Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Molecular implementation of simple logic programs

This article has been updated


Autonomous programmable computing devices made of biomolecules could interact with a biological environment and be used in future biological and medical applications1,2,3,4,5,6,7. Biomolecular implementations of finite automata8,9 and logic gates4,10,11,12,13 have already been developed14,15,16,17,18. Here, we report an autonomous programmable molecular system based on the manipulation of DNA strands that is capable of performing simple logical deductions. Using molecular representations of facts such as Man(Socrates) and rules such as Mortal(X) ← Man(X) (Every Man is Mortal), the system can answer molecular queries such as Mortal(Socrates)? (Is Socrates Mortal?) and Mortal(X)? (Who is Mortal?). This biomolecular computing system compares favourably with previous approaches in terms of expressive power, performance and precision2,4,8,9,11,12,19. A compiler translates facts, rules and queries into their molecular representations and subsequently operates a robotic system that assembles the logical deductions and delivers the result. This prototype is the first simple programming language with a molecular-scale implementation.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Molecular implementation of propositional logic statements and deductions.
Figure 2: Molecular implementation of simple logic programs.
Figure 3: Long deductions.
Figure 4: ‘Who is suitable for the army?’ and ‘Who is suitable for the academy?’.
Figure 5: Bottom-up deductions.

Similar content being viewed by others

Change history

  • 24 August 2009

    In the version of this Letter initially published online, the 'Query' that appeared in lines 1, 3, 5 and 7 of Fig. 3b was incorrect. This has been corrected for all versions of the Letter.


  1. Gardner, T. S., Cantor, C. R. & Collins, J. J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  3. Basu, S., Gerchman, Y., Collins, C. H., Arnold, F. H. & Weiss, R. A synthetic multicellular system for programmed pattern formation. Nature 434, 1130–1134 (2005).

    Article  CAS  Google Scholar 

  4. Seelig, G., Soloveichik, D., Zhang, D. Y. & Winfree, E. Enzyme-free nucleic acid logic circuits. Science 314, 1585–1588 (2006).

    Article  CAS  Google Scholar 

  5. Rinaudo, K. et al. A universal RNAi-based logic evaluator that operates in mammalian cells. Nature Biotechnol. 25, 795–801 (2007).

    Article  CAS  Google Scholar 

  6. Deans, T. L., Cantor, C. R. & Collins, J. J. A tunable genetic switch based on RNAi and repressor proteins for regulating gene expression in mammalian cells. Cell 130, 363–372 (2007).

    Article  CAS  Google Scholar 

  7. Kobayashi, H. et al. Programmable cells: interfacing natural and engineered gene networks. Proc. Natl Acad. Sci. USA 101, 8414–8419 (2004).

    Article  CAS  Google Scholar 

  8. Benenson, Y. et al. Programmable and autonomous computing machine made of biomolecules. Nature 414, 430–434 (2001).

    Article  CAS  Google Scholar 

  9. Stojanovic, M. N. & Stefanovic, D. A deoxyribozyme-based molecular automaton. Nature Biotechnol. 21, 1069–1074 (2003).

    Article  CAS  Google Scholar 

  10. Breaker, R. R. Engineered allosteric ribozymes as biosensor components. Curr. Opin. Biotechnol. 31–39 (2002).

    Article  CAS  Google Scholar 

  11. Macdonald, J. et al. Medium scale integration of molecular logic gates in an automaton. Nano Lett. 6, 2598–2603 (2006).

    Article  CAS  Google Scholar 

  12. Zhang, D. Y., Turberfield, A. J., Yurke, B. & Winfree, E. Engineering entropy-driven reactions and networks catalyzed by DNA. Science 318, 1121–1125 (2007).

    Article  CAS  Google Scholar 

  13. Isaacs, F. J. et al. Engineered riboregulators enable post-transcriptional control of gene expression. Nature Biotechnol. 22, 841–847 (2004).

    Article  CAS  Google Scholar 

  14. Kobayashi, S., Yokomori, T., Sampei, G. & Mizobuchi, K. DNA implementation of simple horn clause computation. IEEE International Conference on Evolutionary Computation, 213–217 (Indianapolis, USA, 1997).

