Competitive dCas9 binding as a mechanism for transcriptional control

Abstract Catalytically dead Cas9 (dCas9) is a programmable transcription factor that can be targeted to promoters through the design of small guide RNAs (sgRNAs), where it can function as an activator or repressor. Natural promoters use overlapping binding sites as a mechanism for signal integration, where the binding of one can block, displace, or augment the activity of the other. Here, we implemented this strategy in Escherichia coli using pairs of sgRNAs designed to repress and then derepress transcription through competitive binding. When designed to target a promoter, this led to 27‐fold repression and complete derepression. This system was also capable of ratiometric input comparison over two orders of magnitude. Additionally, we used this mechanism for promoter sequence‐independent control by adopting it for elongation control, achieving 8‐fold repression and 4‐fold derepression. This work demonstrates a new genetic control mechanism that could be used to build analog circuit or implement cis‐regulatory logic on CRISPRi‐targeted native genes.


Introduction
Regulatory networks integrate environmental and cellular signals to ensure genes are expressed under the correct conditions. Integration can occur at individual promoters through the arrangement of DNA operators to which regulatory proteins bind and either recruit or interfere with transcriptional machinery (van Hijum et al, 2009;Weingarten-Gabbay & Segal, 2014). Within a promoter, the binding of one regulator can also affect the binding of others through positive or negative interactions, for example, through DNA looping or overlapping operators. This collectively generates "cis-regulatory logic", which dictates the conditions for gene expression based on the combination of regulators that are active (Shen-Orr et al, 2002;Shen-Orr et al, 2002;Aerts et al, 2003;Buchler et al, 2003;Hermsen et al, 2006;Mayo et al, 2006;Kaplan et al, 2008;Gertz et al, 2009;van Hijum et al, 2009;Schulthess et al, 2015). For synthetic genetic circuits, the placement of multiple operators within a promoter has been used to implement combinatorial logic, for example, to create an X AND (NOT Y) gate for an edge detector by placing an operator for an activator (X) and repressor (Y) within a promoter (Cox et al, 2007;Murphy et al, 2007;Ellis et al, 2009;Tabor et al, 2009;Sharon et al, 2012;Bacchus et al, 2013;Mogno et al, 2013;Perez-Pinera et al, 2013;Rantasalo et al, 2018;Monteiro et al, 2020;Yu et al, 2021). As a design principle, combining operators is useful for "compressing" large logic operations to reduce the resource burden (Rondon et al, 2019;Groseclose et al, 2020). It is challenging to insert an operator into a promoter because the change in sequence can affect the promoter strength, an effect that can be mitigated with insulators and computational predictions (Brewster et al, 2012;Stanton et al, 2014;Zong et al, 2017Zong et al, , 2018Hoque et al, 2021;preprint: Poole et al, 2021). Prokaryotic promoters are small, thus making it difficult to fit multiple operators and it is difficult or impossible to design operators that bind to multiple regulatory proteins. dCas9 can be programmed to bind to different DNA sequences by changing the targeting sequence of its bound sgRNA (Bikard et al, 2013;Esvelt et al, 2013;Qi et al, 2013;Jiang & Doudna, 2017). DNA binding requires 5-10 bp sgRNA-DNA complementarity adjacent to an NGG PAM sequence (Boyle et al, 2017), although dCas9 can be engineered to reduce the PAM sequence requirements (Kleinstiver et al, 2015;Hu et al, 2018;Nishimasu et al, 2018;Walton et al, 2020;Collias & Beisel, 2021). When bound to DNA, dCas9 covers 30 bp and melts the strands to form a bubble that results in very slow unbinding rates (Sternberg et al, 2014;Jones et al, 2017). Thus, it can function as a repressor by sterically blocking the binding of RNA polymerase (RNAP) to a promoter or by blocking its progression through a gene (Qi et al, 2013). When targeting constitutive E. coli σ70 promoters, repression is strongest when the sgRNA is targeted within the −10 to −35 promoter core and does not depend on which strand is targeted (Bikard et al, 2013;Qi et al, 2013;. Targeting dCas9 downstream of a promoter represses transcriptional elongation, with much stronger repression observed when the sgRNA is targeted to the nontemplate strand (Bikard et al, 2013;Qi et al, 2013). dCas9 can also serve as an activator by fusing it to an activating domain that recruits RNAP (Bikard et al, 2013;Zalatan et al, 2015;Dong et al, 2018;Ho et al, 2020;Kiattisewee et al, 2021). There are often tight spacing requirements for activation, particularly for prokaryotic promoters. Lastly, dCas9 can also be directed to bind to the operators of protein repressors, activators, or enhancers, thus blocking their impact on expression (preprint: Shur & Murray, 2017;Shariati et al, 2019;Liu et al, 2021).
An advantage of using dCas9 is that its regulatory effect can be directed to a promoter without having to insert an operator sequence. This has been used to control the regulation of native genes, for example, controlling enzymes at branch points to redirect flux through a metabolic pathway (Kim et al, 2016;Moser et al, 2018;Tian et al, 2019;Hawkins et al, 2020;Wu et al, 2020b;van Gestel et al, 2021). It also simplifies the integration of multiple signals at a single promoter by designing sgRNAs that target it to different positions. For instance, NOR gates have been constructed using two sgRNAs that target different positions in the output promoter, either of which leads to repression (Lebar & Jerala, 2016;Gander et al, 2017). When multiple sgRNAs target overlapping regions, this leads to mutually exclusive binding (Qi et al, 2013). Tan and co-workers harnessed this effect to control the strength and noise of an E. coli constitutive promoter by co-transcribing different ratios of two sgRNAs that direct dCas9 (fused to an activating domain) to overlapping positions that either recruit or block RNAP (Wu et al, 2020a).
Once expressed, the regulatory effects of dCas9 only end when the protein or sgRNA degrade or are diluted by cell division. Several approaches have been taken to control the activity of either dCas9 or the sgRNAs after they are expressed. One is to express anti-CRISPR proteins derived from phage genomes that bind to and inactivate dCas9 (Bubeck et al, 2018;Nakamura et al, 2019). This leads to the complete inactivation of dCas9, thus eliminating its ability to implement any sgRNA-mediated regulation in the cell. Different sets of genes can be controlled by expressing orthogonal dCas9 variants, each of which binds a different set of sgRNAs (Gao et al, 2016;Kim et al, 2019). These can be changed dynamically from being repressors to activators by expressing the corresponding domains as separate proteins that bind to dCas9 using modular protein-protein interaction domains (Gao et al, 2016). Another approach is to design RNA to bind to and augment the activity of a specific sgRNA. Antisense RNAs will inactivate sgRNAs by targeting them for degradation via the native bacterial Hfq system . The sgRNA can also be designed to fold into an inactive hairpin, thus requiring the coexpression of toehold RNAs to unfold and bind to dCas9 (Oesinghaus & Simmel, 2019;Siu & Chen, 2019;Hochrein et al, 2021). Both of these techniques require modifying the sgRNA to have additional sequences such that it can be bound by the modulating RNA.
While there are many natural examples of different repressors binding to the same operator or a repressor displacing an activator, to our knowledge, there are no examples of a repressor's action being negated by a second protein binding to an overlapping operator. To this end, we have developed a mechanism for sgRNAspecific derepression through competitive dCas9 binding to overlapping regions. Transcription is blocked when a repressing sgRNA (sgR) directs dCas9 to the first position and a second derepressing sgRNA (sgD) directs dCas9 to a mutually exclusive second position that does not impact transcription ( Fig 1A). We find that the two regions are competitive so long as they are within 14 bp and the PAM sequences are between the target sites. The repression/derepression switch is implemented in two ways ( Fig 1B). The first is to design the sgR to overlap the −35 σ70-binding region of promoter and the sgD to bind just upstream. The second approach is to design repression/derepression sites within a gene by exploiting the strand dependence of RNAP elongation inhibition by dCas9. These results demonstrate a new mechanism to control the activity of dCas9directed regulation that could be used for efficient genetic circuit design to integrate signals in a promoter or to derepress subsets of native genes to subregulate genome-encoded functions.

Results
Promoter control through repression/derepression dCas9 can repress a promoter by sterically blocking the binding of RNAP (Figs 1B and 2A) (Bikard et al, 2013;Qi et al, 2013). An E. coli constitutive promoter can be repressed by targeting the repressing sgRNA (sgR) to overlap the −10 or −35 σ70-binding sites (Bikard et al, 2013;Qi et al, 2013;. Our design for derepression is based on using a second sgRNA (sgD) to recruit dCas9 to an upstream site that blocks its ability to bind to the repressing position. Importantly, sgD cannot interfere with RNAP binding or else it will also lead to repression.  A The footprint of dCas9:sgD blocks the binding of dCas9:sgR without requiring that the sgRNA-binding regions overlap. The PAM-adjacent regions of sgRNAs are shown as boxed ends. B The sgR/sgD sequences can be targeted to the promoter or internal to a gene. impact of dCas9:sgRNA binding on mRNA transcription rates, we defined a parameter α as the ratio of maximal mRNA production rates (completely unbound DNA) to the production rate when all DNA is bound by dCas9:sgRNA (saturated DNA). The ideal location to target a repression/derepression sgRNA pair would correspond to a large α for sgR (α >> 1) and α → 1 for sgD, indicating strong repression by sgR and no repression by sgD.
