An endoribonuclease-based incoherent feedforward loop for decoupling resource-limited genetic modules

A significant goal of synthetic biology is to develop genetic devices for accurate and robust control of gene expression. Lack of modularity, wherein a device output does not depend uniquely on its intended inputs but also on its context, leads to poorly predictable device behavior. One contributor to lack of modularity is competition for shared limited gene expression resources, which can induce ‘coupling’ between otherwise independently-regulated genes. Here we quantify the effects of resource competition on engineered genetic systems in mammalian cells and develop a feedfoward controller to make gene expression robust to changes in resource availability. In addition to mitigating resource competition, our feedforward controller also enables adaptation to multiple log-orders of DNA copy number variation and is predictably tunable with upstream open reading frames. Our resource competition characterization along with the feedforward control device will be critical for achieving robust and accurate control


Introduction
A promising strategy for engineering complex genetic devices is to compose together simpler systems that have been characterized in isolation [1][2][3] . A critical assumption of this modular design approach is that subsystems maintain their input/output (i/o) behavior when assembled into larger systems. However, this assumption often fails due to context dependence, i.e., the behavior of a module depends on the surrounding systems 2,4 . There are many sources of context-dependence, including unexpected off-target interactions between regulators and promoters 5 , transcription factor loading by DNA targets 6 , gene orientation 7 , and resource loading by expressed genes 8,9 . To date, much effort has gone into identifying gene regulators with unique binding specificity, e.g. between transcription factors (TFs) and their DNA binding sites. Unique binding specificity enables gene regulators to work orthogonally, since they do not directly interfere with each other's binding and regulation 5 . Nevertheless, even if subsystems are entirely composed of orthogonal regulators, they can become coupled with each other via competition for shared cellular resources 2,[8][9][10][11] .
For example, it has been demonstrated in prokaryotes that genes compete for the usage of ribosomes, such that increased expression from one gene decreases expression from others by sequestering (i.e. loading) the ribosome 8,9 . Little work has been done to understand how resource competition affects engineered genetic devices in eukaryotic cells. Furthermore, while solutions to the ribosome resource competition problem in bacterial cells have appeared recently [12][13][14] , solutions to resource competition in mammalian cells are still missing.
In mammalian cells, loading of several types of cellular resources shared among multiple genes has been shown to affect gene expression, including splicing factors 15 , miRNA processing factors 16 , RISC complexes 17,18 , and the proteasome 19 . A potent form of resource competition called 'squelching' occurs when transcriptional activators (TAs) or strong promoters sequester transcription coactivator proteins (CoAs) and/or general TFs (GTFs), reducing transcription of other genes 20-28 . At sufficiently high expression levels of a given TA, these transcriptional resources are sequestered even from the TA molecules bound to the target promoter, yielding a bell-like dose-response curve, where the expression of the TA's target gene peaks at an intermediate level of TA and then decreases as the TA concentration is further increased (often referred to as 'self-squelching') 22,24 . As many established synthetic eukaryotic gene regulation systems utilize TAs, squelching represents a potentially pervasive problem in the space of eukaryotic genetic engineering. Here, we consider competition for gene expression resources as a general problem, investigate the quantitative consequences of resource competition on mammalian genetic circuits, and introduce an engineering solution.
We first developed an experimental model system to recapitulate the effects of transcriptional resource competition and provide in-depth characterization of these effects. We then used this model system to evaluate the performance of a feedforward controller designed to cancel the effects of resource loading on gene expression. Specifically, our model system utilizes Gal4 TAs of varying strength to measure the extent to which TA expression sequesters transcriptional resources from non-target genes. We developed a mathematical model that explains the effects of transcriptional resource sequestration by TAs on expression of target and non-target genes of the TA. We then measured the effect of different Gal4 TAs on commonly-used constitutive promoters in various mammalian cell lines to identify combinations of activators and promoters in each cell line where minimal effect on the non-target promoters is observed. Overall, our results provide extensive analysis for determining the extent to which transcriptional resource competition affects gene circuit behavior in mammalian cells.
Our ultimate goal is to make the output protein level of a given genetic device insensitive to changes in available gene expression resources, including CoAs and GTFs. By doing so, we can effectively decouple the behavior of resource-coupled genetic devices. To approach this problem, we regard resource availability as a disturbance input to a genetic device and design a controller that can be added to any device to 'cancel out' the effect of resource competition on the device's output. In prokaryotes, it has been shown that quasi-integral feedback control can make the output protein level of a genetic device insensitive to changes in ribosome availability 13 . In both prokaryotes and eukaryotes, incoherent feedforward loops (iFFLs) have been used to make gene expression levels insensitive to the copy number of a gene 29,30 . Here, we engineered an iFFL using CasE, an endoribonuclease (endoRNase) from a type I CRISPR system, to make a genetic device's output insensitive to changes in the availability of transcriptional resources (Figure 1a-d). Through experiments in mammalian cells, we show that iFFLs can make the output protein level of a genetic device insensitive to variations in availability of gene expression resources. We further found that our iFFL design performs well in combination with different activators and cell lines, demonstrating that our solution is general and applicable to a variety of contexts. Beyond resource competition, our iFFL design also makes a genetic device's output insensitive to multiple log-order changes in gene copy number, substantially improving upon previously published miRNA-based designs 29,31 . In addition, the iFFL reduces the dynamic effects of plasmid uptake and dilution on protein expression during transient transfection, thereby broadening the time window over which stable expression levels can be achieved. Overall, our iFFL design will find broad utility for engineering mammalian genetic devices which behave as predicted in a context-independent manner.

