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Neural network computation with DNA strand displacement cascades

Nature volume 475, pages 368–372 (2011)Cite this article

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Abstract

The impressive capabilities of the mammalian brain—ranging from perception, pattern recognition and memory formation to decision making and motor activity control—have inspired their re-creation in a wide range of artificial intelligence systems for applications such as face recognition, anomaly detection, medical diagnosis and robotic vehicle control1. Yet before neuron-based brains evolved, complex biomolecular circuits provided individual cells with the ‘intelligent’ behaviour required for survival2. However, the study of how molecules can ‘think’ has not produced an equal variety of computational models and applications of artificial chemical systems. Although biomolecular systems have been hypothesized to carry out neural-network-like computations in vivo3,2,4 and the synthesis of artificial chemical analogues has been proposed theoretically5,6,7,8,9, experimental work10,11,12,13 has so far fallen short of fully implementing even a single neuron. Here, building on the richness of DNA computing14 and strand displacement circuitry15, we show how molecular systems can exhibit autonomous brain-like behaviours. Using a simple DNA gate architecture16 that allows experimental scale-up of multilayer digital circuits17, we systematically transform arbitrary linear threshold circuits18 (an artificial neural network model) into DNA strand displacement cascades that function as small neural networks. Our approach even allows us to implement a Hopfield associative memory19 with four fully connected artificial neurons that, after training in silico, remembers four single-stranded DNA patterns and recalls the most similar one when presented with an incomplete pattern. Our results suggest that DNA strand displacement cascades could be used to endow autonomous chemical systems with the capability of recognizing patterns of molecular events, making decisions and responding to the environment.

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Figure 1: The seesaw gate motif and the construction of linear threshold gates.
Figure 2: A linear threshold circuit that computes the three-bit XOR function.
Figure 3: A four-neuron Hopfield associative memory.

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References

  1. Rojas, R. Neural Networks: A Systematic Introduction (Springer, 1996)

    Book  Google Scholar 

  2. Bray, D. Protein molecules as computational elements in living cells. Nature 376, 307–312 (1995)

    Article  ADS  CAS  Google Scholar 

  3. Mjolsness, E., Sharp, D. H. & Reinitz, J. A connectionist model of development. J. Theor. Biol. 152, 429–453 (1991)

    Article  CAS  Google Scholar 

  4. Buchler, N. E., Gerland, U. & Hwa, T. On schemes of combinatorial transcription logic. Proc. Natl Acad. Sci. USA 100, 5136–5141 (2003)

    Article  ADS  CAS  Google Scholar 

  5. Hjelmfelt, A., Weinberger, E. D. & Ross, J. Chemical implementation of neural networks and Turing machines. Proc. Natl Acad. Sci. USA 88, 10983–10987 (1991)

    Article  ADS  CAS  Google Scholar 

  6. Baum, E. B. Building an associative memory vastly larger than the brain. Science 268, 583–585 (1995)

    Article  ADS  CAS  Google Scholar 

  7. Mills, A. P., Yurke, B. & Platzman, P. M. Article for analog vector algebra computation. Biosystems 52, 175–180 (1999)

    Article  CAS  Google Scholar 

  8. Kim, J., Hopfield, J. J. & Winfree, E. in Advances in Neural Information Processing Systems Vol. 17 (eds Saul, L. K., Weiss, Y. & Bottou, L. ) 681–688 (MIT Press, 2004)

    Google Scholar 

  9. Zhang, D. Y. & Seelig, G. in DNA Computing and Molecular Programming (eds Sakakibara, Y. & Mi, Y. ) 176–186 (Lecture Notes in Computer Science, Vol. 6518, Springer, 2011)

    Book  Google Scholar 

  10. Laplante, J. P., Pemberton, M., Hjelmfelt, A. & Ross, J. Experiments on pattern recognition by chemical kinetics. J. Phys. Chem. 99, 10063–10065 (1995)

    Article  CAS  Google Scholar 

  11. Mills, A. P., Jr, Turberfield, M., Turberfield, A. J., Yurke, B. & Platzman, P. M. Experimental aspects of DNA neural network computation. Soft Comput. 5, 10–18 (2001)

    Article  Google Scholar 

  12. Lim, H. W. et al. In vitro molecular pattern classification via DNA-based weighted-sum operation. Biosystems 100, 1–7 (2010)

    Article  CAS  Google Scholar 

  13. Kim, J. & Winfree, E. Synthetic in vitro transcriptional oscillators. Mol. Syst. Biol. 7, 465 (2011)

    Article  Google Scholar 

  14. Adleman, L. M. Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994)

    Article  ADS  CAS  Google Scholar 

  15. Zhang, D. Y. & Seelig, G. Dynamic DNA nanotechnology using strand-displacement reactions. Nature Chem. 3, 103–113 (2011)

    Article  ADS  CAS  Google Scholar 

  16. Qian, L. & Winfree, E. A simple DNA gate motif for synthesizing large-scale circuits. J. R. Soc. Interface 10.1098/rsif.2010.0729 (published online 4 February 2011)

