Synthetic mixed-signal computation in living cells

Abstract

Living cells implement complex computations on the continuous environmental signals that they encounter. These computations involve both analogue- and digital-like processing of signals to give rise to complex developmental programs, context-dependent behaviours and homeostatic activities. In contrast to natural biological systems, synthetic biological systems have largely focused on either digital or analogue computation separately. Here we integrate analogue and digital computation to implement complex hybrid synthetic genetic programs in living cells. We present a framework for building comparator gene circuits to digitize analogue inputs based on different thresholds. We then demonstrate that comparators can be predictably composed together to build band-pass filters, ternary logic systems and multi-level analogue-to-digital converters. In addition, we interface these analogue-to-digital circuits with other digital gene circuits to enable concentration-dependent logic. We expect that this hybrid computational paradigm will enable new industrial, diagnostic and therapeutic applications with engineered cells.

Figure 1. Genetic comparators with different activation thresholds.

(a) The low-threshold H₂O₂ comparator circuit. OxyR is constitutively expressed from a low-copy plasmid (LCP) and activates transcription of bxb1 recombinase from either the oxySp or oxySp* promoter on the same LCP in response to H₂O₂. Bxb1 translation is altered by the strength of the ribosome-binding site (RBS). Bxb1 inverts the gfp expression cassette located between inversely oriented attB and attP sites (triangles) on a bacterial artificial chromosome (BAC), thus turning on GFP expression. The gfp cassette has a ribozyme sequence for cleaving the 5′-untranslated region of an mRNA transcript (RiboJ), a computationally designed RBS, the gfp-coding sequence and a transcriptional terminator. (b) The per cent of GFP-positive cells at different H₂O₂ concentrations as measured by flow cytometry. Different combinations of the oxySp and oxySp* promoters, and RBSs exhibit different H₂O₂ thresholds and basal levels for GFP activation. The oxySp* and RBS30 combination (red diamonds) had the lowest threshold and a narrow transition band (shaded region). (c) The medium-threshold H₂O₂ comparator circuit. The same as a, except with the katGp promoter instead of the oxySp or oxySp* promoters, and phiC31 recombinase and its att inversion sites instead of bxb1 recombinase and its att inversion sites. (d) Different combinations of the katGp promoter and RBSs had different H₂O₂ thresholds and basal levels for GFP activation. The katGp and RBS31 combination (red triangles) had a medium H₂O₂ threshold and narrow transition band (shaded region). (e) The high-threshold H₂O₂ comparator circuit. The same as a, except with either the katGp promoter or ahpCp promoter instead of the oxySp or oxySp* promoters, and tp901 recombinase and its att inversion sites instead of bxb1 recombinase and its att inversion sites. (f) Different combinations of katGp and ahpCp promoters and RBSs exhibited different H₂O₂ thresholds for GFP activation. The katGp and RBS33 combination (red diamonds) had the highest threshold and a narrow transition band (shaded region). Lines are sigmoidal fits to the data (Supplementary Note 1). The errors (s.d.) are derived from flow cytometry experiments of three biological replicates, each of which involved n>30,000 gated events.

Figure 2. Band-pass filters assembled from low-pass and high-pass filters.

(a) The low-threshold and medium-threshold band-pass filter circuit. OxyR is constitutively expressed and activates transcription of bxb1 and phiC31 in response to H₂O₂. Bxb1 inverts the gfp cassette to enable expression from the upright proD promoter, while PhiC31 inverts the proD promoter to turn off GFP production. (b) The per cent of GFP-positive cells at different H₂O₂ concentrations as measured by flow cytometry for the circuit shown in a (black circles). The transfer functions of the comparators composing the band-pass were characterized to generate the predicted band-pass transfer function (black line), R²=0.75 (Supplementary Fig. 7). The dashed black line demarcates the 50% ON relative input range. (c) The low-threshold and high-threshold band-pass filter circuit. Same as a, except RBS33 and tp901 replace RBS31 and phiC31, respectively. (d) Same as b, but for the circuit shown in c. R²=0.95. The transfer functions of the comparators are shown in Supplementary Fig. 8. (e) Abstraction of band-pass genetic circuits. H₂O₂ activates OxyR in an analogue manner. Activated OxyR activates expression of bxb1 and either phiC31 or tp901 depending on the circuit used (a or c, respectively). The activation threshold is set by the promoters and RBS-controlling recombinase expression. The expression of GFP is dependent on bxb1 expression AND (NOT) phiC31 or tp901 expression. The errors (s.d.) are derived from flow cytometry experiments of three biological replicates, each of which involved n>30,000 gated events.

