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Synthetic analog computation in living cells

Abstract

A central goal of synthetic biology is to achieve multi-signal integration and processing in living cells for diagnostic, therapeutic and biotechnology applications1. Digital logic has been used to build small-scale circuits, but other frameworks may be needed for efficient computation in the resource-limited environments of cells2,3. Here we demonstrate that synthetic analog gene circuits can be engineered to execute sophisticated computational functions in living cells using just three transcription factors. Such synthetic analog gene circuits exploit feedback to implement logarithmically linear sensing, addition, ratiometric and power-law computations. The circuits exhibit Weber’s law behaviour as in natural biological systems4, operate over a wide dynamic range of up to four orders of magnitude and can be designed to have tunable transfer functions. Our circuits can be composed to implement higher-order functions that are well described by both intricate biochemical models and simple mathematical functions. By exploiting analog building-block functions that are already naturally present in cells3,5, this approach efficiently implements arithmetic operations and complex functions in the logarithmic domain. Such circuits may lead to new applications for synthetic biology and biotechnology that require complex computations with limited parts, need wide-dynamic-range biosensing or would benefit from the fine control of gene expression.

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Figure 1: Positive-feedback linearization of gene circuits for wide-dynamic-range analog computation.
Figure 2: Analog behaviour versus digital.
Figure 3: Log-domain analog computation.

References

  1. 1

    Chen, Y. Y., Galloway, K. E. & Smolke, C. D. Synthetic biology: advancing biological frontiers by building synthetic systems. Genome Biol. 13, 240 (2012)

    Article  Google Scholar 

  2. 2

    Cardinale, S. & Arkin, A. P. Contextualizing context for synthetic biology: identifying causes of failure of synthetic biological systems. Biotechnol. J. 7, 856–866 (2012)

    CAS  Article  Google Scholar 

  3. 3

    Sarpeshkar, R. Analog versus digital: extrapolating from electronics to neurobiology. Neural Comput. 10, 1601–1638 (1998)

    CAS  Article  Google Scholar 

  4. 4

    Ferrell, J. E. Signaling motifs and Weber’s law. Mol. Cell 36, 724–727 (2009)

    CAS  Article  Google Scholar 

  5. 5

    Sarpeshkar, R. Ultra Low Power Bioelectronics: Fundamentals, Biomedical Applications, and Bio-Inspired Systems 651–694, 753–786 (Cambridge Univ. Press, 2010)

    Book  Google Scholar 

  6. 6

    Sprinzak, D. et al. Cis-interactions between Notch and Delta generate mutually exclusive signalling states. Nature 465, 86–90 (2010)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Canton, B., Labno, A. & Endy, D. Refinement and standardization of synthetic biological parts and devices. Nature Biotechnol. 26, 787–793 (2008)

    CAS  Article  Google Scholar 

  8. 8

    Giorgetti, L. et al. Noncooperative interactions between transcription factors and clustered DNA binding sites enable graded transcriptional responses to environmental inputs. Mol. Cell 37, 418–428 (2010)

    CAS  Article  Google Scholar 

  9. 9

    Clark, B. & Hausser, M. Neural coding: hybrid analog and digital signalling in axons. Curr. Biol. 16, R585–R588 (2006)

    CAS  Article  Google Scholar 

  10. 10

    Daniel, R., Woo, S. S., Turicchia, L. & Sarpeshkar, R. in Biomedical Circuits and Systems Conference (BioCAS 2011) 333–336 (IEEE, 2011)

    Book  Google Scholar 

  11. 11

    Tavakoli, M. & Sarpeshkar, R. A sinh resistor and its application to tanh linearization. IEEE J. Solid-State Circuits 40, 536–543 (2005)

    ADS  Article  Google Scholar 

  12. 12

    Wild, J., Hradecna, Z. & Szybalski, W. Conditionally amplifiable BACs: switching from single-copy to high-copy vectors and genomic clones. Genome Res. 12, 1434–1444 (2002)

    CAS  Article  Google Scholar 

  13. 13

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

    ADS  CAS  Article  Google Scholar 

  14. 14

    Stricker, J. et al. A fast, robust and tunable synthetic gene oscillator. Nature 456, 516–519 (2008)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Elowitz, M. B. & Leibler, S. A synthetic oscillatory network of transcriptional regulators. Nature 403, 335–338 (2000)