Characterization of transcriptional resource competition
Cells provide a finite pool of resources for gene expression. To express any one gene, the cell must allocate resources to this gene, thereby reducing the availability of resources to other genes. Here, we consider the effect of this reduced availability of resources on the output of a genetic device. Specifically, we define a genetic device as a system composed of one gene that takes regulatory inputs (e.g. sequence-specific TFs) and gives the gene's expressed RNA and/or protein as output. We further define a genetic module as one or more genetic devices that are linked together by regulatory interactions. Experimentally, we include fluorescent markers to measure the expression level of non-fluorescent proteins in some modules. Independently-regulated devices become implicitly coupled by competition for gene expression resources, wherein expression of a gene in one device 'loads' the pool of resources, thereby decreasing resource availability to other devices (Figure 1a). Because of this coupling, the i/o behavior of a genetic device or module becomes dependent on the presence of other devices and modules in the cell.
Previous studies have shown that competition for transcriptional resources including coactivators (CoAs) and general transcription factors (GTFs) can reduce gene expression levels 32 . Transcriptional activators (TAs) in eukaryotes are comprised of a DNA-binding domain (DBD) and an activation domain (AD), the latter of which recruits CoAs and/or GTFs to initiate transcription 33 . When a given TA is in excess, the binding between the TA and CoAs/GTFs in solution and at off-target DNA loci can form unproductive complexes that sequester these factors 24 , a phenomenon referred to as squelching 20 . Importantly, ADs alone, without a DBD, can also cause squelching 23 .
We recapitulated competition for transcriptional resources by different genetic devices using the genetic model system shown in Figure 1e. The Gal4 DBD was fused to several ADs of varying potency (Supplementary Figure 1), of which five were chosen for in-depth study: VP16, VPR, and the individual components of VPR (VP64, Rta, and p65). Our model system comprises two genetic modules, each with one or more genetic devices: (i) a device with a constitutive gene: CMV:Output 1 and (ii) Gal4 TA expression: hEF1a:Gal4-AD and a Gal4-activated gene:  (Figure 1f). Each curve was similar in shape, with the main difference being the amount of Gal4 TA needed to reduce CMV-driven expression by half, which varied by over 20-fold between Gal4-VP64 and Gal4-VPR.
Resource sequestration due to addition of Gal4 TAs can occur at different stages of gene expression: (a) the expression of Gal4 itself requires both transcriptional and translational resources, (b) the action of Gal4 activating its target causes additional sequestration of both types of resources due to expression of the target gene, and (c) Gal4 directly binds to and sequesters transcriptional resources in solution and/or at off-target DNA loci 24 . We validated that the Gal4 TAs repress CMV transcription by RT-qPCR measurement of CMV-driven mRNA levels (Supplementary Figure 4a-b). Indeed, CMV-driven mRNA levels were knocked down ∼2-fold by Gal4-VP16 and ∼16-fold by Gal4-VPR (Supplementary Figure 4b). In the same samples, a fraction of the cells were collected for flow cytometry to measure protein expression levels. The magnitude of knockdown of protein levels closely matched that of the mRNA levels ( Supplementary Figure 4c), suggesting that most of the knockdown was caused at the transcriptional level. Additional experiments showed that VPR alone and Gal4-VPR both knock down CMV expression, but neither the Gal4 DBD nor the luminescent protein Fluc2 do so (Supplementary Figure 4d). Because these proteins were expressed by the same promoter and thus place similar demands on gene expression resources, we concluded that (a) is negligible compared to (b) and (c). Furthermore, the knockdown of CMV expression by Gal4-VPR was similar regardless of whether the Gal4 target gene was present, indicating that in this system, (b) is small compared to (c). Thus, the AD, whether fused or not to the TA (Gal4), sequesters transcriptional resources from the CMV promoter and is the major player in the observed knock down of the CMV output expression.
We also characterized the dose-response curves of the Gal4 TAs activating the target gene (UAS:Output 2 ). Consistent with prior studies 22,24 , the activation dose-response curve of some activators (Gal4-Rta, Gal4-p65, and Interestingly, the relative UAS:Output 2 between each activator was strongly dose-dependent; for example, Gal4-p65 drove ∼6-fold higher expression than Gal4-VP64 at the lowest DNA dosage, whereas Gal4-VP64 drove nearly 2-fold higher expression than Gal4-p65 at the highest DNA dosage (Supplementary From prior work, it is unclear whether the minimum concentration of TA necessary for maximal activation of on-target genes is sufficient to knock down non-target genes. We thus compared the expression of CMV:Output 1 to UAS:Output 2 at each level of each Gal4 TA to measure the trade-off in expression of both genes. We found that for each Gal4 TA, maximum UAS:Output 2 expression occurred at a concentration of Gal4 that knocked down CMV:Output 1 by at least 2-fold (Supplementary Figure 2c). Overall, these results indicate that for TAs to drive high levels of expression, significant knockdown of non-target genes is likely to be observed.
Finally, we validated that our results measured in transient transfection were consistent with the behavior of genetic devices integrated into the genome. To do so, we integrated into HEK-293FT cells one of two lentiviral constructs: (i) an rtTA activator and an rtTA-driven fluorescent reporter (Supplementary Figure 8) or (ii) a Gal4-driven fluorescent reporter (Supplementary Figure 9). Following lentiviral integration, we transfected both cell lines with Gal4 activators and found that both rtTA-and Gal4-driven expression were negatively affected by Gal4 activators at high activator dosages. The responses of the non-target tet-on system and on-target promoter were both well-predicted by the model fits from our transfection experiments (Supplementary Note 3). Thus, our resource competition results are extensible to genes located in various contexts.

