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.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
Nature Communications Open Access 24 September 2022
Nature Communications Open Access 07 July 2022
Distributed Computing Open Access 23 October 2021
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Chen, Y. Y., Galloway, K. E. & Smolke, C. D. Synthetic biology: advancing biological frontiers by building synthetic systems. Genome Biol. 13, 240 (2012)
Cardinale, S. & Arkin, A. P. Contextualizing context for synthetic biology: identifying causes of failure of synthetic biological systems. Biotechnol. J. 7, 856–866 (2012)
Sarpeshkar, R. Analog versus digital: extrapolating from electronics to neurobiology. Neural Comput. 10, 1601–1638 (1998)
Ferrell, J. E. Signaling motifs and Weber’s law. Mol. Cell 36, 724–727 (2009)
Sarpeshkar, R. Ultra Low Power Bioelectronics: Fundamentals, Biomedical Applications, and Bio-Inspired Systems 651–694, 753–786 (Cambridge Univ. Press, 2010)
Sprinzak, D. et al. Cis-interactions between Notch and Delta generate mutually exclusive signalling states. Nature 465, 86–90 (2010)
Canton, B., Labno, A. & Endy, D. Refinement and standardization of synthetic biological parts and devices. Nature Biotechnol. 26, 787–793 (2008)
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)
Clark, B. & Hausser, M. Neural coding: hybrid analog and digital signalling in axons. Curr. Biol. 16, R585–R588 (2006)
Daniel, R., Woo, S. S., Turicchia, L. & Sarpeshkar, R. in Biomedical Circuits and Systems Conference (BioCAS 2011) 333–336 (IEEE, 2011)
Tavakoli, M. & Sarpeshkar, R. A sinh resistor and its application to tanh linearization. IEEE J. Solid-State Circuits 40, 536–543 (2005)
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)
Qian, L. & Winfree, E. Scaling up digital circuit computation with DNA strand displacement cascades. Science 332, 1196–1201 (2011)
Stricker, J. et al. A fast, robust and tunable synthetic gene oscillator. Nature 456, 516–519 (2008)
Elowitz, M. B. & Leibler, S. A synthetic oscillatory network of transcriptional regulators. Nature 403, 335–338 (2000)
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)
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)
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)
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)
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)
Tabor, J. J. et al. A synthetic genetic edge detection program. Cell 137, 1272–1281 (2009)
Tamsir, A., Tabor, J. J. & Voigt, C. A. Robust multicellular computing using genetically encoded NOR gates and chemical ‘wires’. Nature 469, 212–215 (2011)
Auslander, S., Auslander, D., Muller, M., Wieland, M. & Fussenegger, M. Programmable single-cell mammalian biocomputers. Nature 487, 123–127 (2012)
Isaacs, F. J. et al. Engineered riboregulators enable post-transcriptional control of gene expression. Nature Biotechnol. 22, 841–847 (2004)
Win, M. N. & Smolke, C. D. Higher-order cellular information processing with synthetic RNA devices. Science 322, 456–460 (2008)
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)
Khalil, A. et al. A synthetic biology framework for programming eukaryotic transcription functions. Cell 150, 647–658 (2012)
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)
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)
Lu, T. K., Khalil, A. S. & Collins, J. J. Next-generation synthetic gene networks. Nature Biotechnol. 27, 1139–1150 (2009)
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.
Massachusetts Institute of Technology, with which all the authors are affiliated, has filed a PCT patent application based on this work.
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)
About this article
Cite this article
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
This article is cited by
Nature Communications (2022)
Nature Communications (2022)
Distributed Computing (2022)
Multimedia Tools and Applications (2022)
Molecular device design based on chemical reaction networks: state feedback controller, static pre-filter, addition gate control system and full-dimensional state observer
Journal of Mathematical Chemistry (2022)