NOR gate architecture

We built a universal, single-gene logic gate, in our case a NOR gate (Fig. 1a). The NOR gate outputs are then gRNAs that match the target sequences on other NOR gate promoters (Fig. 1b). Our NOR gates are genomically integrated into yeast cells (Fig. 1c). We avoided using RNA polymerase (Pol) III promoters to express gRNAs20,30,31,34 because they have low expression levels relative to Pol II promoters and are more difficult to engineer45,46. By programming the NOR gate input target sequences and output gRNA sequences in a set of gates, we were able to construct a variety of circuit topologies (Fig. 1d).

Figure 1: Schematic of the NOR gate architecture and circuit composition. (a) A NOR gate input stage consists of a Pol II pGRR promoter that is fully repressed by the binding of either one or both of its cognate gRNA-dCas9-Mxi1 complexes. The output stage of the NOR gate is a gRNA transcript, flanked by self-cleaving ribozymes (RGR). Cleavage sites are indicated by red arrows. The cleavage of the ribozymes prevents nuclear export of the gRNA, indicated by dotted grey arrow. (b) The process of NOR gate library construction. Our library consists of a set of 400 two-input pGRR promoters and 20 RGR outputs for a total of 8,000 possible NOR gates. (c) Genomically integrating NOR gates into S. cerevisiae. (d) Arbitrary circuits are constructed by integrating multiple NOR gates into a single strain. Full size image

Second, we required a consistent ‘OFF’ state for our NOR gates that corresponded to complete or near complete repression of the output promoter (Supplementary Fig. 1). we used the chromatin remodelling repression domain Mxi1 to take advantage of the eukaryotic cell’s ability to repress gene expression, by fusing this domain to dCas9 (ref. 30) (Fig. 2a). When compared with a number of repression domains, Mxi1 showed the strongest repression (Supplementary Fig. 2). Our results suggest that such repression provides a significantly improved and more consistent ‘OFF’ signal compared with repression via steric hindrance (Fig. 2b), in which dCas9 is interfering with transcriptional initiation, but is not remodelling chromatin. A mathematical model of our NOR gates, fit to both steady-state and time response data, predicts them have effectively zero transcriptional leak in their OFF states. Additionally, the model predicts that repression via steric hindrance leaks more than repression via dCas9-Mxi1 (Fig. 2b).

Figure 2: Orthogonality and repression via dCas9-Mxi1. (a) A constitutive promoter drives expression of gRNAs paired with a combinatorial library of cognate promoters. Orthogonality of the gRNA guide sequences was tested by crossing the 20 pGRR i,null promoters, each expressing GFP, with the 20 gRNA i , creating 400 different strains of yeast. Fluorescence values of each strain were measured using flow cytometry. Fluorescence values from one biological replicate are displayed in the matrix. (b) Dose response curves are shown for repression via dCas9-Mxi1 and dCas9 repression via steric hindrance of pGRR driving GFP at three separate positions in the promoter. The three positions are annotated on the pGRR promoter representation. At all three positions, at maximal induction, dCas9-Mxi1 represses the promoter to a lower fluorescence level than dCas9 alone. Model fits predicted the parameter value L, representing transcriptional leak, for all curves. At all three positions the predicted L value is as small or smaller for dCas9-Mix1 than for steric repression. Error bars represent the s.d. of three biological replicates measured over three separate experiments. Full size image

Our approach allowed for the construction of the largest eukaryotic gene circuits, to the best of our knowledge, ever demonstrated (Table 1).

Table 1 Synthetic circuit size comparison. Full size table

The gate NOR i,j,k , with input signals r i and r j and output r k , consists of a gRNA-responsive Pol II promoter (pGRR i,j ) input stage, driving an output stage, ribozyme-flanked gRNA (RGR k ) (Fig. 1a). According to NOR logic, r k is high only when both r i and r j are low. A signal, r i , is defined as a gRNA complexed with a dCas9-Mix1 fusion protein that confers strong transcriptional repression when bound to DNA30. The gRNA signals are distinguished by their unique 5′ guide sequence. A 20-component library of signals defining r 1 –r 20 was used in this work (Supplementary Table 1). The pGRR i,j promoter contains two, 20 base-pair (bp) target sites that match r i and r j respectively. Since we designed 20 signals, there are 203=8,000 total NOR gates in the set. A NOR i,j,k functions as a NOT j,k if the pGRR i,j contains two identical target sites, if the pGRR i,j contains only one target site from the 20 component library (pGRR i,null ) or if r i is simply not used in the circuit. A target sequence of ‘null’ refers to a pGRR that contains a target sequence that does not match any gRNA used in the containing circuit.

Input stage promoter design

The pGRR i,j promoter is tightly repressed when gRNA-dCas9-Mxi1 is bound to one or both of its two 20 bp target sites. The core region of the pGRR i,j , the minimal pCYC1 promoter, was chosen based on its successful use with dCas9 in the past32. Because the promoter has relatively low expression levels and we wanted its output to have a strong ON output when not repressed, an upstream activating sequence (UAS) from the strong pGPD promoter47 was added, forming the base pGRR promoter. The UAS increased the unrepressed expression level of the pGRR output by approximately threefold while maintaining the same OFF state expression level in the presence of r i and r j , further separating the digital ON and digital OFF levels (Supplementary Fig. 3a). A pGRR promoter map highlighting all relevant sequence features is included in Supplementary Fig. 4. A library of 11 pGRR i,j promoters, with i and j chosen from the 20 guide sequences, showed limited expression variability when driving GFP, with an ∼18% s.d. from the mean (Supplementary Fig. 3b) Of the 20 pGRR i,null :GFP constructs (i ranging from 1 to 20), 16 were repressed to or near the level of Saccharomyces cerevisiae autofluorescence in the presence of the corresponding signal r i (Supplementary Fig. 1).

Output stage RNA design

Two different RNA pol II expression methods were used in this work (Supplementary Fig. 5). The first was an RGR design utilizing a 5′ minimal hammerhead ribozyme (mHH) and a 3′ hepatitis delta virus ribozyme (HDV), flanking the gRNA48. The second was an ‘insulated’ RGR (iRGR) with the mHH replaced by an avocado sunblotch viroid (ASBV) ribozyme. Both designs are intended to post-transcriptionally remove nuclear export signals, the 5′ cap and 3′ poly-A tail49,50. It has been shown that RNA device folding can be insulated from surrounding sequence context through computational sequence selection51,52. Ten guide sequences were chosen for the RGR architecture that were computationally predicted to confer proper folding of the mHH 5′ ribozyme. Ten more guide sequences were chosen for the iRGR context whose ASBV 5′ ribozyme is predicted to fold properly regardless of guide sequence. We observed similar levels of dCas9-Mxi1-mediated repression with gRNAs expressed from both iRGR and RGR constructs (Supplementary Fig. 6). Interestingly, RGR transcripts lacking a 5′ ribozyme also showed dCas9-Mxi1-mediated repression. These results are consistent with previous studies that indicate a majority of 5′ extended gRNA target sequences are processed to 20 nucleotides53. No significant crosstalk was observed when all r 1–10 (RGR design) and r 11–20 (iRGR design) were paired with all pGRR 1-20,null :GFP among noncognate pairs (Fig. 2a and Supplementary Fig. 7). Out of 20 total RGRs (RGR 1–10 and iRGR 11–20 ) when targeted to their cognate pGRR 1-20,null :GFP constructs, 16 repressed fluorescence to or near the level of autofluorescence for S. cerevisiae (Supplementary Fig. 1).

Logic circuits

As a demonstration of the complex circuits possible with our NOR gates, six two-input, one-output digital logic circuits were built by integrating up to five NOR gate cassettes into various selectable loci in the yeast genome (Fig. 3a–f). The output of each circuit was made observable by having the last NOR gate drive the expression of GFP. The circuits were constructed from the 16 guide sequences of the 20-component library that exhibited the strongest repression (Supplementary Fig. 1). The truth table for each gate was experimentally obtained by constructing four separate strains, one for each pair of possible input values, in which the corresponding gRNA input signals were expressed from constitutive promoters (Supplementary Table 2).

Figure 3: NOR gate-based logic circuits. (a–f) Six different two-input logic circuits constructed by interconnecting NOR gates. For each of the four input possibilities (−−, −+, +−, and ++), a distinct strain was constructed with the corresponding inputs expressed off of constitutive promoters (for logical +), or not integrated at all (for logical −). Fluorescence values were collected using flow cytometry of cells growing in log phase. The histograms represent population fraction from three different biological replicates measured during a single experiment and were normalized so that area sums to unity. Fluorescence population ratios of the circuits are included in the Supplementary Table 3. Full size image

We observed fluorescence intensity differences in the digital ON and OFF states in various circuits. To distinguish circuit state, value bands for digital ON, OFF and Undefined, fluorescence values were determined with the 16 guide sequences and their cognate pGRR promoters used in circuit construction (Supplementary Fig. 8). For the state of a circuit to be considered ON or OFF we specified that a majority of cell population fall in the expected fluorescence band. Population fraction tables for all circuits can be found in Supplementary Table 3.

Circuits containing different NOR gate variants can exhibit a range of behaviours. For example, 15 versions of the XOR, from Fig. 3e, constructed using different NOR gates exhibited a range of performance (Supplementary Fig. 9). We hypothesize that circuit performance variations are due to expression differences in the pGRR promoters and repression efficiency variations of the gRNA in the individual NOR gates of the circuit.

Cascades

To test the limits of size and complexity our NOR gate circuits can achieve inverter cascades of depth one through seven were composed with NOT gates (Fig. 4a). The cascade of depth D was made by the addition of a NOT gate to repress the input stage of the depth D–1 cascade. Each successive addition of a NOT gate inverter resulted in switching the behaviour of the output GFP expression. As seen previously with the two-input logic circuits, there is considerable variability within the ON and OFF states. However, circuits that are expected to exhibit ON or OFF behaviour are clearly distinguishable from one another according to our digital ON and OFF specification. As cascade depth increased the fluorescence levels of the OFF states for all of the odd depth cascades increased. Similarly, except for the cascade of depth 6, as cascade depth increased the fluorescence levels of the ON states decreased. This suggests a gradual degradation of circuit function as the number of layers increased. Similar behaviour was also observed for other repression cascades that were constructed (Supplementary Fig. 10). Alternative versions of 6 gRNA cascades were constructed and showed variability in their levels of ON (Supplementary Fig. 11).

Figure 4: Repression cascade characterization. (a) Repression cascades of one to seven gRNAs. Cascades were created with sequential genomic integrations of NOT gates. The final output of each cascade is a NOT gate that expresses GFP. Each NOT gate represses the output of a subsequent NOT gate. Cascades with an even number of layers express a high level of GFP, creating a digital ON output, and odd depth cascades express low levels of GFP, creating a digital OFF output. Fluorescence measurements were taken using flow cytometry. The histograms represent population fraction from three different biological replicates measured during a single experiment and were normalized so that area sums to unity. Fluorescence population ratios of the circuits are included in Supplementary Table 3. (b) Temporal dynamics for cascades of one to four gRNAs. Expression of the input gRNA was induced with β-estradiol. A model of the cascade, in which each layer is treated as a Hill function, was used to fit the data. The plot shows the data from one biological replicate. As the number of layers in the cascade increases, signal degradation and increased time to steady state is observed. (c) The steady-state response function for the four inducible cascades. Error bars represent the s.d. of three biological replicates measured over three separate experiments. (d) A representation of the model. The model was used to generate the fits for the steady-state and kinetic inducible cascade experiments. Full size image

To investigate the temporal characteristics of the inverter cascades, we analysed the kinetics of cascades of depth one through four. A β-estradiol-inducible promoter54 was used to activate transcription of the input gRNA and GFP expression was periodically measured over the course of ∼30 h of log phase growth (Fig. 4b). With increasing cascade depth, a clear delay in output response was evident, with the cascades reaching half-maximal expression at 4.1±0.5, 10.8±1.0, 12.0±1.2 and 17.8±1.0 h (residual s.d. deviation) for cascades of depth one through four respectively. The dose response curves of the four cascades were also measured after passaging cells over 5 days (Fig. 4c). Consistent with the steady-state cascades, the induction of a gRNA targeting the input of the cascade switched the output of the cascade from OFF to ON (even depth cascades) or from ON to OFF (odd depth cascades). Some signal degradation with successive layers was observed (Fig. 4c), suggesting a limit to the possible depth of the cascades.

Mathematical modelling

A kinetic model was constructed to capture the behaviour of our synthetic cascades. The model combines successive Hill functions to represent simple transcription and repression associated with each gRNA-dCas9-Mxi1 signal. The parameters v d and k d roughly capture expression and repression strengths of the promoters driving each gRNA-dCas9-Mxi1 signal, r d . The parameter L represents the transcriptional leak as a percentage of the maximal expression of a given gate when maximally repressed parameters n and b capture the cooperativity of repression. Degradation/dilution of gRNA-dCas9-Mxi1 signals respectively (Fig. 4d). The steady-state dose response and kinetic time course for inducible cascade data were both fit to the model (Fig. 4b,c). Due to the different growth conditions of the steady-state and kinetic cascade experiments, two separate model fits were generated for each experiment. As inducible cascades were built in such a way that they shared many of the same pGRR and gRNA components (Fig. 4b), parameters for the one-, two-, three- and four-layer cascades were shared between the models and fit simultaneously. To address potential model identifiability issues parameter values were constrained based on published biological values (Supplementary Table 4). The fitting results were found to correlate well with the experimental data. The measured ∼18% s.d. from the mean for the promoter strength values matches well with the ∼24% s.d. from the mean of the promoter strength parameters, v d (Supplementary Table 4).