    Google Scholar 

  17. Qian, L. & Winfree, E. Scaling up digital circuit computation with DNA strand displacement cascades. Science 332, 1196–1201 (2011)

    Article  ADS  CAS  Google Scholar 

  18. Muroga, S. Threshold Logic and its Applications Vol. 18 (Wiley-Interscience, 1971).

  19. Hopfield, J. J. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl Acad. Sci. USA 79, 2554–2558 (1982)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  20. McCulloch, W. S. & Pitts, W. A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biol. 5, 115–133 (1943)

    MathSciNet  MATH  Google Scholar 

  21. Kautz, W. H. The realization of symmetric switching functions with linear-input logical elements. IRE Trans. Electron. Comput. EC-10, 371–378 (1961)

    Article  MathSciNet  Google Scholar 

  22. Wegener, I. The complexity of the parity function in unbounded fan-in, unbounded depth circuits. Theor. Comput. Sci. 85, 155–170 (1991)

    Article  MathSciNet  Google Scholar 

  23. Hajnal, A., Maass, W., Pudlák, P., Szegedy, M. & Turan, G. Threshold circuits of bounded depth. J. Comput. Syst. Sci. 46, 129–154 (1993)

    Article  MathSciNet  Google Scholar 

  24. Müller, D. E. in Symp. on the Application of Switching Theory (eds Aiken, H. & Main, W. F. ) 289–297 (Stanford Univ. Press, 1963)

    Google Scholar 

  25. Lederman, H., Macdonald, J., Stefanovic, D. & Stojanovic, M. N. Deoxyribozyme-based three-input logic gates and construction of a molecular full adder. Biochemistry 45, 1194–1199 (2006)

    Article  CAS  Google Scholar 

  26. Amari, S. I. Characteristics of sparsely encoded associative memory. Neural Netw. 2, 451–457 (1989)

    Article  Google Scholar 

  27. Soloveichik, D., Seelig, G. & Winfree, E. DNA as a universal substrate for chemical kinetics. Proc. Natl Acad. Sci. USA 107, 5393–5398 (2010)

    Article  ADS  CAS  Google Scholar 

  28. Fernando, C. T. et al. Molecular circuits for associative learning in single-celled organisms. J. R. Soc. Interface 6, 463–469 (2009)

    Article  CAS  Google Scholar 

  29. Pei, R., Matamoros, E., Liu, M., Stefanovic, D. & Stojanovic, M. N. Training a molecular automaton to play a game. Nature Nanotechnol. 5, 773–777 (2010)

    Article  ADS  CAS  Google Scholar 

  30. Rosenfeld, N. et al. MicroRNAs accurately identify cancer tissue origin. Nature Biotechnol. 26, 462–469 (2008)

    Article  CAS  Google Scholar 

  31. Simmel, F. C. Towards biomedical applications for nucleic acid nanodevices. Nanomedicine 2, 817–830 (2007)

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank P. Rothemund, P. Yin, D. Woods, D. Soloveichik and N. Dabby for comments on the manuscript. We also thank R. Murray for the use of experimental facilities. This work was supported by the NSF (grant nos 0728703 and 0832824 (The Molecular Programming Project)) and by HFSP award no. RGY0074/2006-C.

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Authors and Affiliations

  1. Bioengineering, California Institute of Technology, Pasadena, 91125, California, USA

    Lulu Qian & Erik Winfree

  2. Computer Science, California Institute of Technology, Pasadena, 91125, California, USA

    Erik Winfree

  3. Computation and Neural Systems, California Institute of Technology, Pasadena, 91125, California, USA

    Erik Winfree & Jehoshua Bruck

  4. Electrical Engineering, California Institute of Technology, Pasadena, 91125, California, USA

    Jehoshua Bruck

Authors
  1. Lulu Qian
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  2. Erik Winfree
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  3. Jehoshua Bruck
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Contributions

L.Q. designed the system, performed the experiments and analysed the data; L.Q. and E.W. performed the in silico training and wrote the manuscript; E.W. guided the project and discussed the design and the data; and J.B. initiated and guided the project, and discussed the manuscript.

Corresponding author

Correspondence to Erik Winfree.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Figure 1-28 with legends, Supplementary Methods, Supplementary Text and Data comprising: 1 The seesaw DNA gate motif; 2 Four types of seesaw gates; 3 Four transformation rules; 4 Circuit design lessons learned from experiments; 5 In silico training of dual-rail monotone Hopfield associative memories; 6 A four-neuron dual-rail monotone Hopfield associative memory; 7 Modeling and simulations; 8 Sequences, Supplementary Tables 1-7 and additional references. (PDF 19348 kb)

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Qian, L., Winfree, E. & Bruck, J. Neural network computation with DNA strand displacement cascades. Nature 475, 368–372 (2011). https://doi.org/10.1038/nature10262

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