A system was designed to evaluate how targeting sgR and sgD to different positions in the promoter impacts the effectiveness of repression and derepression. Two inducible promoters were used to independently transcribe sgR (IPTG-inducible P Tac ) and sgD (Vanillic acid-inducible P Van ) encoded on a p15A plasmid. The targeted constitutive promoter (P C1 ) was built based on the −35 to +1 core of P Gate08 (Zhang & Voigt, 2018) to which a randomly generated 100-bp sequence was added upstream (Materials and Methods). Positions in P C1 were selected to be targeted for sgR/ sgD by exploiting NGG PAM sites in the promoter sequence ( Fig  2B). The sgR and sgD sequences were designed based on the same scaffold (Zhang & Voigt, 2018), with mutations the 20-bp spacer sequence corresponding to the target region of the promoter (Appendix Table S2). To measure promoter activity, P C1 was placed upstream of a ribozyme (Lou et al, 2012) and gene encoding red fluorescent protein (rfp). From the same plasmid, dCas9 was expressed using the aTc-inducible P Tet promoter. A concentration of 1.25 nM aTc was used for all experiments and leads to approximately 500 dCas9 molecules per cell during exponential growth (Zhang & Voigt, 2018).
Experiments were performed to measure the promoter activity that results when dCas9 is targeted to different positions. The plasmids were transformed into E. coli and cultures were grown in defined media (EZ Rich) and induced with aTc and either IPTG or Vanillic acid (Van) for 5.5 h (Materials and Methods). Fluorescence was then measured using flow cytometry. First, we compared the repression obtained by targeting the −10 (sgR P1 ) or −35 (sgR P2 ) positions of the promoter ( Fig 2B). Upon maximum sgR expression (1 mM IPTG), both sgRs are able to repress the promoter by˜30fold ( Fig 2C). This result is consistent with previously observed fold-repressions at these locations Zhang & Voigt, 2018).
A model was derived to capture the repression of a promoter by dCas9:sgR, where P and P R are the concentrations of promoters in the unbound and bound state, S R is the concentration of dCas9:sgR, and K R is the association constant. The production of mRNA transcripts m from the promoter is described by where β m is the maximum transcription rate, β is the leaky transcription rate, and δ m is the degradation rate. Solving for steadystate yields This equation can be further converted to the activity of the output promoter P C1 , where y is in arbitrary units (au) of RFP fluorescence and y max /y min are the maximum/minimum measured values. x R is the strength of the promoter driving the expression of sgR, measured as au of RFP fluorescence and κ R is rescaled to be in the same units. This assumes that the binding of sgR to dCas9 to form S R is in the linear (unsaturated) regime. Equation 4 was fit to the sgR P1 and sgR P2 induction curves (Fig 2C), and the parameters were extracted (Table 1). We then designed experiments to determine the constraints of targeting dCas9:sgD to the promoter without evoking repression ( Fig 2D). Seven positions were selected between −28 and −66 regions of the promoter, including orientations that target both strands ( Fig 2B). The promoter activity was measured for each position when sgD is expressed (100 µM Van) and unexpressed (0 µM Van), and these data were used to estimate α as the ratio of these values ( Fig 2D and E). We observed that α continuously decreases as the sgD targets regions farther from the promoter core, indicating weaker repressive abilities ( Fig 2E). When sgD targets regions upstream of −60, negligible repression was observed.
It has been previously shown that dCas9:sgRNAs will compete for binding when their target regions overlap (Qi et al, 2013;Wu et al, 2020a). However, the distance constraints we measured showed that it would not be possible to obtain repression/derepression by targeting overlapping regions. Even if we used the upperbound on TSS distance for the repressing sgRNA (30 bp) and the lower-bound on distance for the derepressing sgRNA (60 bp), the sgRNA target sequences would still have to be 10 bp away from each other. We hypothesized that while we could not utilize sgRNA target overlap, we may still be able to harness steric hindrance effects from overlap of the dCas9 protein footprint on DNA. To investigate this, we examined a crystal structure of the dCas9-sgRNA-DNA complex (Nishimasu et al, 2014), which shows that dCas9 has an overhang of˜9 bp on the PAM-proximal binding side, but only a˜1 bp overhang on the PAM-distal side of the sgRNA target. This indicated that we might be able to obtain competitive dCas9 binding without overlapping the sgRNA binding regions if we oriented two sgRNAs with their PAM sequences facing each other.
To test this hypothesis, we redesigned the system to express sgR P2 from a choline (Chol)-inducible promoter and sgD P5 from a Vaninducible promoter ( Fig 2F). These promoters were chosen because they are not predicted to append disruptive 5 0 sequences onto the sgRNAs (Qi et al, 2013;Meyer et al, 2019). In accordance with the crystal structure estimation of dCas9's DNA footprint, we designed sgD P5 to be 14 bp from sgR P2 . To bind sgD P5 at this distance, we had to introduce a 3-bp mutation from −60 to −62 of P C1 to create a PAM site for sgD P5 , resulting in P C2 . We screened for derepression by fully inducing sgR P2 with 9 mM Chol and titrating the expression of sgD P5 from 0 to 100 µM Van. Derepression occurred in a graded manner as more sgRNA is expressed, ultimately returning the promoter activity to its unrepressed state ( Fig 2G).