Model fits of the steady-state and time course data predict the transcriptional leak of repression due to dcas9-Mxi1, the value of L, to be effectively zero, L=0.6±0.1% (s.d.), equivalent to the production of roughly one transcript every 5 to 10 cell divisions. The reported value of L was calculated as the average of the predicted transcriptional leak from the model fits from Fig. 2b. To demonstrate the ability of dCas9-Mxi1 to decrease transcriptional leak compared with steric repression via dCas9, gRNA dose response curves of repression at three pGRR promoter target site positions were performed using dCas9 and dCas9-Mxi1 (Fig. 2b). At maximal induction, dCas9-Mxi1 represses the promoter to a lower fluorescence level than dCas9 alone at all three positions. Repression via steric hindrance showed promoter positional variations in predicted leak parameter values. The observed positional variation is consistent with previous results32. In all three positions dCas9-Mxi1 was predicted to have the same or lower leak parameter L. These data indicate that in the context of our NOR gates, dCas9-Mxi1 confers stronger and more consistent repression than dCas9 alone. Alternative plots comparing dCas9 and dCas9-Mxi1 repression as a function of inducible promoter activation driving gRNA are included in Supplementary Fig. 12.

The temporal responses of the cascades were predicted from simulations using randomly sampled parameters within the range of the model fit. Parameter values for kinetic simulations were resampled from the model fit using the kinetic time course experimental data. Response times were found to rise linearly (r2=0.83) with increasing circuit depth. Linear regression analysis estimated the slope of the increase in response time per layer to be equal to 184.9±0.2 (s.e.m.) min layer−1 (Fig. 5a), consistent with our experimental results. Response delay was found to depend primarily on the degradation/dilution rate b of gRNA-dCas9-Mxi1 (Supplementary Fig. 13) that controls the overall timescale of the dynamics.

Figure 5: Model predictions and analysis of repression cascades. (a) Simulations of time to half-maximal response using the model. Increasingly layered cascades show a positive linear relationship between circuit time to half-maximal response and circuit depth, with a slope of 184.9±0.2 (s.e.m.) min layer−1. The first four data points highlighted in purple are experimental data from Fig. 4b. (b) Signal degradation, δ, in a cascade increases as transcriptional leak of the gates increase. Boxplots of δ values were plotted with binned values of the leak parameter L. At values of L <1.75% the spread of performance of the cascades is significantly larger. The bin containing the steady-state experimentally predicted value of dCas9-Mxi1, L=0.6±0.1% (s.d.), is highlighted in purple. The bins highlighted in orange and yellow contain the predicted L values for the steric repression measurements in Fig. 2 of position 1, L=25.0%, and position 3, L=61.3%, respectively. Full size image

To extrapolate the model to predict the effect of leak on signal degradation for deeper cascades, cascades of various lengths were simulated, with increasing values of L, using randomly sampled parameter sets within the range of dose response experimental fits. Dynamic range of a cascade length D, ρ D , was calculated for each cascade. Here dynamic range is defined as the log fold change of the maximal and minimal response of a cascade, . A log-linear relationship was found between ρ D and D. This relationship was used to calculate the signal degradation, δ, representing the percent loss in dynamic range per each additional layer (Fig. 5b).

Signal degradation was found to be largely dependent on the transcriptional leak parameter, L (Fig. 5b and Supplementary Fig. 12). As leak increases, δ, on average, increases. At values of L >80%, the median value of δ trends to ∼80%. At values of L <1.75%, the spread of performance of the cascades is significantly larger. In this range the performance of the cascade is more sensitive to other parameters in the model. Our estimate of leak from the dose response experiments, L= 0.6±0.1% (s.d.), falls within the sensitive range, indicating the importance of utilizing well-performing NOR gates in large circuits built using our architecture. In addition, these data show the significance of reducing NOR gate leak when constructing larger circuits.