Activator and non-target promoter combinations with minimal coupling
We extended the genetic model system of Figure  From the Output 1 fold-changes in Figure 2c, we can extract patterns that help guide design choices for specific combinations of promoters and TAs that minimize coupling between modules due to resource competition.
Comparing the Gal4 TAs, we saw that across cell lines, Gal4-VP16 and -VP64 had relatively weak effects and Gal4-Rta, -p65, and -VPR had relatively strong effects. Gal4-VP64 and -VP16 caused less than a 20% change in  Figure 12c). However, there were cases where different promoters were affected more or less strongly in different cell types. For example, in both HEK cell lines, the hEF1a promoter was less affected by Gal4 TA competition than the CMV promoter, whereas in CHO-K1 cells the opposite was seen (Figure 2c). The Gal4 TA with the strongest negative effect on a given promoter was also not necessarily the same between cell lines. For instance, Gal4-VPR typically showed the strongest knockdown in HEK cells, whereas Gal4-Rta and Gal4-p65 did so in HeLa and CHO cells, respectively. Thus, while many patterns were preserved between cell lines, the effects of resource competition in one cell line do not necessarily predict the effects in others.
The constitutive promoters we tested varied more than 2 orders of magnitude in strength and originated from both viral and human DNA. Some promoters drove expression that was nearly undetectable (Supplementary Figure 13 So far we have focused on how coupling between the constitutive promoters (Module 1) and the Gal4 TAs (Module 2) affects expression of the promoters (Output 1 ); however, this coupling can also work in reverse such that Gal4-driven expression (Ouptut 2 ) is affected by Module 1. We thus examined the effects of resource sequestration by the constitutive reporters on Gal4-driven activation of UAS:Output 2 . We found that the expression UAS:Output 2 was largely the same between samples with the same Gal4 TA but different promoters (Supplementary Figure 10 While we have assumed thus far that effects from resource competition are entirely derived from the AD of a TA such as Gal4, it has been shown that reducing the strength of or eliminating DNA-DBD binding may relieve the effects of transcriptional resource loading by TAs 27 . We therefore compared the effect that VPR alone, Gal4-VPR, and VPR fused to a zinc finger protein (ZFP), dCas9, and rTetR had on expression of each of the constitutive promoters tested above. We found that the effects on each promoter followed a similar trend, with rTetR-VPR showing the most similar effects to Gal4-VPR, dCas9-VPR showing the least strong effects, and ZFP-VPR being the only variant to not knock down the CMV-based promoters ( Supplementary Figure 18a-c). The effects on each constitutive promoter were similar for dCas9-VPR +/-gRNA as well as rTetR-VPR +/-Dox (Supplementary Figure   18d), indicating that expression by these specific promoters did not significantly load gene expression resources and that Dox or gRNA binding are not required for rTetR-VPR or dCas9-VPR to sequester resources, respectively.
Overall, the characterization results in Figure 2c  on the same strand of DNA with no insulator in between, helping to couple their transcriptional inputs and kinetics 35 .
We placed the CasE target sites in the 5'UTR because Cas6-family endoRNases more strongly knock down gene expression when target sites are in the 5'UTR rather than the 3'UTR 36 (DiAndreth et al., manuscript in preparation).
The ability of our iFFL to make output expression level insensitive to resource availability is revealed through a mathematical model of the iFFL. The model also predicts that the robustness of the iFFL-regulated output can be tuned through variable numbers of short upstream open reading frames (uORFs) 37 in the 5'UTR of the endoRNase transcription unit. With reference to Figure 3a, the iFFL module consists of an endoRNase (x) that targets the mRNA m y of the output protein (y) for cleavage. The two proteins are encoded on the same DNA plasmid and driven by identical promoters. This ensures that the two genes share the same pool of transcriptional resources (i.e., CoAs). We assume that the endoRNase x enzymatically degrades the output's mRNA following Michaelis-Menten kinetics.
Under these assumptions, the steady state output protein concentration can be written as (see Supplementary Note 5 for derivations): where R := R T X · R T L lumps the free concentrations of the transcriptional resource R TX and the translational resource V y := α y β y γ y kκ y δ y , and and re-write (1) as: Note that by (2), for a fixed output gene, the parameter V y is fixed and does not change with any physical parameter of the endoRNase. On the other hand, changing the physical parameters governing the production, decay, and enzymatic reactions of the endoRNase only changes the lumped parameter . According to (3), for u · R/ 1, we have y ≈ Y max := V y · , which is independent of R, and therefore independent of the free concentrations of both transcriptional and translational resources. This implies that if we design the parameter to be sufficiently small, the iFFL module's output can adapt to variations in resource availability.
To experimentally quantify the iFFL module's robustness to resource availability, we use the fluorescence level of a co-transfected transfection marker (TX Marker) protein z as a proxy for the free amount of resources R. This is because the steady state of z can be written as z = V z · u · R, where V z is a lumped parameter independent of u and R and defined similarly to V y in (2) (see Supplementary Note 5 for more details). This enables us to re-write y in (3) as a function of the experimentally measurable quantity z: We thus introduce an experimentally quantifiable inverse measure of robustness, Z 50 , which is the TX Marker's fluorescence level at which the iFFL module's output is half of its maximum value (see Figure 3b) (i.e. y ≥ Y max /2 for all z ≥ Z 50 ). By substituting y = Y max /2 into equation (3), we find Z 50 = V z , implying that robustness increases as the parameter decreases.
We therefore constructed a library of resource-decoupled device modules with different parameters. To construct this library, we increased the number of uROFs (n) in the 5'UTR of the endoRNase's transcript m x to effectively increase the dissociation constant κ x between the ribosome and m x 37 , thus increasing . With reference to Figure 3c, the relationship between n and κ x has been experimentally characterized in 38 , where the authors measured expression of a constitutive fluorescent protein p with different numbers of uORFs in the 5'UTR of its transcript. Since the expression level of a constitutive gene is inversely proportional to the dissociation constant between ribosome and its transcript (i.e., p ∝ 1/κ x , see Supplementary Note 5), we have where p(n) and κ x (n) are the steady state expression of p and the dissociation constant between ribosome and protein p's mRNA transcript in the presence of n uORFs, respectively. Since we have derived from equation (4) that (i) Y max and Z 50 are both proportional to and hence proportional to κ x and that (ii) κ x (n) = (relative κ x )(n) × κ x (0) according to (5), our model predicts that Y max = Y max (n) and Z 50 = Z 50 (n) are both proportional to relative κ x .
To verify this model prediction, for n = 0, 1, 2, 4, 8 and 12, we plot the iFFL modules' output (y) for different levels of TX Marker (z). The shape of the experimentally measured TX Marker vs output dose response curves (see Figure 3d for select samples and Figure 6b for all data) matches well with the model prediction in Figure 3b, suggesting that Z 50 is a reasonable inverse measure of the module's robustness. We therefore fit the experimental data with (4) and evaluate the fitting function to describe Y max and Z 50 for different n in the experimental data. In Figure   3e, we plot Y max and Z 50 against the relative κ x values listed in Figure 3c, which we excerpted from Figure. 21 in the Supplementary data of Gam et al. 38 . We observe that Y max and Z 50 are both linearly related to relative κ x , indicating that our model (4) can capture the salient steady state behavior of the iFFL module. For a fixed output gene (i.e. given V y ), since Z 50 and Y max only depend on according to (3), our model also highlights a key design trade-off for an iFFL module: increasing maximum output Y max via tuning necessarily increases Z 50 , which indicates a decrease in robustness. The number of uORFs on endoRNase's transcript can thus serve as a convenient knob to balance this trade-off between robustness and maximum expression level. To increase Y max without affecting Z 50 , the relative promoter copy number of the output can be increased relative to the endoRNase, as we demonstrate with poly-transfection 38 in Supplementary Figure 19.
In addition to robustness to variations in free transcriptional and translational resource concentrations, the iFFL can also attenuate the effect of DNA plasmid variation (i.e. changes in u) on the module's output. In fact, since u and R are clustered together in (3), our analysis on the module's robustness to R carries over directly when analyzing its robustness to u: when uR , we have y ≈ V y according to (3), which is independent of u. Robustness to variations in u also includes temporal variability of DNA concentration, which is present in transient transfection experiments due to dilution of DNA plasmids as cells grow and divide. As one decreases the number of uORFs in the endoRNase's transcript, our model predicts that the iFFL module becomes more robust to DNA copy number variability in the sense that it's output remains the same for a wider range of DNA copy numbers (i.e. smaller Z 50 ).
This allows the module's output to maintain Y max for a longer period of time as DNA concentration gradually decreases, a phenomenon we observed both experimentally (see Supplementary Figure 33) and numerically (see Supplementary Figure 37).

The resource-decoupled module's output is robust to resource loading by Gal4 TAs
To determine the extent to which the output expression of the iFFL design is insensitive to resource loading, we To quantify the degree to which an iFFL or UR module is sensitive to resource loading by Gal4-VPR, we measured the fold-changes relative to nominal output (i.e. the median output in the absence of Gal4-VPR) and from those computed robustness scores: Our results from co-transfecting the iFFL and UR plasmids with increasing amounts of Gal4-VPR show that variants of the iFFL with 4 or fewer uORFs in front of CasE are significantly less affected by Gal4-VPR than the UR controls (Figure 4b-d). At the highest dosage of Gal4-VPR tested (30 ng), the output of the UR samples decreased between 2-and 3-fold, whereas the iFFL variants with 4x or 2x uORFs changed by less than 1.5-fold (Figure 4b). In terms of robustness, most UR samples ranged between 30% and 60% regardless of the nominal output level. The iFFL samples with lower nominal output (higher CasE levels obtained via fewer uORFs) showed high robustness  Figure 4, we saw larger fold-changes in iFFL variants with 8 uORFs compared to those with fewer. The robustness scores of UR-activator combinations across cell lines were as low as ∼30% and less than a third (30.7%) of the combinations had robustness above 80% (Figure 5e). By contrast, the iFFL variants had robustness above 80% for the large majority of combinations (81.5%). On average, the robustness scores of the UR variants ranged between 60% and 75%, whereas those of the iFFL variants ranged between 85% and 90%.
The distribution of robustness scores per cell line for all iFFL and UR variants, as well as constitutive promoters from Figure 2, are compared in Figure 5f. We found that the iFFLs variants showed the highest robustness in HeLa To ensure that our results were not specific to the CMVi promoter, we repeated the experiments in Figures 4 & 5 with a version of the iFFL which replaces the CMVi promoters with hEF1a ( Supplementary Figures 24-28). As with the CMVi iFFL, variants of the hEF1a iFFL with fewer uORFs (smaller ) showed reduced fold-changes and higher robustness scores in response to Gal4 TAs than UR variants with comparable nominal outputs ( Supplementary   Figures 24 & 26). Compared to the CMVi iFFL, the hEF1a iFFL generally showed higher fold-changes and lower robustness scores, especially in U2OS and HeLa cells co-transfected with Gal4-Rta (Supplementary Figure 26).
Interestingly, the hEF1a iFFL output for variants with 4 or fewer uORFs was slightly increased (<1. To quantify the extent of adaptation of iFFL output expression to DNA copy number, we compared the median expression of cells in finely-sampled transfection marker-delineated bins to the fit value of Y max , and considered a bin to be 'adapted' to copy number variation if log 10 (output) was within 5% of log 10 (Y max ) (i.e. the log-scale robustness score was above 95% - Figure 6c). As expected based on the model, increasing by increasing the number of uORFs decreases the range over which the iFFL output adapts to DNA copy number (Figure 6d). Since Y max is also correlated to , fit values of Y max are also highly correlated with the adaptation range (Supplementary Figure 32b).
We repeated these experiments and analyses with the CMVi-driven CasE iFFL and found similar results (Supplementary Figure 32c-f).
Since the iFFL can adapt to DNA copy number variations between cells, we investigated whether the iFFL can also adapt to DNA copy number variations within a single cell. In particular, we measured iFFL output over time

Discussion
The development of sophisticated synthetic genetic circuits will be enabled through improved understanding of how the function of a genetic component is affected by its context 2 . Competition between genes and their products for shared gene expression resources is an important factor causing context-dependence. Several biomolecules at all levels of gene expression in mammalian cells are known to be shared among many genes and known to induce couplings in their expression 15-20,26,28,32,33 . However, the effects of competition for these resources on engineered genetic systems has not been systematically investigated. We thus focused on understanding the extent to which competition between genetic devices for shared transcriptional resources affects gene expression in synthetic genetic systems. While improved characterization of resource competition effects can improve genetic circuit design 9 , it has also been shown that gene expression controllers can be used to automatically mitigate the effects of resource competition in bacterial systems [12][13][14] . To provide a solution to the resource competition problem in mammalian cells, we thus developed a simple genetic controller that can be added to any genetic device to make its expression level robust to resource availability. This iFFL effectively makes gene expression robust to resource loading by different Gal4 TAs across cell lines, demonstrating the applicability of the system to variable transcriptional contexts.

Transcriptional resource competition
From our characterization of resource competition, we found that constitutive promoters are affected disparately by different Gal4 TAs ( Figure 2). The differences in promoter responses may result from the promoters utilizing different subsets of transcriptional resources 40 : there are hundreds of transcriptional cofactors (including CoAs and subunits of the mediator complex) that interact with native and synthetic TFs 41,42 . It was recently shown that TATA-box based and CpG island-based core promoters are activated by different subsets of CoAs 43 . Consistent with these results, we found that the responses of promoters with large CpG islands to Gal4 TAs were more similar to each other than to promoters without CpG islands (Supplementary Figure 15).
In each cell line, we identified several combinations of promoters and Gal4 TAs for which the TA minimally affected promoter expression. These 'non-coupled' combinations may result from the TA recruiting different specific CoAs than those used by the constitutive promoter, and/or from the promoter having relatively high affinity for CoAs.
The combinations with minimal or reduced coupling will be useful for choosing parts in synthetic genetic circuits that, when combined together, enable more accurate prediction of circuit behavior. Additionally, relatively strong constitutive promoters that are less affected by resource loading may be utilized as more reliable transfection markers.
A previous study called into question whether squelching by TAs was an artifact that only affected episomal genes by showing that self-squelching only occurs if the TA-driven promoter is in a plasmid, but not in the genome 44 .
However, other experiments have demonstrated coupling between signal-responsive genes in the genome 45 and there is growing evidence for the role of squelching in natural gene regulation 32 . Our results show that both non-target squelching and self-squelching can indeed affect integrated genes (see Supplementary Note 3 & Supplementary   Figures 8-9). Thus, our results are extendable to various contexts, including episomal and genomic genetic systems.

EndoRNase-based iFFLs decouple genetic device expression levels from resource inputs
In various cell lines and in combination with different Gal4 TAs, we showed that our endoRNase-based iFFL design can effectively cancel-out the effects of transcriptional resource competition on gene expression output controlling the ratios of genetic device components to maximize device performance 38 , making dCas9-based circuits robust to shared dCas9 resources 51,52 , and precisely setting the levels of signaling receptors to achieve unique input functions 53 .
To our knowledge, we are the first to show that iFFLs can be used to mitigate the effects of resource competition.
For over a decade it has been known that the iFFL topology may enable a genetic device's output to adapt to perturbations 54 . This property have been exploited to create iFFLs that can adapt to DNA copy number variation 29,30 or inducer input levels 31 . Previous solutions to the ribosome competition problem in bacteria utilized negative feedback loops (NFBLs) 12,13 . An advantage of NFBLs is that they can tolerate unknown dynamics in the output gene expression process, whereas iFFLs require the effect of the disturbance to exactly be canceled out by the controller species. Conversely, iFFLs are generally much simpler to design and operate. Recent work showed that combining miRNA-based iFFLs and NFBLs yielded circuits with some properties of both control mechanisms 39 , indicating that iFFLs and NFBLs are not mutually exclusive and can synergize when used together.
In bacteria where competition for ribosomes is most prominent 8 , it has been proposed that centralized controllers for ribosome levels can ensure a constant supply regardless of loads placed on the ribosome 14 . Conversely, the number of CoAs and GTFs competed for by eukaryotic TAs and promoters is likely far too large to build such a centralized controller 41 . Even if the mediator complex were the only shared transcriptional resource, it is comprised of dozens of domains 55 , each of which would need to be controlled.