  15. Kobayashi, S. Horn clause computation with DNA molecules. J. Comb. Optim. 3, 277–299 (1999).

    Article  Google Scholar 

  16. Siewicz, P., Janczak, T., Mulawaka, J. J. & Plucienniczak, A. The inference via DNA computing. Congress on Evolutionary Computation, 988–993 (Washington, USA, 1999).

  17. Siewicz, P., Janczak, T., Mulawaka, J. J. & Plucienniczak, A. The inference based on molecular computing. Int. J. Cybern. Syst. 31/3, 283–315 (2000).

    Google Scholar 

  18. Uejima, H., Hagiya, M. & Kobayashi, S. Horn clause computation by self-assembly of DNA molecules. Lecture Notes in Computer Science, DNA Computing 7, 308–320 (2002).

    Article  Google Scholar 

  19. Adar, R. et al. Stochastic computing with biomolecular automata. Proc. Natl Acad. Sci. USA 101, 9960–9965 (2004).

    Article  CAS  Google Scholar 

  20. Sterling, L. & Shapiro, E. The Art of Prolog: Advanced Programming Techniques (MIT Press, 1986, 1994).

    Google Scholar 

  21. Lloyd, J. W. Foundations of Logic Programming (Springer-Verlag, 1987).

    Book  Google Scholar 

  22. Bratko, I. Prolog Programming for Artificial Intelligence (Addison-Wesley, 2001).

    Google Scholar 

  23. Covington, M. A. Natural Language Processing for Prolog Programmers (Prentice Hall, 1994).

  24. Gazdar, G. & Mellish, C. S. Natural Language Processing in Prolog: an Introduction to Computational Linguistics (Addison-Wesley, 1989).

    Google Scholar 

  25. Shapiro, E. Concurrent Prolog: Collected Papers, Vols 1 and 2 (MIT Press, 1987).

    Google Scholar 

  26. Tarnland, S. A. Horn clause computability. J. Comb. Optim. 17, 215–226 (1977).

    Google Scholar 

  27. Shapiro, E. Alternation and the computational complexity of logic programs. J. Logic Programming 1, 19–33 (1984).

    Article  Google Scholar 

  28. Benenson, Y., Adar, R., Paz-Elizur, T., Livneh, Z. & Shapiro, E. DNA molecule provides a computing machine with both data and fuel. Proc. Natl Acad. Sci. USA 100, 2191–2196 (2003).

    Article  CAS  Google Scholar 

  29. Maslow, A. A theory of human motivation. Psychol. Rev. 50, 370–396 (1943).

    Article  Google Scholar 

  30. Winfree, E. Biochemical logic: submerged circuits of floating DNA. ENGenious, 52–54 (2007).

Download references


We thank R. Adar, M. Kahan and B. Gil for their assistance and advice and A. Mishali and G. Brodsky for the preparation of the figures. This research was supported by The Israel Science Foundation grant no. 285/02, a research grant from the Clore Center for Biological Physics, a research grant from the Louis Chor Memorial Trust, a research grant from the Estate of Funnie Sherr, the Cymerman-Jubskind Prize, the Estate of Karl Felix Jakubskind and by the European Union FP7-ERC-AdG. S.K. is supported by the Yeshaya Horowitz association through the Center for Complexity Science. E.S. is the Incumbent of the Harry Weinrebe Professorial Chair of Computer Science and Biology and of the France Telecom–Orange Excellence Chair for Interdisciplinary Studies of the Paris ‘Centre de Recherche Interdisciplinaire’ (FTO/CRI).

Author information

Authors and Affiliations



E.S. led the project. T.R. conceived the biomolecular design and the compiler and designed and performed the experiments. T.R. and S.K. wrote the analysis tools and automated the experimental protocols. T.R. and E.S. wrote the paper.

Corresponding author

Correspondence to Ehud Shapiro.

Supplementary information

Supplementary information

Supplementary information (PDF 1419 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ran, T., Kaplan, S. & Shapiro, E. Molecular implementation of simple logic programs. Nature Nanotech 4, 642–648 (2009).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing