The Parameter-Fitness Landscape of lexA Autoregulation in Escherichia coli

Feedback mechanisms are critical to control physiological responses. In gene regulation, one important example, termed negative autoregulation (NAR), occurs when a transcription factor (TF) inhibits its own production. NAR is common across the tree of life, enabling rapid homeostatic control of gene expression. NAR behavior can be described in accordance with its core biochemical parameters, but how constrained these parameters are by evolution is unclear. Here, we describe a model genetic network controlled by an NAR circuit within the bacterium Escherichia coli and elucidate these constraints by experimentally changing a key parameter and measuring its effect on circuit response and fitness. This analysis yielded a parameter-fitness landscape representing the genetic network, providing a window into what gene-environment conditions favor evolution of this regulatory strategy.

levels in the cell and, therefore, the activation state of the entire SOS gene network (Fig. 1A). Unregulated expression of some SOS genes is toxic. For example, sulA encodes a protein that inhibits cell division and lack of LexA regulation is lethal to cells (13)(14)(15). Additionally, hyperregulation of SOS genes can also be detrimental, as bacteria that are incapable of activating the SOS response, by virtue of the presence of a noncleavable LexA protein, exhibit decreased survival after DNA damage (16)(17)(18). Therefore, we hypothesized that the full native SOS circuit context constrains lexA-NAR circuit parameters due to fitness effects on the cell. We sought to quantify this effect within the context of a previously described NAR-circuit model (7) and to examine its dependence on sulA activity and the degree of genotoxicity in the cellular environment.
Three main biochemical parameters describe an NAR circuit (7) (Fig. 1B), but only two of the parameters have been studied systematically in native circuit contexts. The first parameter, ␣, the first-order rate constant for the degradation of repressor (Fig. 1B, "␣"), was examined in the SOS system using LexA variants with a range of autoproteolysis rates. Those studies showed that higher self-cleavage rates resulted in lower steady-state LexA levels and greater amounts of SOS activation (19,20). The second parameter, ␤, or "promoter strength," is the rate of mRNA synthesis in the unrepressed state of the promoter and dictates the maximum rate of synthesis of repressor protein (Fig. 1B, "␤"). This parameter was investigated in the SOS system by using a tetracyclineinducible lexA promoter in a lexA deletion (⌬lexA) strain (P tet -lexA), enabling titratable control of lexA promoter activity without autorepression. As predicted by modeling (7), these experiments showed NAR that led to more-rapid "turn-off" kinetics, permitting faster exit from growth inhibition after DNA damage (21). In the present report, we investigate the third parameter, k, which is the defining feature of an NAR circuit, as it relates the magnitude of the promoter's repression for a given repressor concentration (Fig. 1B, "k"). Of note, the mathematical framework derived to model NAR parameters (7) is based on a Michaelis-Menten model of promoter activity, X, where the unrepressed promoter activity, ␤, is modulated by the action of a repressor, R: In this formulation, [R] represents the concentration of the repressor and k represents the effective affinity of the repressor for the promoter (i.e., the concentration at half-maximal repression). At the steady-state repressor concentration, [R] s , the rate of repressor synthesis, X, is equal to its rate of degradation, ␣·[R] s : Solving for k yields the following: To study the effect of specifically modulating k in the lexA-NAR circuit, we used site-directed mutagenesis to make a series of lexA promoters with mutations in the LexA operator sites. We engineered six mutant E. coli strains, exhibiting a wide range of LexA affinity at the lexA promoter, and characterized NAR circuit kinetics, input dynamic range, SOS functions, and fitness. The LexA steady-state concentrations of the strains ranged over 2 orders of magnitude, and our experiments showed that this impacted fitness and SOS functions at both extremes, thus revealing the constraints on NAR circuit parameters. We conclude by deriving a fitness landscape for the lexA-NAR circuit informed by our experimental data.

RESULTS
Construction of E. coli strains with a range of k values for the lexA-NAR circuit. We sought to create a series of mutant lexA strains with different values of k and reasoned that this could be accomplished by introducing mutations into the promoter that are expected to specifically alter LexA-operator binding affinity. The lexA promoter has two known LexA operators located near the transcription start site (operators I and II) (22,23) and a putative third, upstream operator (operator III) (24). Therefore, prior to deriving the full series of experimental constructs, we first determined the contribution of each operator to LexA-mediated repression. To do this, we introduced different combinations of a previously described T ¡ C point mutation into the operator halfsites (see Fig. S1A in the supplemental material) (25), which severely abrogated LexA-operator affinity (Fig. S1B). To measure the effect of the mutations on LexA repressor activity, we utilized a green fluorescent protein (GFP)-reporter plasmid in which gfp is under the control of the lexA promoter (P lexA -gfp) (26) and analyzed expression in both the parental wild-type (wt; lexA ϩ ) and ⌬lexA cells. Expression in ⌬lexA cells serves as an important control, enabling measurement of the promoter's inherent (LexA-independent) transcription activity. The mutations completely inactivated operators I and II but had no effect when introduced into operator III (Fig. S1C). In ⌬lexA cells, promoter activity was relatively unaffected (Fig. S1D), confirming that the mutations caused a specific loss of LexA-mediated repression. Further analysis of operator III demonstrated that it was not functional for repression (Fig. S2); thus, we conclude that the lexA promoter has only two LexA operators.