Adaptation of iFFL expression to its DNA copy number
In addition to resource loading, we found that our iFFL design is also robust to static and dynamic variability in its DNA copy number ( Figure 6). Our endoRNase-based iFFL output adapted to copy number variation over ∼1-2 log  interesting new mechanism to control the temporal dynamics of iFFLs.

Conclusions
Overall, we have presented characterization of transcriptional resource competition in mammalian cells and the design and performance testing of an endoRNase-based iFFL design which mitigates the effects of resource competition on gene expression. Our characterization of resource competition will be useful both for designing genetic circuits with minimal competition among genetic devices composing the circuits, as well as for predicting the behavior of complex circuits composed of genetic devices which compete for shared resources. Our iFFL is a simple and accurate controller of gene expression that will find many uses in engineering mammalian cells. Altogether, this work will enable more accurate bottom-up design of genetic systems in mammalian cells, facilitating the development of more complex and reliable circuits for applications in cell therapy, tissue/organoid engineering, and cellular bioproduction.

Acknowledgements
We would like to acknowledge Douglas Lauffenburger and Ahmad Khalil for discussion as well as Olga Parkin, Cameron Haase-Pettingell, and Darlene Ray for administrative support.

Modular plasmid cloning scheme
Plasmids were constructed using a modular Golden Gate strategy similar to previous work in our lab 38,57 . Briefly, basic parts (insulators, promoters, 5'UTRs, coding sequences, 3'UTRs, and terminators -termed level 0s (pL0s)) were assembled into transcription units (TUs -termed level 1s (pL1s)) using BsaI Golden Gate reactions. TUs were assembled into multi-TU plasmids using SapI Golden Gate reactions. To make lentivirus transfer plasmids, pL0s or pL1s were cloned into a vector derived from pFUGW (AddGene plasmid #14883) using either BsaI or SapI Golden Gate, respectively. Genbank files for each plasmid and vector backbone used in this study are described in Supplementary Table 6

Lentivirus production and infection
Lentivirus production was performed using HEK-293FT cells and second-generation helper plasmids MD2.G confluency, trypsinized, and 1 × 10 6 cells were resuspended in 2 mL of viral supernatant and together added to a pre-treated 6-well tissue culture plate (Costar). To facilitate viral uptake, we added polybrene (Millipore-Sigma) to a final concentration of 8 µg/mL. Cells infected by lentiviruses were expanded and cultured for at least two weeks before use in experiments using the conditions for culturing HEK-293FT cells described above.

Flow cytometry
To prepare samples in 96-well plates for flow cytometry, the following process was followed: media was aspirated, 50 µL PBS (Corning) was added to wash the cells and remove FBS, the PBS was aspirated, and 40 µL Trypsin-EDTA (Corning) was added. The cells incubated for 5-10 minutes at 37deg C to allow for detachment and separation.
Following incubation, 80 µL of DMEM without phenol red (Gibco) with 10% FBS was added to inactivate the trypsin. Cells were thoroughly mixed to separate and suspend individual cells. The plate(s) were then spun down at with 1% BSA (Thermo Fisher), 5 mM EDTA (VWR), and 0.1% sodium azide (Sigma-Aldrich) to prevent clumping.
For prepping larger plates, all volumes were scaled up in proportion to surface area and samples were transferred to 5 mL polystyrene FACS tubes (Falcon) after trypsinization. For standard co-transfections, 10,000-50,000 cells were collected per sample. For the poly-transfection experiment and transfections into cells harboring an existing lentiviral integration, 100,000-200,000 cells were collected per sample.
For the experiments shown in Figure 1 and Supplementary Figure 2 When first analyzing the data in Figure 4, we found that the measurements of fold-changes and robustness for the UR variants with diluted output plasmid DNA were sensitive to the fluorescent gating strategy used in the analysis.
Our typical gating routine of selecting cells positive for either the output or the transfection marker yielded fold-changes of the diluted UR variants that were much larger than when gating on cells positive for just the output.
Conversely, both gating strategies yielded similar fold-changes for the iFFL variants regardless of their nominal output. We suspect that the difference in measurements for the diluted UR variants may result from (i) reduced UR plasmid uptake when forming lipid-DNA complexes for co-transfection with the Gal4-VPR plasmid (which is larger than the DNA-mass-offsetting plasmid Gal4-None) and/or (ii) repression of UR output expression below the autofluorescence threshold. Since these confounding factors could not be distinguished, we report the results for the follows an exponential distribution. We thus fit an exponential distribution using the MATLAB function 'fitdist()' (https://www.mathworks.com/help/stats/fitdist.html) to the differences between time-stamps of collected cells. Before fitting, we removed inter-cell times larger than the 99.9 th percentile to prevent biasing by large outliers. The characteristic parameter of the exponential distribution (λ) is the inverse of the average time between events. Thus, the event rate is given by 1 λ (i.e. the mean of the exponential distribution). To ensure a known and controlled flow rate, any sample for which we would measure the concentration was collected via the HTS attached to the flow cytometer. The flow rate of the HTS was can be set through the FACSDiva Software (BD) controlling the instrument. The flow rate of each sample was recorded and input into the calculation.