We then determined the promoter response when different amounts of sgR and sgD are expressed. This response can be viewed as a cis-regulatory logic operation (Mayo et al, 2006) Fig S4). Output from the promoter increased with sgD induction and decreased with sgR expression.
It has been shown that the co-expression of multiple sgRNAs titrates a shared dCas9 resource away from the co-expressed sgRNAs (Zhang & Voigt, 2018;Huang et al, 2021). This could complicate the interpretation of the derepression data, where the expression of sgD could deplete the dCas9 pool, thus indirectly reducing the concentration of dCas9:sgR in the cell. To test for this effect, we performed a control experiment where we maximally expressed a sgR and then titrated in either a non-targeting sgRNA (sgN) (does not bind to the promoter or genome) or an off-target sgRNA (sgO) (binds to an inert region of the plasmid) (Appendix Fig  S2). Neither of these sgRNAs showed derepression, indicating that the derepression we observed was not due to dCas9 titration.
Our model was then expanded to include derepression. Equation 1 can be modified to include the competitive reaction of dCas9:sgD (S D ) binding to the promoter to form P D , where K D is the association constant between S D and P. The production of mRNA transcripts m from the promoter is described by ◀ Figure 2. Repression and derepression targeted to a promoter.
A The interactions between dCas9:sgR and dCas9:sgD and RNAP are shown. The dashed arrow and blunt-end indicate RNAP's inability to bind the promoter and nonideal repression of RNAP-binding by a sgD, respectively. B Positions of P C1 tested for targeting sgR and sgD. The boxes on the sgRNAs mark the PAM-adjacent regions, the orientation of which determines which strand is targeted. C Repression by the expression of sgRs. The experiments are performed with plasmids pDAA043 and pDAA656 for sgR P1 and sgR P2 , respectively. Both plasmids contain sgD P2 (uninduced for these experiments). The curve was fit to Equation 4, yielding the parameters shown in Table 1. The x-axis is converted from the concentration of inducer (IPTG) to promoter activity as described in the Materials and Methods. Inducer concentrations: 0, 0.977, 1. 95, 3.91, 7.81, 15.6, 31.3, 62.5, 125, 250, 500, 1,000 µM IPTG. D The position dependence of repression. The dashed blunt-end arrow indicates non-ideal repression by a derepression sgRNA. The experiments are performed with plasmids pDAA042, 043, 050, 051, 654, 052, and 044 for sgD P1 -sgD P7 (Appendix Table S1). The circuits also contain sgR P1 (uninduced for these experiments). The pDAA654 plasmid testing sgD P5 used the promoter P C2 , all other sgDs used P C1 . E "sgRNA distance" is the distance from the +1 site of the promoter to the closest DNA-RNA base pair in the sgRNA sequence. The lower subpanel shows values of α for the sgDs tested in (D) as function of their distance from the +1 site. The horizontal dashed line is drawn at α = 1 (ideal α value). The arrow marks sgD P5 , which was selected to build the repression/derepression circuit. The error bars were calculated as σ = |A/B|((σ A /A) 2 + (σ B /B) 2 ] 1/2 , where A and B are the means with 0 and 100 µM Van sgD induction, respectively, and σ A and σ B are the standard deviations of these measurements. Upper subpanel shows a schematic representation of how "sgRNA distance" values are calculated. F Genetic circuit schematic of the circuit based on sgR P2 and sgD P5 circuit, encoded on a single plasmid (pDAA107). Part sequences are provided in Appendix Table S2, and the full plasmid sequence is in Appendix Table S3. G Derepression induction curve for sgD P5 with full sgR P2 induction. The line is a fit to Equation 8 with parameters in Table 1.  where β m /α R and β m /α D are the maximum transcription rates when either S R or S D are bound to the promoter. Solving for steady-state yields As described for Equation 4, this can be further converted to the activity of the output promoter P C2 , This equation was then fit to the 2-dimensional response of the promoter to the expression of sgR and sgD (Fig 2H). This fit was performed while keeping the parameters previously fit to Equation 4 for sgR P2 (κ R , α R , y min , and y max ) constant. The fit is shown as the heatmap coloration in Fig 2H, the parameters for which are provided in Table 1. The newly fit association constant κ D for sgD is similar to κ R indicating that sgR P2 and sgD P5 have similar apparent binding strengths. Additionally, the observed α D of 1 is consistent with sgD P5 having little repressive effect on its own.

Dynamics of derepression
Qi et al (2013) showed that, in exponentially growing E. coli, the dynamics of sgRNA-based repression of RFP was identical to the cellular growth rate. This is consistent with complete repression of protein expression and first-order degradation of the protein due to dilution by cell division (Del Vecchio & Murray, 2015;Potvin-Trottier et al, 2016). However, when the authors removed the repressing sgRNA, RFP fluorescence increased with a doubling time slower than the cellular growth rate.
We monitored the dynamics of repression and derepression for the promoter repression/derepression sgRNA pair sgR P2 + sgD P5 over the course of 8 h (Materials and Methods). Starting with uninduced cells in exponential phase, we diluted cells into repressing conditions (10 mM Chol, 1.25 nM aTc). Consistent with previous work, RFP fluorescence reduced at the rate of cellular division (Fig 3). After 6 h, RFP expression was 100-fold lower than the initial uninduced condition. We then washed the cells and diluted them into fresh media inducing only the derepression sgRNA, sgD P5 (1.25 nM aTc and 100 µM Van). This led to 47-fold derepression within 2 h.

Control of transcriptional elongation through repression/ derepression
dCas9 can block transcription when it is directed to bind internally to a gene by physically interfering with the progression of RNAP ( Fig 4A). However, being located in a gene complicates the design of a derepressing sgRNA position, which must bind to disrupt the repressing sgRNA without itself blocking elongation. To this end, we exploited the strand dependence of dCas9-based elongation repression, where it has been found that RNAP elongation is more likely to terminate when it collides with the PAM-proximal side of a dCas9-DNA complex (Fig 4B) (Bikard et al, 2013;Qi et al, 2013;Vigouroux et al, 2018). Similar to the promoter repression/derepression mechanism, these constraints on sgR and sgD repressive effects can be captured empirically with the parameter α, which is the maximum fold-repression of mRNA production rates under saturating conditions.
A genetic system was constructed to test this design. dCas9 produces stronger repression when it is directed to the 5'-end of the gene (Bikard et al, 2013;Qi et al, 2013), so we selected a position at +232 to be targeted by a repressing sgRNA (sgR O1 ) (Fig 4C). This location was chosen because it has two adjacent PAM sites that could be used for targeting sgD, one of which has the same 14 bp spacing as was found to be optimal when derepressing a promoter (sgD O2 ). sgR O1 was placed under the control of a Chol-inducible P BetI promoter. It has been observed that elongation repression can be weaker with stronger promoters, presumably due to dislodgement of dCas9 by RNAP (Vigouroux et al, 2018). To evaluate this effect, we used an IPTG-inducible promoter (P Tac ) to drive the transcription of the rfp reporter. When the promoter is strong (1 mM IPTG), we observed an 8-fold repression of RFP upon the maximum induction of sgR O1 (10 mM Chol) (Fig 4D). While we initially developed the models in Equations 4 and 9 for the promoter repression/ derepression mechanism, these models can be generalized to the elongation repression/derepression mechanism if the promoter states P, P R , and P D are instead considered to be general DNA states. Therefore, the data for sgR O1 were fit to Equation 4 ( Table 1). The α for sgR O1 is 4-fold lower than that from promoter repression (Table  1), indicating a limitation of elongation repressive control at this location. The dependence of repression on the P Tac activity was then measured (Fig 4E). Repression by sgR O1 initially increased with promoter strength, but then levels off at 30-fold repression (Fig 4E). Previous work showed that elongation repression is promoterstrength invariant for saturating levels of dCas9 and for strong promoters (Vigouroux et al, 2018).
Two sgDs were designed to target positions up-(sgD O2 ) and down-stream (sgD O1 ) of the sgR O1 position (Fig 4C). These were placed under the control of a Van-inducible promoter, as before. We initially attempted to calculate α for these derepressing sgRNAs; however, induction of sgD O2 resulted in higher, rather than lower, RFP expression. This effect was likely due to leaky sgR O1 expression of sgR O1 from P BetI which is derepressed when sgD O2 is induced ( Fig   4F). Nonetheless, we tested the derepression capabilities of sgD O1 and sgD O2 (Fig 4G). To do this, sgR O1 was maximally expressed (10 mM Chol) with the strongest induction of the rfp reporter (1 mM IPTG). Maximum expression of sgD O2 (100 µM Van) showed 4-fold derepression (Fig 4G). This derepression was confirmed to not be a  result of the titration of dCas9 (Appendix Fig S2). In contrast, sgD O1 did not show any derepression and instead its expression slightly reduces the expression of the reporter, implying it may have its own repressing effect. The regulatory logic for the co-expression of sgR O1 and sgD O2 was then determined (Fig 4H). Similar to promoter repression/derepression, the elongation mechanism exhibited increasing expression with sgD induction and decreasing expression with sgR induction (error bars for each measurement are provided in Appendix Fig S4). Equation 8 was then fit to the 60-point sampling of the system, with x R corresponding to P BetI activity and x D corresponding to P Van activity values. The fit parameters imply that the derepressing sgRNA association constant κ D was 2.5-fold lower than the repressing sgRNA association constant κ R (Table 1).
The dependence of derepression on the P Tac promoter strength was then measured by varying IPTG (Fig 4E). Similar to the promoter strength test for relative repression, we normalized the fluorescence to that of the P Tac -only plasmid (pDAA040). For each level of P Tac induction, the relative expression during derepression was calculated as the ratio of the RFP fluorescence from the P Tac -only plasmid to the RFP fluorescence from the circuit plasmid with maximal sgR O1 and sgD O2 induction (10 mM Chol and 100 µM Van). From this experiment, we observed that derepression is invariant over a wider range of transcription rates than that observed for repression.

Ratiometric performance of the repression/derepression
Ratiometric signal processing describes a circuit that responds to the relative value of two inputs, as opposed to their absolute magnitude. Naturally occurring ratiometric responses have been observed in ATP/ADP management (Atkinson, 1968), X versus autosomal chromosome levels (Madl & Herman, 1979), circadian clock determination (Li et al, 2016), cancer cell clinical resistance (Raisova et al, 2001), and sugar source utilization in yeast (Escalante-Chong et al, 2015). To examine the ratiometric performance of our repression/ derepression mechanisms, we looked at the circuit outputs relative to the ratio of promoter activities producing sgD and sgR (P Van / P BetI ). From this, we observed that the promoter repression/derepression circuit effectively responded to over 2 orders of magnitude of sgD/ sgR ratios with a 50-fold dynamic range (Fig 5A). In contrast, the elongation mechanism had a smaller overall dynamic range (10-fold) and the circuit did not perform predictably across all ratios (Fig 5B).

Discussion
This work introduces a new mode of regulatory control, where the binding of a repressor is displaced by the binding of a nearby derepressor. This motif, where both repressor and derepressor bind to the same operator, has not been observed in natural systems. This may be due to the difficulty of designing a common operator that binds to multiple proteins and a derepressing protein that blocks the repressor, but not RNAP. The programmability of CRISPRi makes the design of multiple sgRNAs binding nearby sites almost trivial and the size of dCas9, and its melting of DNA, simplifies its use to sterically inhibit the binding or elongation of RNAP. Note that the off-rate of dCas9 binding DNA is very slow, effectively irreversible, until it is displaced by DNAP or RNAP (Sternberg et al, 2014;Jones et al, 2017;Vigouroux et al, 2018). In our repression/derepression mechanism, this makes it unlikely that dCas9:sgD can displace dCas9:sgR when it is already bound. Rather, it depends on which binds first, with DNAP replication (and to a lesser-extent RNAP ▸ Figure 4. Repression/derepression by blocking RNAP progression within a gene. A The interaction between RNAP and dCas9:sgR and dCas9:sgD are shown. Transcription is "ON" when full-length transcripts are produced. The dashed lines indicate non-ideal repression by sgD. B When dCas9 is bound to the non-template strand, the PAM is proximal to RNAP, and dCas9 tends to stay bound after collision. When dCas9 is bound to the template strand, the PAM is distal to RNAP collision and RNAP can continue to elongate. C Repressing and derepressing sgRNA binding sites tested relative to rfp. D Repression of transcriptional elongation by sgR O1 . The circuit is encoded on plasmid pDAA056, which also includes sgD O2 (uninduced in these experiments). The curve was fit to Equation 4, yielding the parameters shown in Table 1. The x-axis is converted from the concentration of inducer (Chol) to promoter activity as described in the Materials and Methods. Inducer concentrations: 0, 9.77, 19.5, 39.1, 78.1, 156, 313, 625, 1,250, 2,500, 5,000, 10,000 µM Chol. E The dependence of sgR O1 repression and sgD O2 derepression on the strength of the promoter controlling the repressed gene (P Tac ). "Relative expression" was calculated as the ratio of the fluorescence obtained in the absence of a guide RNA (pDAA040) by the fluorescence obtained by the expression of the guide RNAs shown in the legend (10 mM Chol or 10 mM Chol/100 µM Van, using pDAA056). The lines are a visual guide. The x-axis is converted from the concentration of inducer (IPTG) to promoter activity as described in the Materials and Methods. Inducer concentrations: 0, 0.977, 1. 95, 3.91, 7.81, 15.6, 31.3, 62.5, 125, 250, 500, 1,000 µM IPTG. The error bars were calculated as σ = |A/B|((σ A /A) 2 + (σ B /B) 2 ] 1/2 , where A is the mean of the P Tac -only expression, B is the mean of the circuit with either sgR O1 or sgR O1 + sgD O2 induction, and σ A and σ B are the standard deviations of their measurements. F Fully induced P Tac activity with and without induction of sgDs. Plasmids pDAA057 and pDAA056 were used for the sgD O1 and sgD O2 experiments, respectively. sgR O1 was present but uninduced. G Derepression induction curves with full sgR O1 induction. The curve was fit to Equation 8, yielding the parameters shown in Table 1. The x-axis is converted from the concentration of inducer (Van) to promoter activity as described in the Materials and Methods. Inducer concentrations: 0, 0. 0977, 0.195, 0.391, 0.781, 1.56, 3.13, 6.25, 12.5, 25, 50, 100 µM Van. H Two-dimensional response function for the induction of sgR O1 and sgD O2 . The circles are experimental measurements colored by the mean fluorescence values of three biological replicates performed on different days (standard deviations in Appendix Fig S4). The continuous color in the background is the model prediction using Equation 8, R 2 = 0.87 (Appendix Fig S4). The x-axis and y-axis are converted from Van and Chol to promoter activity, respectively (Materials and Methods). Inducer concentrations: [0,0.195,0.391,0.781,1.56,3.13,6.25,12.5,25,50,100 µM Van] and [0,37.0,111,333,1,000,3,000,9, elongation) "resetting" the DNA state at the rate of plasmid replication (cellular growth rate) and RNAP elongation (promoter strength) (Jones et al, 2017;Vigouroux et al, 2018). Thus, the kinetics of the system reaching steady state are expected to be dependent on growth phase and may impact their use in circuits with components with faster dynamics (Mishra et al, 2014;Takahashi et al, 2015;Ali Al-Radhawi et al, 2019;Westbrook et al, 2019). Repression/derepression could be applied to design synthetic circuits that perform new signal integration functions. As simple cisregulatory logic, the operation performed by these circuits is A IMPLY B where sgD (B) overrides the regulation imposed by sgR (A) (Figs 2G and 3G). If instead the displaced regulator were an activator (based on dCas9 recruiting RNAP (Dong et al, 2018;Fontana et al, 2020a;Ho et al, 2020;Villegas Kcam et al, 2021)), this logic would be A NIMPLY B.