    ADS  CAS  PubMed  Google Scholar 

  16. 16

    McMillen, D., Kopell, N., Hasty, J. & Collins, J. J. Synchronizing genetic relaxation oscillators by intercell signaling. Proc. Natl Acad. Sci. USA 99, 679–684 (2002)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Madar, D., Dekel, E., Bren, A. & Alon, U. Negative auto-regulation increases the input dynamic-range of the arabinose system of Escherichia coli. BMC Syst. Biol. 5, 111 (2011)

    Article  Google Scholar 

  18. 18

    Nevozhay, D., Adams, R. M., Murphy, K. F., Josić, K. & Balázsi, G. Negative autoregulation linearizes the dose–response and suppresses the heterogeneity of gene expression. Proc. Natl Acad. Sci. USA 106, 5123–5128 (2009)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Shen-Orr, S. S., Milo, R., Mangan, S. & Alon, U. Network motifs in the transcriptional regulation network of Escherichia coli. Nature Genet. 31, 64–68 (2002)

    CAS  Article  Google Scholar 

  20. 20

    You, L., Cox, R. S., Weiss, R. & Arnold, F. H. Programmed population control by cell–cell communication and regulated killing. Nature 428, 868–871 (2004)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Tabor, J. J. et al. A synthetic genetic edge detection program. Cell 137, 1272–1281 (2009)

    Article  Google Scholar 

  22. 22

    Tamsir, A., Tabor, J. J. & Voigt, C. A. Robust multicellular computing using genetically encoded NOR gates and chemical ‘wires’. Nature 469, 212–215 (2011)

    ADS  CAS  Article  Google Scholar 

  23. 23

    Auslander, S., Auslander, D., Muller, M., Wieland, M. & Fussenegger, M. Programmable single-cell mammalian biocomputers. Nature 487, 123–127 (2012)

    ADS  Article  Google Scholar 

  24. 24

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

    CAS  Article  Google Scholar 

  25. 25

    Win, M. N. & Smolke, C. D. Higher-order cellular information processing with synthetic RNA devices. Science 322, 456–460 (2008)

    ADS  CAS  Article  Google Scholar 

  26. 26

    Xie, Z., Wroblewska, L., Prochazka, L., Weiss, R. & Benenson, Y. Multi-input RNAi-based logic circuit for identification of specific cancer cells. Science 333, 1307–1311 (2011)

    ADS  CAS  Article  Google Scholar 

  27. 27

    Khalil, A. et al. A synthetic biology framework for programming eukaryotic transcription functions. Cell 150, 647–658 (2012)

    CAS  Article  Google Scholar 

  28. 28

    Dueber, J. E., Yeh, B. J., Chak, K. & Lim, W. A. Reprogramming control of an allosteric signaling switch through modular recombination. Science 301, 1904–1908 (2003)

    ADS  CAS  Article  Google Scholar 

  29. 29

    Hahnloser, R. H. R., Sarpeshkar, R., Mahowald, M. A., Douglas, R. J. & Seung, H. S. Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit. Nature 405, 947–951 (2000)

    ADS  CAS  Article  Google Scholar 

  30. 30

    Lu, T. K., Khalil, A. S. & Collins, J. J. Next-generation synthetic gene networks. Nature Biotechnol. 27, 1139–1150 (2009)

    CAS  Article  Google Scholar 

Download references

Acknowledgements

We would like to thank J. Nungesser for assistance with figures and members of the Lu and Sarpeshkar laboratories for discussions. This work was supported in part by a campus collaboration initiative from Lincoln Labs (R.D. and R.S.), the US National Science Foundation (R.D., J.R.R., R.S. and T.K.L.) under grant number 1124247, and the Office of Naval Research (J.R.R. and T.K.L.) under grant number N000141110725.

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Authors

Contributions

R.D., R.S. and T.K.L. designed the study. R.D. and J.R.R. performed experiments and collected data. R.D., J.R.R., R.S. and T.K.L. invented the analog circuit motifs. R.D., R.S. and T.K.L. developed the analog circuit motifs and associated models and simulations. All authors analysed the data, discussed results and wrote the manuscript.

Corresponding authors

Correspondence to Rahul Sarpeshkar or Timothy K. Lu.

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Competing interests

Massachusetts Institute of Technology, with which all the authors are affiliated, has filed a PCT patent application based on this work.

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Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1-53, Supplementary Tables 1-4, and Supplementary References (see Table of Contents for more details). (PDF 6125 kb)

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Daniel, R., Rubens, J., Sarpeshkar, R. et al. Synthetic analog computation in living cells. Nature 497, 619–623 (2013). https://doi.org/10.1038/nature12148

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