RT-qPCR
Transfections for qPCR were conducted in 24-well plates (Costar). RNA was collected 48   For fitting both the resource competition and iFFL models, we used the MATLAB function 'lsqcurvefit()' (https://www.mathworks.com/help/optim/ug/lsqcurvefit.html), which minimizes the sum of the squares of the residuals between the model and the data. As the function input values we used the level of either the Gal4 TA (in the case of resource competition -as measured by Gal4 Marker) or the transfection marker (in the case of the iFFL). For fitting the Gal4 TA dose-response data, the residuals were computed between the median CMV:Output 1 or UAS:Output 2 levels and function outputs directly. In addition, all median values computed from different experimental repeats were pooled together before fitting. For fitting iFFL and UR models, the residuals were computed between the log 1 0-and biexponentially-transformed levels of the output protein of interest and the log 1 0and biexponentially-transformed function outputs, respectively. In experiments with the hEF1a iFFL being tested only in HEK-293FT cells, the entire morphologically-gated population of cells was used for fitting. In hEF1a iFFL experiments containing multiple cell types, to prevent the model from over-fitting the untransfected population in more difficult-to-transfect cells, the cells in each sample were analytically binned into half-log-decade-width bins based on the transfection marker, and an equivalent number of cells from each bin were extracted, combined, and used for fitting. In samples with the CMVi iFFL, the relatively high expression of the CMVi promoter compared to the hEF1a promoter (which is used as a transfection marker and proxy for DNA/resource input level z) in most cell lines imposes non-linearity in the transfection marker vs output curve at low plasmid DNA copy numbers per cell.
This non-linearity led us to gate cells positive for either the iFFL output or the transfection marker for fitting. For the resource competition models, all parameters for all Gal4 TAs were fit simultaneously using a custom function, 'lsqmultifit()', that was created based on 'nlinmultifit()' on the MATLAB file exchange (https://www.mathworks.com/matlabcentral/fileexchange/ 40613-multiple-curve-fitting-with-common-parameters-using-nlinfit).
Goodness of fit was measured by computing the normalized root-mean-square error CV(RMSE). CV(RMSE) was computed with the following equation: Where y(x i ) is the value of the data at the input value x i ,ȳ is the mean of y for all values of x, and f (x i ) is the function output at input value x i .  Figure 1 iFFL-based approach for decoupling modules with shared limited resources.   (TX) and translational (TL) resources (R). When the gene is regulated by an endoRNase (x), an unintended increase (decrease) in R increases (decreases) the amount of endoRNase to reduce (increase) the amount of the output by enhancing its mRNA degradation. This action compensates for the unintended increase (decrease) in the regulated gene's production rate due to variations in R. Since the same pool of TX and TL resources is also used to express the transfection marker z in a transient transfection experiment, we use the marker's concentration z as a proxy to quantify R experimentally. (b) The steady state output level (y) of the iFFL can be written as a function of the marker level (z). We evaluate the performance of an iFFL by (i) its maximum output (Y max ) and (ii) its robustness to variation in R and therefore z, characterized by (Z 50 ). In our model, both Y max and Z 50 are linear functions of , which can be used as a design parameter (see equation (2)). is proportional to the decay rates of the endoRNase and output mRNA and is inverseley proportional to the production rate and catalytic efficiency of the endoRNase. (c) An increase in the number of uORFs in the 5' UTR of the endoRNase's transcript leads to a decrease in its TL initiation rate. We model it as an increase in the dissociation constant between the ribosome and the endoRNase's mRNA  plots show the mean (µ) ± relative error ( 1 ln(10) · σ µ ) of medians for three experimental repeats. We use relative error rather than standard deviation (σ) to more accurately represent error on the log-scale of the y-axis 59 . Fold-changes (Fold-∆s were computed by dividing the median level of Output at a given concentration of Gal4-VPR by the Nominal Output level (the median level of Output at 0 ng Gal4-VPR). The Fold-∆ plots show the mean ± standard