However, this digital combinatorial logic does not capture the potential for new signal integration performed by these mechanisms. The signal integration follows a graded, rather than switchlike transition (Figs 2H and 3H), and this can be used to build useful analog functions. The circuit based on the repression/derepression of a promoter (sgR P2 and sgD P5 ) is capable of responding to transcriptional input ratios over two orders of magnitude (Fig 5A). Ratiometric signal processing is common in natural regulatory systems and is usually achieved by a motif where two species compete for a third component and only one of the bound species results in the output (Atkinson, 1968;Madl & Herman, 1979;Raisova et al, 2001;Berg et al, 2009;  competition can occur at a DNA binding site where an activating transcription factor competes with an inactive or repressive transcription factor (Perli & Lu, 2017;Zeng et al, 2019). Ratiometric circuits can be used to determine which of two continuously variable signals is larger. The sgR P2 /sgD P5 circuit in log-space is performing a (sgD -sgR) calculation, which if connected to a cooperative switch-like output could act as a single neuron in a neural network .
Another consideration is the transfer of this repression/derepression mechanism for transcriptional control in organisms other than E. coli. Repression of transcriptional elongation via dCas9 binding has been shown to work in a variety of different bacterial species (Peters et al, 2016(Peters et al, , 2019Rock et al, 2017), so we expect the elongation repression/derepression mechanism to be applicable to other species. Transferring this mechanism to eukaryotes is more difficult because dCas9 is only capable of modest elongation repression in eukaryotic systems Qi et al, 2013). Repression in eukaryotic systems is often accomplished through the fusion of chromatin-remodeling proteins to dCas9, which are capable of robust and reversible repression of transcription (Gilbert et al, , 2014Zalatan et al, 2015;Mandegar et al, 2016). Derepressing these systems could be accomplished by targeting a dCas9 lacking the fused repression domains to the same DNA location. This approach would require two different dCas9 species, which could be accomplished using dCas9 orthologs (Esvelt et al, 2013;Kim et al, 2019;Gasiunas et al, 2020) or by encoding repression domain recruitment within the sgRNA scaffold (Zalatan et al, 2015).
Various approaches have been developed to place native genes under synthetic regulatory control through the insertion of synthetic  A, B (A) Promoter repression/derepression circuit experimental results with a ratiometric interpretation. The upper subpanel is a genetic circuit schematic of the sgR P2 + sgD P5 circuit (full schematic shown in Fig 2F). Lower subpanel is the data from Fig 2H replotted as the ratio of the two inputs. The x-axis values are derived by taking the ratio of P Van activity to P BetI activity. (B) The upper subpanel is a genetic circuit schematic of the sgD O2 + sgR O1 circuit. The lower subpanel is the elongation repression/derepression circuit data ( Fig 4H) replotted as the ratio of the two inputs. For both parts, the x-axis values are derived from converting Chol (sgR) and Van (sgD) values to promoter activity (Materials and Methods) and then dividing sgD promoter activity by sgR promoter activity. promoters (e.g., that respond to T7 RNAP) or other regulatory motifs (Warner et al, 2010;Wang et al, 2012;Na et al, 2013). CRISPRi has been rapidly adopted because it can exert regulatory control without having to mutate the target; however, it only imparts a single on/off signal. To this end, depression/derepression can be used to inactivate the effects of CRISPRi in the control of native genes Weinberg et al, 2017;Moser et al, 2018;Henningsen et al, 2020). For example, CRISPRi/a has been used to dynamically repress or activate enzymes to control carbon flux in metabolic engineering applications (Moser et al, 2018;Peng et al, 2018;Lu et al, 2019;Tian et al, 2019;Fontana et al, 2020b). Derepression allows for the disruption of a subset of the genes being influenced by an activating or repressing sgRNA; in effect, this would introduce cis-regulatory logic into the native genes without needing to insert operators. In this work, we had to deal with the challenge of identifying or designing PAM sites so that the sgR and sgD binding sites are appropriately positioned to satisfy the distance constraints. This restricts their utility in the control of genome-encoded genes, where the likelihood of PAM sites being appropriately positioned in a promoter is small or restricts where the regulation can occur within a gene. This is likely why the effect that we observed for the blockage and release of elongation is small. However, recent efforts to engineer dCas9 to not require a PAM site have made progress (Kleinstiver et al, 2015;Hu et al, 2018;Nishimasu et al, 2018;Walton et al, 2020;Collias & Beisel, 2021). Collectively, these advances will allow the programming of cis-regulatory logic to be applied to any gene in the genome without having to insert or modify genomic DNA.

