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Synthetic analog computation in living cells


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.


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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 and Affiliations



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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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).

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