator: a program for the construction of DNA sequences. In: Jonoska N, Seeman N (eds) Proceedings of the DNA-based computers 7. LNCS, vol 2340. Springeer, Berlin, pp 23–32

  • Garzon MH, Oehman C (2001) Biomolecular computation in virtual test tubes. In: Jonoska N, Seeman N (eds) Proceedings of the DNA-based computers 7. LNCS, vol 2340. Springer, Berlin, pp 117–128

  • Garzon M, Phan V, Roy S, Neel A (2006) In search of optimal codes for DNA computing. In: Mao C, Yokomori T (eds) Proceedings of the DNA computing 12. LNCS, vol 4287. Springer, Berlin, 143–156

  • Hartemik J, Gifford DK, Khodor J (1999) Automated constaint-based nucleotide sequence selection for DNA computation. In: Kari L, Rubin H, Wood D (eds) Proceedings of the DNA based computers 4. Biosystems 52(1–3):227–235

  • Hartemink J, Gifford DK (1999) Thermodynamic simulation of deoxyoligonucleotide hybridization for DNA computation. In: Rubin H, Wood D (eds) Proceedings of the DNA-based computers 3. DIMACS series in discrete mathematics and theoretical computer science. AMS Press, Providence, pp 25–38

  • Hopcroft J, Ullman J, Motwani R (2001) Introduction to automata theory, languages and computation, 2nd edn. Addison Wesley, Boston

    MATH  Google Scholar 

  • Hussini S, Kari L, Konstantinidis S (2003) Coding properties of DNA languages. Theor Comput Sci 290:1557–1579

    Article  MATH  MathSciNet  Google Scholar 

  • Jonoska N, Mahalingam K, Chen J (2005) Involution codes: with application to DNA coded languages. Nat Comput 4(2):141–162

    Article  MathSciNet  Google Scholar 

  • Jonoska N, Kari L, Mahalingam K (2006) Involution solid and join codes. In: Ibarra O, Dang Z (eds) Developments in language theory: 10th international conference. LNCS, vol 4036. Springer, Berlin, pp 192–202

  • Kari L, Mahalingam K (2007a) Involutively bordered words. Int J Found Comput Sci 18:1089–1106

    Article  MathSciNet  Google Scholar 

  • Kari L, Mahalingam K (2007b) Watson–Crick conjugate and commutative words. In: Garzon M, Yan H (eds) Preproceedings of the DNA computing 13. Springer, Berlin, pp 75–87

  • Kari L, Mahalingam K (2007c) Watson–Crick bordered words and their syntactic monoid. In: Domaratzki M, Salomaa K (eds) International workshop on language theory in biocomputing, Kingston, Canada, pp 64–75

  • Kari L, Konstantinidis S, Losseva E, Wozniak G (2003) Sticky-free and overhang-free DNA languages. Acta Inf 40:119–157

    Article  MATH  MathSciNet  Google Scholar 

  • Kari L, Konstantinidis S, Losseva E, Sosik P, Thierrin G (2005a) Hairpin structures in DNA words. In: Carbone A, Pierce N (eds) Proceedings of the DNA computing 11. LNCS, vol 3892. Springer, Berlin, pp 158–170

  • Kari L, Konstantinidis S, Sosik P (2005b) Bond-free languages: formalizations, maximality and construction methods. Int J Found Comput Sci 16: 1039–1070

    Article  MATH  MathSciNet  Google Scholar 

  • Kari L, Mahalingam K, Thierrin G (2007) The syntactic monoid of hairpin-free languages. Acta Inf 44(3):153–166

    Article  MATH  MathSciNet  Google Scholar 

  • Kari L, Mahalingam K, Seki S (2009) Twin-roots of words and their properties. Theor Comput Sci 410(24–25):2393–2400

    Article  MATH  MathSciNet  Google Scholar 

  • Lothaire M (1997) Combinatorics of words. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Lyndon RC, Schutzenberger MP (1962) On the equation a M = b N c p in a free group. Mich Math J 9:289–298

    Article  MATH  MathSciNet  Google Scholar 

  • Marathe A, Condon A, Corn R (1999) On combinatorial DNA word design. In: Winfree E, Gifford D (eds) Proceedings of the DNA based computers 5. DIMACS series in discrete mathematics and theoretical computer science. AMS Press, Providence, pp 75–89

  • Shyr HJ (2001) Free monoids and languages. Hon Min Book Company, Taiwan

    Google Scholar 

  • Soloveichik D, Winfree E (2006) Complexity of compact proofreading for self-assembled patterns. In: Carbone A, Pierce N (eds) Proceedings of the DNA computing 11. LNCS, vol 3892. Springer, Berlin, pp 305–324

  • Tulpan D, Hoos H, Condon A (2003) Stochastic local search algorithms for DNA word design. In: Hagiya M, Ohuchi A (eds) Proceedings of the DNA-based computers 8. LNCS, vol 2568. Springer, Berlin, pp 229–241

  • Yu SS (1998) d-minimal languages. Discret Appl Math 89:243–262

    Article  MATH  Google Scholar 

  • Yu SS (2005) Languages and codes. Lecture notes. Department of Computer Science, National Chung-Hsing University, Taichung

Download references

Acknowledgements

Research supported by Natural Sciences and Engineering Research Council of Canada Discovery Grant and Canada Research Chair Award for Lila Kari.

Author information

Author notes

  1. Kalpana Mahalingam

    Present address: Department of Mathematics, Indian Institute of Technology, Chennai, 600035, India

Authors and Affiliations

  1. Department of Computer Science, University of Western Ontario, London, ON, N6A 5B7, Canada

    Lila Kari & Kalpana Mahalingam

Authors
  1. Lila Kari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kalpana Mahalingam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lila Kari.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kari, L., Mahalingam, K. Watson–Crick palindromes in DNA computing. Nat Comput 9, 297–316 (2010). https://doi.org/10.1007/s11047-009-9131-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11047-009-9131-2

Keywords

Search

Navigation