Computational methods
The random 100-bp sequence within P C1 was generated using the online Random DNA Sequence Generator (http://www.faculty.ucr. edu/˜mmaduro/random.htm) with the GC content set to 50%. Non-linear fitting was completed with the Python scipy.optimize.curve_fit() function.

Induction assays
All growth was performed in 96-well V-bottom plates (Roskilde, Denmark, #249952) at 1,000 rpm in a microplate shaker (ELMI, #DTS-4). The day before, individual colonies were inoculated into 150 µl EZ Rich media and Kan for overnight (16 h) growth at 37°C. The next day, cultures were diluted 200-fold by adding 0.75 µl of overnight culture into 150 µl of EZ Rich media and Kan. After 2-h growth, cultures were diluted 1,000-fold into inducing conditions by adding 6 µL of culture into 198 µl fresh media and Kan and then 5 µl of that dilution into media with inducers and Kan. To induce dCas9, aTc was added to a final concentration of 1.25 nM in all experiments. Growth was performed for 5.5 h, after which samples were prepared for flow cytometry.

Flow cytometry analysis
Fluorescence characterization was performed using a BD LSR Fortessa flow cytometer with the HTS attachment (BD, Franklin Lakes, NJ). Samples were prepared by aliquoting 40 μl of cell culture into 160 μl of PBS containing 200 µg/ml Kan. All samples were run in standard mode at a flow rate of 2 μl/s. RFP fluorescence measurements were made using the green (561 nm) laser, and all data were derived from the PE-Texas Red-A channel (PMT voltage of 700 V). The FSC and SSC voltages were 650 and 270 V, respectively. At least 10,000 events were collected for each sample, and the Cytoflow Python package (https://github.com/cytoflow/ cytoflow) was used for analysis, including gating. The geometric mean fluorescence is calculated for all cytometry distributions.

Promoter input calculations
The following procedure was followed to convert inducer concentrations (e.g., [IPTG]) to the activities of the inducible promoter (e.g., P Tac ) reported in RFP fluorescence (au). This approach has been described previously (Nielsen et al, 2016;Zhang & Voigt, 2018). Using a separate plasmid based on pDAA038, the response function of the inducible system was measured separately by measuring RFP fluorescence using cytometry. The RFP fluorescence values in au for the inducer concentrations were then plotted as "Promoter Activity". The response functions used are shown in Appendix Fig S1.

Repression/derepression dynamics
All growth was performed at 37°C and 350 rpm in an Innova44 (Eppendorf, NY, USA) with a 1-inch throw. The day before the experiment, a starter culture was initiated by inoculating a colony into 2 ml EZ-rich media with Kan in a 15-ml test tube. The next day, this culture was diluted to an OD 600 of 0.025 into 40 ml of fresh EZrich media with Kan. This was allowed to grow for 2 h in a 250-ml Erlenmeyer flask to bring the cells to OD 600 = 0.5. At this point, a time point was taken for t = 0 and cells were diluted to OD 600 = 0.00035 in an Erlenmeyer flask using fresh media with 10 mM Choline and 1.25 nM aTc. After 2 h of growth, 30-min time points were taken. At each time point, 1 ml of culture was removed, spun down (1 min at 16,000 g), and then resuspended in 300 µl of PBS and 2 mg/ml Kan and analyzed by cytometry. To transfer into derepressing conditions, 28 ml of culture was washed twice by centrifugation at 12°C at 4,300 g for 5 min. Then, the cultures were diluted to OD 600 = 0.035 in 40 ml of media with 100 µM Van, 10 mM Choline, and 1.25 nM aTc.

Data availability
This study includes no data deposited in external repositories.
Expanded View for this article is available online.