The experiments described above yielded two constructs with a complete loss of LexA repression due to inactivation of both operators I and II (2R1L and 2L2R1L1R), as well as constructs with reduced repression due to inactivation of only a single operator (e.g., 2L2R) ( Fig. 2A and B). Next, to create constructs with enhanced repression, we introduced mutations into operator I in a serial manner (using 2L2R as a starting template) that made it more similar to the E. coli consensus operator sequence ( Fig. 2A), which is the DNA sequence that has the highest known affinity for LexA (27). We selected operator I for mutagenesis because, unlike operator II, it does not overlap highly conserved RNA polymerase (RNAP) binding sequences of the promoter, allowing us to make mutations that were unlikely to affect the promoter's inherent transcription activity. To ensure this, we also measured the promoter activity of each construct in ⌬lexA cells and found no major perturbations (Fig. S1E). As anticipated, promoter activity measurements in this "consensus" series (cons01 to cons11) decreased with greater similarity to the E. coli consensus operator sequence, yielding a collection of promoters with a range of levels of LexA repression that spanned that of the wt promoter (Fig. 2B).
We also further validated alteration of k by determining the promoter activation thresholds for a subset of promoters across this range of LexA repression (wt, 2L2R, cons06, and cons11). To do this, we measured the induction of promoter activity across a broad range of UV light-induced DNA damage and determined the UV dose that resulted in half-maximal activation (50% effective dose [ED 50 ]) (Fig. S3A). Consistent with the expected alterations in k, the ED 50 value for 2L2R was the lowest, that for cons11 was the highest, and that for cons06 was intermediate, with cons06 having the value closest to that of the wt promoter (Fig. S3B). Notably, the 2R1L and 2L2R1L1R promoters were excluded from this analysis because, consistent with a complete lack of repression, they did not show DNA damage induced by UV light. Finally, we note that a prior study of 14 mutant recA promoters, employing an analogous method, showed ED 50 values that were highly correlated (r ϭ 0.96, P Ͻ 0.0001) to biochemical measurements of LexA-operator binding (27). We conclude that the range of promoter activities that we report in Fig. 2B was due to differences in LexA binding affinity and that the range extends from the complete loss of LexA repression (2R1L and 2L2R1L1R), to an intermediate level of reduced repression (2L2R), to a level similar to wt repression (cons06), and finally to a level of repression exceeding that of the wt (cons11).
Having identified candidate promoters using the GFP-reporter plasmid system described above, we next introduced the wt, cons11, cons06, 2L2R, 2R1L, and 2L2R1L1R promoters into the endogenous lexA locus of the E. coli chromosome. Here, we refer to the parental wild-type and lexA deletion strains as the lexA ϩ and ⌬lexA strains, respectively, and refer to the resultant recombinant strains as the lexA wt , lexA cons11 , lexA cons06 , lexA 2L2R , lexA 2R1L , and lexA 2L2R1L1R strains. These strains harbor intact lexA-NAR circuits that are fully integrated into the native SOS gene network. The lexA 2R1L and lexA 2L2R1L1R strains are also fully integrated, but their lexA-NAR circuits lack autoregulation because LexA does not repress their mutant lexA promoters. Below, we refer to the latter two strains collectively as lexA 0 strains to denote the complete absence of autorepression. We selected the set of promoters for strain construction described above since they represent a range for the parameter k in this system with values between the two LexA repression extremes: lexA 0 (no repression, k ¡ ∞) and ⌬lexA (no expression, k ¡ 0). The ranking of the strains in terms of the expected values for k is as follows: ⌬lexA Ͻ lexA cons11 Ͻ lexA wt ϳ lexA cons06 Ͻ lexA 2L2R Ͻ lexA 0 . Of note, the double-operator configuration of the wt promoter is speculated to facilitate positive Operator sequences (I and II) and the Ϫ10 site are indicated by horizontal lines, and the transcription start site is indicated with a bent arrow. Arrows indicate positions that were mutated in the alignment, and specific mutations are bolded. Conserved CTG motifs are indicated with capital letters, and operators shaded in gray were completely inactivated by mutation. (B) Promoter activity of mutant P lexA -gfp promoter constructs. Fluorescence intensity (GFP) measurements were acquired in lexA ϩ cells and normalized (% expression) to signal from an unrepressed control strain (⌬lexA ϭ 100%). Plotted values and error bars represent means and standard deviations, respectively (n ϭ 4). Black bars indicate promoters selected for strain construction. (C) Relative LexA levels in mutant lexA strains. LexA levels were quantified by immunoblotting and normalized to the signal obtained in the lexA ϩ control strain. Each circle represents a value from a replicate blot (n ϭ 3). Horizontal lines and error bars represent geometric means and standard deviations, respectively. Error bars are not visible due to small variances between replicate values. (D) SOS target gene promoter activity in mutant lexA strains. Three different SOS reporter plasmid derivatives were used to assess promoter activity in the indicated strains: P Hi -gfp (red), P Lo -gfp (blue), and P No -gfp (gray) contain LexA operators with high, low, and no LexA affinity, respectively. Fluorescence intensity (GFP) measurements are normalized (% expression) to signal from an unrepressed control strain (⌬lexA ϭ 100%). Plotted values and error bars represent means and standard deviations, respectively (n ϭ 3). Strains that lack autorepression are also labeled "lexA 0 ." cooperative binding interactions between LexA dimers (11,20,22,23,28). Therefore, we selected the cons06 construct for strain construction for the additional reason that its degree of LexA repression was similar to that seen with the wt promoter and yet it contains only a single operator, leading to our reasoning that a direct comparison of lexA cons06 to lexA wt would provide insight into the importance of the double-operator configuration (see Discussion).
Changing the value of k independently of other NAR circuit parameters is predicted to change the steady-state concentration of the repressor (see equation 3), which, in turn, would change the expression of repressor target genes. Therefore, to characterize and validate the mutant strains, we first measured their relative LexA levels by quantifying LexA immunoblots (Fig. 2C). As expected, no LexA immunoblot signal was detected in ⌬lexA cells (Fig. S4A) and lexA wt cells exhibited LexA levels similar to those seen with the parental lexA ϩ strain. LexA levels in lexA cons11 were close to the limit of detection (Fig. S4B), at about one-tenth that of lexA wt . This represents a significant reduction, as it is comparable to the amount of LexA depletion that resulted from 30 J/m 2 of UV-induced DNA damage (Fig. S4C). LexA levels in lexA cons06 were similar to those seen with lexA wt , and levels in lexA 2L2R were between those seen with the lexA wt and the lexA 0 strains. Consistent with the absence of autorepression, the lexA 0 strains had the highest LexA levels, which were about 23-fold higher than shown by the lexA wt cells. Next, to determine the impact on target gene expression, we transformed the mutant strains with the following three different SOS GFP-reporter plasmids, which were based on the recA promoter (27): one plasmid had a promoter with a high affinity for LexA (P Hi -gfp), another plasmid had a promoter with low affinity for LexA (P Lo -gfp), and, as a control, we also included a promoter with no affinity for LexA (P No -gfp). We then compared the levels of promoter activity between the strains (Fig. 2D). As expected, we observed near-maximal activity (93% to 101%) with the P No -gfp reporter plasmid in all strains, signifying a complete lack of repression of gfp expression. For the P Lo -gfp reporter plasmid, we observed similar levels of activity for lexA ϩ , lexA wt , and lexA cons06 (52% to 58%), decreased activity for lexA 2L2R (38%), further reduced activity for the lexA 0 strains (29%), and near-maximal activity for lexA cons11 (98%). For the P Hi -gfp reporter plasmid, we observed Ͻ9% activity for all of the strains except lexA cons11 , which displayed 92% activity. Overall, we found that target gene expression was inversely correlated with the amount of LexA present in the cell and conclude that the altered steady-state LexA concentrations of the mutant strains affected the activity of SOS gene promoters with both high and low LexA affinity. Interestingly, promoter activity was near-maximal in the lexA cons11 strain even after transformation with the P Hi -gfp plasmid, a very-low-copy-number plasmid containing the highest-affinity LexA operator sequence. This raised the possibility that lexA cons11 may have a constitutively active SOS response (see below).
Having validated significant alterations to the parameter k in the mutant strains, we next took advantage of our unique experimental system to quantify k for each strain. In the strains that we derived, the quantity ␤/␣ of the lexA-NAR circuit is constant and can be inferred from the LexA steady-state concentration of the lexA 0 strains, [LexA] 0 , as follows: Thus, to quantify k for each strain, we used our measurements of LexA levels ( Fig. 2C) as the input for equation 5. For the value of [LexA] 0 , we averaged the two lexA 0 strain measurements since both model the complete absence of autorepression (as shown below, we also grouped measurements from the lexA 0 strains together for this reason). We found that the value for k spanned 3 orders of magnitude among the strains with intact autorepression (Table 1).
Circuit input sensitivity, dynamic range, and target gene expression kinetics of mutant strains. To determine the effect of k on input sensitivity, dynamic range, and target gene expression kinetics, we measured the promoter activity of the P lexA -gfp and P Hi -gfp reporter plasmids (i.e., the circuit "output") in the mutant strains as a function of time over a range of different DNA damage doses (i.e., the circuit "input"). We chose the P lexA -gfp and P Hi -gfp promoters for this analysis because they have low LexA affinity and high LexA affinity, respectively, and have expression kinetics that are representative of "early" and "late" SOS genes, respectively (27). We excluded the ⌬lexA and lexA cons11 strains from this analysis because they display constitutive SOS GFP-reporter activity and the circuit could not be further induced. The remaining strains were inducible and have values for k and [LexA] s that are equal to or greater than wild type. We hypothesized that the higher values for [LexA] s in the mutant strains would be an impediment to SOS activation and, therefore, decrease circuit sensitivity, increase dynamic range, and slow target gene expression kinetics.
First, to understand the effect of k on the input sensitivity and dynamic range of the circuit, we plotted the highest promoter activity value obtained (PA peak ) as a function of UV dose and analyzed the dose-response curves. We used the value for the UV dose that half-maximally activated the promoter (ED 50 ) as a measure of circuit "input sensitivity" and the difference between the ED 90 and ED 10 values (R) as a measure of "input dynamic range" (Fig. 3A). Consistent with past studies (27), we found that the ED 50 values for P Hi -gfp induction were higher than those of for P lexA -gfp induction (Fig. 3B, left), indicating that a larger UV dose is required to activate the higher-LexAaffinity promoter. However, here, our data newly enabled us to test the hypothesis that elevated [LexA] s values decrease circuit sensitivity (i.e., increase ED 50 values), but we found no significant association between ED 50 and [LexA] s values (Fig. S5A). Similarly, we found that the R value for the P Hi -gfp promoter was higher than that for the P lexA -gfp promoter but, again, that there was no significant association between R and [LexA] s (Fig. S5B). We conclude that increasing [LexA] s by altering the value of k, or even eliminating autorepression entirely, does not impact the input sensitivity or dynamic range in this system.
Next, to understand the effect of k on target gene expression kinetics, we measured the amount of time that was required for the promoter to reach 50% of its maximal signal activity (t on ) and then to return to 50% of its maximal activity (t off ) for each DNA damage dose. To understand the degree to which the mutant strain value deviated from that determined for the wild-type strain, we calculated Δt on and Δt off , representing the difference between the value determined for the mutant strain and that representing the wild-type strain (Fig. 3C). We found that the Δt on and Δt off values were relatively invariant with respect to DNA damage dose, and so we plotted the average values for comparison (Fig. 3D). In contrast to the ED 50 and R values, which exhibited no correlation with [LexA] s , we found that the Δt on and Δt off values were significantly correlated with [LexA] s (Fig. S5C). The highest Δt on values were exhibited by lexA 0 cells (Δt on ϭ 5 min for P lexA -gfp and 16 min for P Hi -gfp); thus, our analysis quantified this extreme state of the lexA-NAR circuit. Consistent with an overall slower DNA repair process, the Δt off values were similar to or greater than the Δt on values for each strain.
Taking the results together, analysis of the lexA cons11 mutant revealed that decreasing the value of k (to below the wild-type value) in this system collapsed the input dynamic range due to a [LexA] s value that is ϳ10% that of the wild-type strain. Conversely, increasing the [LexA] s value by altering the value of k reduced the duration of "turn-on" kinetics of target gene expression by as much as 16 min. We infer that it takes the cell more time to inactivate the larger amount of LexA present. Interestingly, higher LexA steady-state levels had no effect on the circuit's input sensitivity or dynamic range. We conclude that additional SOS regulatory features are able to compensate for higher LexA levels and, eventually, to meter out the same circuit output at any level of DNA damage. Thus, the primary effect of increasing the value of k is to slow the turn-on kinetics of the SOS response. DNA damage survival and fitness of mutant strains. Activation of the SOS response results in enhanced survival of DNA damage due to temporally ordered induction of expression of "early" DNA repair genes involved in nucleotide excision repair (NER) and "late" damage-tolerant DNA polymerases capable of error prone translesion synthesis (TLS) (9). Therefore, to test for alterations in SOS effector function, we first measured survival rates under conditions of UV light exposure and the ability of the mutants to induce mutagenesis, which is the signature of TLS activity. We found that the rate of survival that was exhibited by the ⌬lexA and lexA cons11 strains after a UV dose of 40 J/m 2 was approximately 3-fold-higher than that exhibited by the lexA wt strain (Fig. 4A). This finding suggests that preinduction of the SOS DNA damage repair and tolerance activities in the ⌬lexA strain provides additional UV tolerance and that the lexA cons11 strain is similar to the ⌬lexA strain in this regard. The ability of the lexA cons06 and lexA 2L2R strains to survive this insult was similar to that shown by the lexA wt strain. In contrast, lexA 0 cells showed approximately 2-fold-lower survival than the lexA wt cells, revealing a defect in SOS effector function. The defect was not due to an inability to induce damage-tolerant polymerases, however, as lexA 0 cells had the same level of induced mutagenesis as lexA wt (Fig. S6). This result is consistent with our finding of lexA 0 cells having the same input sensitivity and dynamic range as lexA wt cells and suggests that the UV survival defect is primarily due to slower SOS turn-on kinetics.
We next measured growth kinetics and relative fitness levels in the absence of exogenous DNA damage. Monitoring growth of each strain in monoculture, we found the ⌬lexA and lexA 0 strains displayed lower growth rates than the other strains (Fig. 4B), with the ⌬lexA strain exhibiting the slowest growth and also lower density in stationary phase (Fig. S7). To quantify relative fitness levels, each mutant strain was also competed against the lexA ϩ parental strain in coculture using a competitive growth assay. Similarly to their growth in monoculture, the ⌬lexA and lexA 0 strains showed decreased fitness; however, this assay also revealed a fitness defect in the lexA cons11 strain (Fig. 4C) that was not made apparent by monitoring growth in monoculture (Fig. 4B). We also obtained a similar result when a subinhibitory amount of the DNA strand cross-linking agent mitomycin C (MMC) was added to the media (Fig. S8). These results contrast with those from the UV survival experiments described above, where the ⌬lexA and lexA cons11 strains displayed a survival advantage over the lexA wt strain, demonstrating that this advantage is restricted to high amounts of DNA damage. We conclude that lowering the [LexA] s level by altering k can increase fitness after a lethal dose of DNA damage but results in decreased fitness with lower, subinhibitory amounts of DNA damage. Conversely, raising the [LexA] s level by altering k decreases fitness whether in the presence or the absence of DNA damage.
Our analysis of the lexA cons11 strain showed that lowering the value of k can reduce the level of [LexA] s enough in terms of target gene expression, UV survival, and fitness in competitive growth assays to mimic the ⌬lexA strain. However, we noted that lexA cons11 differed from the ⌬lexA strain in other assays: it displayed normal growth in monoculture (Fig. 4B) and yielded intermediate phenotypes for UV-induced mutagenesis (Fig. S6) and relative fitness under subinhibitory MMC conditions (Fig. S8). These results show that some degree of SOS gene regulation by LexA remained in lexA cons11 cells. The mutant lexA strains studied here were constructed in a ⌬lexA background since ⌬lexA strains are not viable in a sulA ϩ background. This conditional lethality is due to the inhibition of cell division by the SulA protein in ⌬lexA strains, as sulA is repressed by LexA. However, it is unknown whether the complete absence of LexA protein (⌬lexA) is necessary for lethality or, instead, if very low [LexA] s levels (ϳ10% of wild-type levels), as observed in the lexA cons11 strain, are sufficient for sulA repression and viability. Therefore, we attempted to complement the mutant strains with sulA ϩ on a very-lowcopy-number plasmid by transformation. As expected, we readily obtained sulA ϩ transformants in the lexA ϩ strain but obtained no transformants in the ⌬lexA strain. Transformation of sulA ϩ into the mutant strains occurred with a level of efficiency similar to that seen with the lexA ϩ strain, with the notable exception being the lexA cons11 strain, where we also did not obtain any transformants (see Table S1 in the supplemental material). This result demonstrates how the presence of a toxic target gene in a network can further constrain NAR circuit parameters. The low value of k leads to persistently low LexA levels and does not permit growth, phenocopying lexA deletion. We conclude that the presence of sulA ϩ in the SOS gene network of E. coli imposes a potent constraint on the range of permissible lexA-NAR circuit parameter values.
Fitness landscape of lexA-NAR circuit parameters. The analysis described above enabled us to derive an NAR parameter-fitness landscape using our experimental data in combination with the previously developed mathematical framework (7). To do this, we utilized an equation that relates the steady-state concentration of the repressor, [LexA] s , to the parameters k and ␤/␣ to construct a three-dimensional (3D) surface describing the relationships among these three parameters (see Materials and Methods, equation 6). Then, we used our experimental data to plot our mutant strains onto this surface and also to overlay a fourth "relative fitness" parameter onto the surface using a color gradient (Fig. 5). The mutant E. coli strains constructed in the present study were plotted on the same surface isoline of the landscape [defined by log 10 (␤/␣) ϭ 1.3], since they share a value for this parameter. lexA cons11 occupies the red (nonviable) portion of the plot because the low value of [LexA] s in this strain results in lethal expression of sulA. In the plot, the strains span the entire fitness landscape, from lexA cons11 (red ϭ nonviable) to lexA wt and lexA cons06 (blue ϭ high fitness) and, finally, to lexA 0 (green ϭ intermediate fitness). Additionally, this framework accommodates the results from a prior study of an E. coli mutant (Fig. 5, "P tet -lexA") that completely lacked autoregulation but that had the same LexA steady-state levels as a wild-type strain due to a lower value of ␤ for the promoter (21). This mutant strain displayed a growth defect after sublethal DNA damage and is therefore shown with a fitness level lower than that of the wild-type strain in the plot. In this framework, alterations of lexA-NAR circuit parameters are the result of specific changes in DNA that alter the key biochemical reactions of NAR. For example, mutations in operator DNA or the portion of lexA encoding its DNA binding domain can alter the value of k (27,29,30), mutations in the portion of lexA encoding its protease domain can alter the value of ␣ (19,(31)(32)(33), and mutations in the lexA promoter that affect RNAP activity can alter the value of ␤. In contrast, the coloration of the plot is modified by the environment, genetic background, and epistatic interactions with the SOS gene network and, therefore, the landscape depicted here represents only a snapshot of the current experimental conditions. In summary, the plot captures the fitness effects of altering the main biochemical parameters of the lexA-NAR circuit, yielding a basic framework suitable to consider the fitness constraints of different evolutionary paths on the landscape (see Discussion).

DISCUSSION
Prior studies of NAR circuit behavior have largely focused on isolated synthetic circuits to validate mathematical models of NAR, demonstrating how NAR circuit parameters affect circuit shutoff kinetics and input dynamic range. However, relatively little parameter space has been analyzed in the context of a native circuit, where the TF still controls the expression of its target genes. In one native circuit study that also used the SOS response as a model, a ⌬lexA strain was complemented with the lexA gene under the regulation of the tet promoter (P tet -lexA), providing a circuit that completely lacked autoregulation but that still exhibited LexA steady-state concentrations similar to those seen with the wild-type strain (21). This study allowed comparison of autogenous and nonautogenous control under conditions where, in the absence of a DNA damage input, the two genetic networks were similarly repressed. After DNA damage, however, the two strains displayed the same circuit turn-on time, but the P tet -lexA strain had a longer shutoff time which was associated with a growth defect (see Fig. 5, "lexA wt " versus "P tet -lexA"). This study supports the hypothesis that NAR represents an adaptation for increasing fitness by speeding up circuit shutoff kinetics. However, a more systematic analysis of the full parameter space was lacking; therefore, it remained unclear how, and to what extent, NAR circuit parameters are more globally constrained by their fitness effects on the cell. To address this issue, we created a novel  (7). Locations of lexA-NAR mutant strains on the plot are indicated with yellow triangles. Strains with extreme parameter values were placed on the edges of the surface, a location with fitness equivalent to the actual parameter values. For example, k ¡ 0 for the ⌬lexA strain since [LexA] s ϭ 0 and k ¡ ∞ for the lexA 0 and P tet -lexA strains since their promoters lack LexA binding sites. The fitness difference between lexA wt and P tet -lexA was demonstrated previously (21). Hypothetical evolutionary paths from P tet -lexA ¡ lexA wt are shown with lines with thick black short dashes (pathway 1), solid lines (pathway 2), and lines with long dashes (pathway 3). Circles highlight fitness cost excursions. Pathway 1 models serial promoter mutations, followed by serial operator mutations, resulting in a fitness cost excursion. Pathway 2 models alternating promoter and operator mutations along a path of continuous fitness increases. Pathway 3 models serial operator mutations, followed by serial promoter mutations, resulting in a fitness cost excursion.
series of E. coli mutants that spanned the full range of the lexA-NAR circuit parameter, k, and measured circuit output, SOS functions, and cellular fitness. These data allowed us to extend the mathematical framework for NAR to include a complete parameterfitness landscape, offering new insights into how lexA-NAR parameters are constrained by their fitness effects on the cell.
First, we found that lexA-NAR circuits with higher values of k, resulting in higher levels of [LexA] s , did not have altered input sensitivity or dynamic range but did have slower turn-on kinetics. In lexA 0 strains, where the [LexA] s value is 23-fold higher than in the wild-type strain, this resulted in reduced survival of DNA damage, which we attribute to the turn-on kinetics of their LexA target genes being 5 to 16 min slower than the kinetics of the wild-type strain. Of note, this timescale is consistent with a prior report from a study that analyzed the ability of delayed SOS activation to rescue cells from lethal DNA damage (34). Thus, although it takes the SOS system more time to degrade the higher amount of LexA present in these mutant strains, the DNA damage sensing reaction performed by RecA (i.e., ssDNA ϩ RecA º RecA*) apparently compensates appropriately, eventually inducing enough degradation of LexA to meter out the same SOS activities as in the wild-type case. However, the slower repair process is associated with a fitness cost, showing that slow turn-on kinetics is a mechanism that constrains the parameters of the lexA-NAR circuit. We also observed a fitness cost with lexA 0 cells in the absence of exogenous DNA damage. Under these conditions, persistently high levels of LexA may hyperrepress the SOS genes that are needed under nonstressful conditions. Alternatively, high LexA levels may interfere with cellular metabolism, either by nonspecific DNA binding or simply due to the metabolic burden of its higher rates of synthesis and degradation. Regardless of the precise mechanism, the fitness defect displayed by lexA 0 cells under these conditions reveals that the lexA-NAR circuit has a value for ␤/␣ that is toxic in the absence of negative feedback. If one considers the evolution of a repressor gene's promoter toward faster circuit shutoff kinetics, speed could be attained by simply increasing the value of ␤/␣ (Fig. 5, pathway "1"). This could be achieved, for example, by promoter mutations that increase RNAP activity. However, our data show that, for the SOS system, this strategy can reduce fitness (Fig. 5, lexA 0 ). Thus, for the circuit to evolve shorter shutoff times without incurring a fitness cost, the value of k must also be altered in proportion to the change in ␤/␣ (Fig. 5, pathway "2").
Second, we found that the value of k is also constrained by fitness effects at lower values. The lexA cons11 strain, where the value of [LexA] s is 10-fold lower than the value measured for the wild-type strain, mimicked the constitutive SOS phenotypes of the ⌬lexA strain, including conditional lethality with sulA ϩ . Thus, lowering the value of k can result in a loss of input dynamic range and a fitness cost due to derepression of toxic genes. Again, considering the evolution of a repressor gene's promoter toward faster circuit shutoff kinetics, speed can be attained by simply decreasing the value of k (Fig. 5, pathway "3"). This could be achieved, for example, by mutation of the lexA operators. However, this pathway is also constrained by fitness effects, which are more severe in the presence of sulA ϩ . Thus, in this case, for the circuit to evolve its shutoff time independently of toxic gene expression, the value of ␤/␣ must also be altered in proportion to the change in k (Fig. 5, pathway "2").
Importantly, fitness landscapes in nature are not static and can be altered by numerous different mechanisms. Thus, traversing the landscape along pathway 2, in contrast to pathways 1 or 3 (Fig. 5), may not show the lowest fitness cost in a dynamic setting where, for example, the genotoxicity of the environment is fluctuating to a greater extent. Also, SOS network genes may acquire mutations that modify their inherent toxicity or regulation by LexA, which would in turn impact the fitness landscape. Furthermore, epistatic effects from other gene-environment interactions are likely to be significant given that the SOS response has additional layers of control in comparison to other stress response pathways. For example, the SOS response is impacted by the RpoS regulon (35-37), which mediates the generalized stress response and is activated by a variety of cellular stresses, including nutrient deprivation and entry into stationary-phase growth. Thus, the landscape derived here is limited to a snapshot under a specific set of experimental conditions, providing a framework for understanding the immediate fitness effects of changing lexA-NAR circuit parameters.
Finally, we included a comparison of the lexA cons06 mutant to the wild-type strain in order to understand the function of the double-operator configuration of the wild-type lexA promoter. We chose the cons06 promoter for this study not only because it contains only a single functional operator but also because lexA cons06 shares the same [LexA] s and basal target gene expression levels as lexA wt , allowing a matched comparison of their circuit input-output features. It has been hypothesized that the doubleoperator structure of the wild-type lexA promoter may enable a cooperative binding mode that speeds up the shutoff kinetics of the lexA-NAR circuit (28). Modeling of cooperative binding of the TF in NAR predicts not only faster shutoff (7) but also a decrease in the input dynamic range (8). It has also been suggested that cooperative binding can promote "mutational robustness" and can potentially foster TF evolution by buffering against the fitness effects of deleterious TF gene mutations (20). In our analysis of the lexA promoter, however, we observed no evidence of interdimer cooperativity in the mode of repression. In agreement with past studies (22,23), we found that operators I and II are equal in their abilities to repress lexA expression (see Fig. S1 in the supplemental material), but, comparing the levels of induction of the cons06 and wt promoters across a wide dose-range of DNA damage, we observed no detectable differences (Fig. S3). Furthermore, our analysis of circuit sensitivity, dynamic range, expression kinetics, and fitness in the fully integrated circuits of the lexA cons06 and lexA wt strains also revealed no differences ( Fig. 3 and 4). Although no formal biochemical analysis of interdimer cooperativity using purified components has been performed to our knowledge, our data show that the double-operator configuration has a negligible effect on transcriptional regulation compared to the single-operator configuration. Thus, the physiological role of the double-operator configuration, at the lexA promoter, remains unclear despite repeated speculation in the literature concerning cooperative binding (11,20,22,23,28). Of note, other SOS genes also contain multiple operators, such as recN (38) and the plasmid-borne colicin genes (39), but most SOS gene promoters contain a single operator. It is possible that one of the two operators of the lexA promoter also regulates input from an alternative TF, but no such factor has been discovered to date. Instead, we favor the idea that the double-operator configuration represents a fine-tuning mechanism for SOS regulation. For example, the E. coli lexA promoter also contains a Dcm methylase recognition site within operator I, and LexA binding is diminished when the DNA is methylated (28), but a regulatory role for this DNA modification has not been established. Interestingly, this Dcm site contains an "extended" sequence motif associated with hypomethylation during exponentialphase growth (40), suggesting a mechanism for differential regulation of the SOS response that is dependent on growth phase. Finally, studies of SOS activation kinetics in single cells have revealed more-complex behavior which is otherwise masked by signal averaging from aggregate cell populations (41). Thus, future investigations of these promoter features in single cells may be needed to fully delineate their specific impact on lexA regulation and lexA-NAR circuit behavior.

MATERIALS AND METHODS
Electromobility shift assay. Recombinant LexA protein was overexpressed and purified as previously described (27). Protein concentrations were determined by Bradford assay. DNA oligonucleotides and 5=-IR700-modified oligonucleotides (see Table S2 in the supplemental material) were purchased from Integrated DNA Technologies, and DNA concentrations were determined by analysis of absorbance at 260 nm. Synthetic DNA operators were constructed by annealing the fluorophore-labeled oligonucleotide with a 1.2ϫ molar excess of its complementary oligonucleotide using a thermocycler program with a slow ramp from 95°C to 25°C. Binding reactions were carried out at room temperature in a 20-l volume. Reaction mixtures contained the indicated amount of LexA protein, 50 nM IR700-labeled operator DNA, 10 ng/l sonicated salmon sperm DNA, 70 mM Tris-HCl (pH 7.6), 150 mM NaCl, 10 mM MgCl 2 , 1 mM dithiothreitol (DTT), and 5% glycerol. After incubation for 5 min, binding reaction mixtures were loaded onto a 6% native polyacrylamide gel and separated by electrophoresis in 0.5ϫ Tris-borate-EDTA (TBE) buffer. Reaction products were visualized by scanning the gel with an Odyssey 9120 infrared imaging system (Li-Cor Biosciences).
Bacterial strains and plasmids. The DNA oligonucleotides used for construction of bacterial strains and plasmids in this study are listed in Table S2. The bacterial strains used in this study were all derivatives of the previously described E. coli K12 MG1655 ⌬sulA::FRT (here, referred to as lexA ϩ ) and ⌬sulA::FRT ⌬lexA::cat-i-sceI (referred to here as "⌬lexA") strains (19). To construct the lexA promoter mutant strains (referred to here as the lexA wt , lexA 2L2R , lexA 2R1L , lexA 2L2R1L1R , lexA cons11 , and lexA cons06 strains), this ⌬lexA strain was transformed with pWRG99 in order to introduce specific mutations into the chromosomal lexA locus via -red-mediated recombination (42). To generate the double-stranded DNA (dsDNA) molecules for recombination, the lexA locus, along with approximately 1 kb of flanking sequence, was PCR amplified from wild-type MG1655 and cloned into pUC19 to make pBCK046. Then, the desired lexA promoter mutations were introduced into pBCK046 by site-directed mutagenesis. The resulting plasmids were used as templates for PCRs to prepare the linear dsDNA molecules for -redmediated recombination. After electroporation of the dsDNA, the desired recombinants were selected by assessing loss of resistance to chloramphenicol. Mutations were confirmed by DNA sequencing. Strains were cured of pWRG99 by culture at 42°C and were evaluated for the loss of ampicillin resistance.
The GFP-reporter plasmids used in this study were derivatives of pUA66-P lexA -gfp from the E. coli promoter collection (GE Dharmacon) (26). Promoter mutations were introduced using site-directed mutagenesis, and the desired mutations were confirmed by DNA sequencing. The low-LexA-affinity (P Lo -gfp), high-LexA-affinity (P Hi -gfp), and no-LexA-affinity (P No -gfp) derivatives of pUA66-P recA -gfp used here have been previously described (27) and are referred to as the "TA," "GG," and "scram" operator derivatives there.
For sulA ϩ plasmid complementation, the sulA locus was cloned into the very-low-copy-number pUA66 vector to make pBCK059 (see Table S2). Vector DNA was prepared by digesting pUA66-P lexA -gfp with XhoI and XbaI, which removed both the lexA promoter and gfp. The desired product was confirmed by restriction analysis and DNA sequencing. Control transformations were carried out with pBCK005, which is also derived from pUA66 but lacks the sulA locus (see Table S2). pBCK005 was also used to control for nonspecific GFP background in promoter activity measurements (see below), as it lacks a promoter for gfp but retains the gfp gene.
Quantitative Western blotting. Protein samples were prepared from overnight cultures using BugBuster protein extraction reagent (Millipore). Samples were combined with Laemmli buffer, boiled, and separated by SDS-PAGE. Proteins were transferred to polyvinylidene difluoride (PVDF) membranes using an iBlot system (Thermo Fisher). LexA was probed using LexA (E-7) mouse monoclonal IgG 2b (1:200 dilution) as the primary antibody and horseradish peroxidase (HRP)-conjugated m-IgG BP-HRP (1:2000) as the secondary antibody (Santa Cruz Biotechnology). LexA was detected by chemiluminescence using a ChemiDoc XRSϩ imaging system (Bio-Rad). Relative LexA levels were quantified by interpolation of a standard curve that was constructed from a dilution series of a sample detected using the same exposure time. Background signal was determined using samples prepared from a ⌬lexA strain. Relative loading levels were determined by quantifying total protein using Coomassie-stained SDS-PAGE gels. For experiments measuring LexA levels over time after UV-induced DNA damage, cells were grown in M9 minimal glucose media at 37°C and pulsed with UV light during mid-exponential phase. Then, aliquots of the culture were taken at the indicated times and processed immediately by pelleting the cells at high speed for 30 s, combining with Laemmli buffer, and boiling.
GFP expression and promoter activity measurements. GFP levels were measured in live cells growing in M9 minimal glucose media using an Infinite F Plex (Tecan) multifunction plate reader as previously described (27). Measurements in the absence of DNA damage were obtained during exponential growth. For each well, the fluorescence intensity value was normalized to cell density by dividing by the value representing the optical density at 595 nm (OD 595 ), and then the logarithm (base 10) calculation was performed. To remove background GFP signal, values representing results from experiments performed using the pBCK005 control plasmid were subtracted.
Promoter activity kinetic measurements after different UV doses were performed and the results analyzed as previously described (27). Briefly, values obtained after taking the first derivative of the "GFP versus time" data were normalized by OD 595 to yield promoter activity (PA) values with units of GFP/min/OD, which reflect the rate of GFP expression at any given time point. The largest PA value in the time trace is defined as the PA peak . PA peak values were plotted as a function of the logarithm of the UV dose and then subjected to nonlinear regression analysis in Prism (GraphPad Software, Inc.) using a variable slope (four-parameter) dose-response model to determine the ED 50 and R values. "PA versus time" traces were analyzed for differences in turn-on and shutoff kinetics as described in the text and figure legends. Averages of results from at least two independent experiments were used for analysis.
UV sensitivity and rifampin mutation frequency. Overnight cultures were diluted 1:100 into 75 ml of fresh M9 minimal glucose media and incubated at 37°C with shaking until they reached an OD 595 of ϳ0.4. Then, 10 ml of culture was irradiated with a UV dose of 40 J/m 2 inside a 10-cm-diameter dish using a UVGL-58 (UVP) UV lamp set to 254 nm. The cultures were then placed in new tubes and allowed to recover by incubation at 37°C with shaking for 1 h. After this recovery period, aliquots were plated on LB agar for total population counts and LB-RIF agar (100 g/ml rifampin (Rif) to score Rif-resistant (Rif r ) mutants. Rif r mutants were counted after 48 h of incubation. "No UV" control cells were treated in the same manner but were not irradiated.
Growth rates. Overnight cultures of each strain were diluted into fresh LB media by a factor of 10 6 , and growth was monitored by OD 595 using an Infinite F Plex (Tecan) multifunction plate reader at 37°C with shaking. Experiments were performed in triplicate for each strain. Values and errors were deter-mined for the maximum growth rate by fitting the growth curves to the Gompertz equation using nonlinear regression.
Relative fitness. To distinguish cells in coculture, we transformed the wild-type parental strain with plasmid pUA66-P Lo -gfp and each mutant strain with pBCK005 to create "GFP-bright" and "GFP-dark" strains, respectively. Overnight cultures of each strain were diluted into fresh LB media by a factor of 10 6 , mixed together in a 1:1 ratio, and incubated for 16 h at 37°C with shaking. The medium was supplemented with 60 g/ml of kanamycin (Kan) for plasmid maintenance. In experiments measuring relative fitness levels in the presence of added genotoxic stress, 1 g/ml MMC was added to the media. To determine the size of the initial populations (N i ) and final populations (N f ), aliquots of the coculture were plated on LB-Kan agar immediately after strain mixing and after the incubation period elapsed, respectively. GFP-bright and GFP-dark colonies were enumerated after overnight incubation using a blue light transilluminator. Relative fitness values (W) were calculated for each wild-type bright -mutant dark strain combination and were then normalized to the wild-type bright -wild-type dark result using the following equation: Relative fitness model of NAR circuit parameters. For a generic NAR circuit, the repressor steady-state concentration, [R] s , can be expressed as a function of k and ␤ ␣ (7) as follows: The 3D plots and color scales were constructed using MatLab (MathWorks) using a log 10 transformation of equation 6. The color gradient of the plots generally correlates with the value of log 10 [R] s . Refinements of the color gradient along the log 10 [R] s isoline were performed using Photoshop (Adobe Systems, Inc.).
Statistical tests. Statistical tests were performed with Prism (GraphPad Software, Inc.).

SUPPLEMENTAL MATERIAL
Supplemental material is available online only.