CRISPR Interference Modules as Low-Burden Logic Inverters in Synthetic Circuits

CRISPR and CRISPRi systems have revolutionized our biological engineering capabilities by enabling the editing and regulation of virtually any gene, via customization of single guide RNA (sgRNA) sequences. CRISPRi modules can work as programmable logic inverters, in which the dCas9-sgRNA complex represses a target transcriptional unit. They have been successfully used in bacterial synthetic biology to engineer information processing tasks, as an alternative to the traditionally adopted transcriptional regulators. In this work, we investigated and modulated the transfer function of several model systems with specific focus on the cell load caused by the CRISPRi logic inverters. First, an optimal expression cassette for dCas9 was rationally designed to meet the low-burden high-repression trade-off. Then, a circuit collection was studied at varying levels of dCas9 and sgRNAs targeting three different promoters from the popular tet, lac and lux systems, placed at different DNA copy numbers. The CRISPRi NOT gates showed low-burden properties that were exploited to fix a high resource-consuming circuit previously exhibiting a non-functional input-output characteristic, and were also adopted to upgrade a transcriptional regulator-based NOT gate into a 2-input NOR gate. The obtained data demonstrate that CRISPRi-based modules can effectively act as low-burden components in different synthetic circuits for information processing.

Therefore, the autofluorescence expression becomes (Eq.S4): ( ) = + ⋅ +( + ⋅ )⋅ 600 ( ) ( 4) Using Eq.S4, the four coefficients were fitted from autofluorescence data of different cultures exhibiting diverse growth rates. The Matlab regress function was used for linear regression fitting in GFPauto calculation. This expression served as a calibration curve providing autofluorescence values that are then subtracted from raw green fluorescence values, given OD600 and µ.

Mathematical modelling of transcriptional cascade and NOR gate
Hill equation models were defined for both circuits and parametrized by fitting experimental data from their individual components to eventually compare model prediction and final circuit behaviour.

Transcriptional cascade model description
A previously adopted steady-state model (Pasotti et al., 2017) was used to describe the HSL-dependent RFP output of the X1TL circuit (Eq.S5).
Parameters have the same meaning and units as in previous work (Pasotti et al., 2017), also summarized in Supplementary Table S2. Briefly, T and L represent the intracellular concentrations of TetR and LacI; Sp,max is the maximum synthesis rate of a generic regulated protein (p = TetR, LacI, RFP). Protein synthesis rate is modelled as a Hill function related to the activity of the upstream promoter (Plux, PLtetO1 and PLlacO1, respectively) with parameters δ, α, K and η, where δ + α is the maximum expression rate, K is the input level corresponding to 50% of the expression rate range and η is the Hill coefficient; Jtet is the resource usage parameter of TetR; the cell load caused by LacI and RFP is assumed to be negligible at the expression levels spanned in the cascade circuit (Pasotti et al., 2017); ΣXλ is the additional load given by the constitutive expression of LuxR. The term D is the scale factor between the maximum synthesis rate of a protein into the actual synthesis rate, obtained as the sum of cell loadrelated factors. The a, µ, γtet and γlac represent the RFP maturation rate, cell growth rate, TetR and LacI protein degradation rates, respectively.
A model predicting the HSL-dependent output of the CRISPRi transcriptional cascade was derived from Eq.S5 by considering the gPtetDEG9:dCas9 repressor (named Cdeg9) instead of TetR, under the following assumptions: the cell load caused by the expression of sgRNA is negligible; the intracellular gPtetDEG9:dCas9 repressor complex was modeled, without describing the constitutive expression of dCas9 and its further binding to gPtetDEG9; the dilution rate of the CRISPRi repressor complex is equal to cell growth rate (Qi et al., 2013); an additional parameter (ΣC) is used in D to account for the GFP value that is slightly lower in the CRISPRi cascade compared with X1TL for HSL = 0 ( Figure 7F), probably due to the presence of an additional plasmid, maintained at medium copy, that may represent a load for the cells (Pasotti et al., 2019). The resulting equations are reported in the Eq.S6 system.

NOR gate model description
A kinetic model of the main regulatory steps occurring in the NOR gate circuit was defined (Eq.S7).
The model describes the binding of the gPluxH:dCas9 repressor complex (Crep) to the unoccupied PluxRep promoter sequence (DF) obtaining the promoter in a repressed state (DR1), the binding of HSL to a LuxR dimer (R2) obtaining the HSL-LuxR complex (Q), the binding of Q to DF obtaining the promoter in a second repressed state (DR2), and the RFP synthesis rate per cell (Scell,NOR) as proportional to DF (with proportionality constant σ·a/(a+µ)). The symbols on the bidirectional arrows of the reactions indicate the resulting dissociation equilibrium constants. Conservation laws are also defined in Eq.S7 for total DNA, repressor and LuxR in cells. A steady-state solution for the free promoter DF was derived under the following assumptions: no significant cell load affects the recombinant strain; the total intracellular amount of repressors (Ctot and R2T) is much higher than the target DNA concentration; the binding events of Crep and Q to the free promoter are mutually exclusive due to the short distance between the CRISPRi target site and the lux box; the activity of the PluxRep promoter in the repressed state is null; Crep is approximated by an IPTG-dependent Hill equation. In the final expression of Scell,NOR, the lumped parameters β = σ· DF and U = R2T/KR are present. A summary of parameter values and units is reported in Supplementary Table S2.

Model implementation and fitting procedure
The models were implemented via Matlab R2017b (Mathworks, Natick, MA). Implicit equations (Eq.S5) were solved with a custom script implementing the fixed point method as it was carried out previously (Pasotti et al., 2017). The lsqnonlin routine, implementing the least squares algorithm, was used to fit experimental data (average values) to estimate the unknown parameters. For the transcriptional cascade, δdeg9, αdeg9, Kdeg9 and ηdeg9 were estimated by fitting the RFP data of the gPtetDEG9 NOT gate ( Figure 7B-C) using the model in Eq.S8.
The ΣC parameter was computed by solving 1+Σ 1+Σ +Σ = , , 1 using the GFP data in Figure 7F for For the NOR gate, the β parameter was computed as ((a+µ)/a)·RFPcontrol, where RFPcontrol is the RFP output value of the control strain in Figure 5H for HSL=0; the RFP data of the No gPluxH condition ( Figure 8B) were fitted with the Scell,NOR equation for Ctot = 0 to estimate the U and KH parameters; the RFP data of the IPTG/PLlacO1-inducible system (Supplementary Figure S5) and of the IgLUX circuit ( Figure 5H) were simultaneously fitted with Eq.S9 to estimate the δI, αI, KI, ηI and KC parameters. A growth rate value was fixed for both fitting and simulations as the typical value measured in the two strains bearing the cascade and the NOR gate. In each panel, the copy number of the sgRNA constitutive cassette (low copy -LC, medium copy -MC) and the copy number of the target (medium copy -MC, high copy -HC) are reported. Two different targeting systems (Tetpanels A, C, E, and Lacpanels B, D, F) are reported: gPtet and gPlac, which repress the PLtetO1 and PLlacO1 promoters, respectively, that drive RFP. Each panel includes four curves: three of them correspond to circuits with the sgRNA under the control of three different constitutive promoters of diverse strengths (weak, medium and strong for J23116, J23100 and J23119, respectively), and one curve corresponds to a non-specific targeting control in which the medium-strength J23100 promoter constitutively transcribes a non-targeting sgRNA: gPlac and gPtet for the PLtetO1 and PLlacO1 promoters in the Tet and Lac systems, respectively. Data points represent the average value and error bars represent the standard errors of the mean of at least 3 independent experiments.
Supplementary Figure S4. GFP values of recombinant strains with HSL-inducible dCas9 and constitutive sgRNA. Data are reported as a function of HSL. In each panel, the copy number of the sgRNA constitutive cassette (low copy -LC, medium copy -MC) and the copy number of the target (medium copy -MC, high copy -HC) are reported. Two different targeting systems (Tetpanels A, C, E, and Lacpanels B, D, F) are reported: gPtet and gPlac, which repress the PLtetO1 and PLlacO1 promoters, respectively, that drive RFP. Each panel includes four curves: three of them correspond to circuits with the sgRNA under the control of three different constitutive promoters of diverse strengths (weak, medium and strong for J23116, J23100 and J23119, respectively), and one curve corresponds to a non-specific targeting control in which the medium-strength J23100 promoter constitutively transcribes a non-targeting sgRNA: gPlac and gPtet for the PLtetO1 and PLlacO1 promoters in the Tet and Lac systems, respectively. Data points represent the average value and error bars represent the standard errors of the mean of at least 3 independent experiments.
Supplementary Figure S5. Transfer function, with RFP as output, of the IPTG-inducible system including PLlacO1. The Ir recombinant strain was used. Data are shown as the average RFP synthesis rate per cell, as a function of IPTG. Data points represent the average value and error bars represent the standard errors of the mean of at least 3 independent experiments.
Supplementary Figure S6. Copy number quantification in recombinant strains with two or more plasmids. All of them include a low-copy vector (highest molecular weight band). The medium-and high-copy vector amounts were quantified relative to the intensity of the low-copy vector. Electrophoresis gel (1% agarose with TBE) pictures, with ethidium bromide staining, are shown for strains H-3dgLAC100,LCPtet,HC and H-3dgLAC100,MCPtet,HC (gel on the left) and H-3dgLAC100,MCPtet,MC (gel on the right). Gel on the left: lanes 1, 5, 6 contain the H-3dgLAC100,MCPtet,HC plasmids at different dilutions, digested with XbaI-SacII (XbaI is a single cutter in all the three plasmids and SacII is a single cutter only in the MC plasmid); lanes 2, 3, 4 contain the H-3dgLAC100,LCPtet,HC plasmids at different dilutions, digested with XbaI-SacII (XbaI is a single cutter in all the three plasmids and SacII does not cut any of the plasmids). Gel on the right: lanes 1, 3, 5 contain the H-3dgLAC100,MCPtet,MC plasmids at different dilutions, digested with XbaI (single cutter in both plasmids); lanes 2, 4, 6 are analogous to lanes 1, 3, 5, but they are relative to a biological replicate. The DNA ladder is GeneRuler 1 Kb (Thermo Scientific), with the lowest band reported in the pictures corresponding to the 1000-bp size.
Supplementary Figure S7. Growth rate values of recombinant strains with constitutive dCas9 and inducible sgRNA. Data are reported as a function of the inducer concentration driving sgRNA expression (HSL, in panels A-D, or IPTG, in panels E-H). In each panel, the CRISPRi targeting system is reported as gPtet, gPlac and gPluxH, which repress the PLtetO1, PLlacO1 and PluxRep target promoters, respectively, that drive RFP. Two different copy number contexts for the target are reported: medium copy (MC) and high copy (HC). Each panel includes two curves, corresponding to circuits with specific or non-specific targeting system. The latter is referred to as control and the used sgRNAs are gPlac (panels A-B), gPtet (panels C-D and G-H) and gPluxH (E-F). Data points represent the average value and error bars represent the standard errors of the mean of at least 3 independent experiments.
Supplementary Figure S8. GFP values of recombinant strains with constitutive dCas9 and inducible sgRNA. Data are reported as a function of the inducer concentration driving sgRNA expression (HSL, in panels A-D, or IPTG, in panels E-H). In each panel, the CRISPRi targeting system is reported as gPtet, gPlac and gPluxH, which repress the PLtetO1, PLlacO1 and PluxRep target promoters, respectively, that drive RFP. Two different copy number contexts for the target are reported: medium copy (MC) and high copy (HC). Each panel includes two curves, corresponding to circuits with specific or nonspecific targeting system. The latter is referred to as control and the used sgRNAs are gPlac ( Figure 7D and 8B, in which experimental data are reported.
H-3dgLAC119,MCPlac,HC HSL-inducible dCas9 in low-copy plasmid with strong constitutive gPlac in medium-copy and the target PLlacO1 promoter driving RFP in high-copy