Figure 3. Multi-bit analogue-to-digital converters.

(a) Ternary (three state) logic gene circuit. OxyR is constitutively expressed and activates transcription of bxb1 and phiC31 in response to increasing concentrations of H₂O₂. Bxb1 unpairs the gfp cassette from the proD promoter, and PhiC31 unpairs the proD promoter from the gfp cassette and pairs it with the rfp cassette. (b) The per cent of cells expressing GFP (green circle) and the per cent of cells expressing RFP (red square) were fit to sigmoidal functions (solid lines). The ‘−1' state (shaded green) is defined as >90% cells being GFP positive. The ‘+1' (shaded red) is defined as >90% of cells being RFP positive. The ‘0' state is when neither −1 nor +1 conditions are met. (c) Abstraction of ternary logic genetic circuit. H₂O₂ activates OxyR, which then activates expression of bxb1 and phiC31 depending on the thresholds set by the promoters and RBS of their respective circuits. GFP expression is repressed by bxb1 OR phiC31 activation, whereas RFP activation is dependent on phiC31 activation. (d) 2-bit analogue-to-digital converter. OxyR is constitutively produced and activates transcription of bxb1, phiC31 and tp901 in response to increasing thresholds of H₂O₂. Bxb1, PhiC31 and TP901 invert gfp, rfp and bfp, respectively, to enable expression from three different upstream proD promoters. (e) The per cent of cells expressing GFP (green circle), RFP (red triangle) or BFP (blue square) was fit to sigmoidal functions (solid lines). The transition band for each circuit is demarcated by a horizontal dashed line of the same colour. Each transfer function had a similar relative input range. (f) Abstraction of 2-bit analog-to-digital converter. H₂O₂ activates OxyR, which then activates expression of bxb1, phiC31 and tp901 depending on the thresholds set by the promoters and RBS of their respective circuits. Bxb1, PhiC31 and TP901 then activate gfp, rfp and bfp expression, respectively. The errors (s.d.) are derived from flow cytometry experiments of three biological replicates, each of which involved n>30,000 gated events.

Figure 4. Mixed-signal computation and concentration-dependent logic.

(a) Mixed-signal gene circuit. OxyR is constitutively produced and activates transcription of bxb1 and phiC31 at two different thresholds of H₂O₂. Both Bxb1 and PhiC31 can invert a gfp expression cassette. Bxb1-based flipping occurs at a lower H₂O₂ concentration than PhiC31-based flipping such that gfp is only in an upright orientation over an intermediate range of H₂O₂. Furthermore, TetR is constitutively produced and represses the pLtetO promoter; this repression is relieved by the presence of aTc. TP901 is expressed from the pLtetO promoter and inverts the proD promoter such that it cannot drive expression from an upright gfp cassette. The resulting circuit implements concentration-dependent logic with an output (GFP) that is ON only if an intermediate level of the input H₂O₂ is present and aTc is not present. (b) The per cent of cells expressing GFP at different concentrations of H₂O₂ in the presence (black square) and absence (red circle) of aTc. When aTc is absent, the circuit implements a band-pass response to H₂O₂, where the data are well fit by the same transfer function (red line) as the black line in Fig. 2b, R²=0.94. When aTc is present, the circuit is OFF. The black line is a straight line between each data point. (c) Abstraction of the mixed-signal gene circuit. H₂O₂ activates OxyR, which then activates expression of bxb1 and phiC31 depending upon the thresholds set by the promoters and RBS of their respective circuits. aTc activates expression of tp901 via inactivation of TetR. GFP is expressed when either Bxb1 or PhiC31 are present AND NOT when TP901 is activated. The errors (s.d.) are derived from flow cytometry experiments of three biological replicates, each of which involved n>30,000 gated events.