Detailed mapping of gene input functions

To measure promoter activity, we used an automated assay based on fluorescent reporter strains (Kaplan et al, 2008). Reporter strains used in this study are from a comprehensive E. coli transcription reporter library (Zaslaver et al, 2006). Each strain in this library bears a low-copy plasmid with GFP under the control of a full-length copy of the promoter of interest. The GFP variant (GFP mut 2; Cormack et al, 1996) in these strains becomes fluorescent within minutes and yields a bright signal. In this study, we used the reporters for the galETK, galP, galS and mglB promoters.

To map the input function of each promoter, cultures of reporter strains were grown in 96-well plates. The plates contained 8 levels of cAMP in the rows and 12 levels of D-galactose in the columns, producing 96 different combinations of the two inducers. A robotic system prepared the medium and set up the plates. Each plate was seeded with one of the reporter strains and transferred to an automated shaker incubator. Each experiment also included a control plate that was seeded with a promoterless reporter strain that was used for fluorescence background subtraction. The plates were periodically transferred by the robot into a multiwell fluorimeter, which allowed measurement of GFP fluorescence and cell optic density (OD) at a resolution of 8 min.

Cells were grown on glucose minimal medium to minimize endogenous production of cAMP and achieve growth rate that is independent of the inducer levels, a condition that enabled accurate mapping of the input function as described (Setty et al, 2003; Kaplan et al, 2008). The range of added cAMP concentration (1–20 mM) led to promoter activities that span the physiological activation range of known CRP-regulated sugar-utilizing genes (Baker et al, 2001; Setty et al, 2003; Kaplan et al, 2008), as well as of a synthetic promoter regulated only by CRP (Supplementary Figure 2). A control strain (cyaA; Holland et al, 1988; Kuhlman et al, 2007) that lacks the ability to produce endogenous cAMP shows results that are very similar to those of the wild-type strain, demonstrating that the effects of endogenous cAMP production are negligible under the present conditions (see Supplementary Figure 1).

Promoter activity was defined as the rate of GFP production per OD unit, x=dGFP/dt/OD (see Materials and methods). The input function was calculated by averaging the promoter activity over a one-cell-generation window in exponential phase (6 h from initial 1:600 inoculation) where promoter activity was constant to a good approximation. The input functions are reproducible to within less than 10% mean error in repetitive experiments.

The galE and galP promoter shows maximal activity at intermediate cAMP levels

In a recent study, we have found that in the presence of galactose, the galE and galP promoter input functions peak at intermediate cAMP levels (Figure 1A and D; see also Kaplan et al, 2008). Their activity increases with cAMP levels up to an intermediate external concentration and then decreases, decaying to about 1/4 of the maximal level for the galP promoter and to about 2/3 for the galE promoter. The galS promoter activity increases with cAMP levels, consistent with the known transcriptional activation of galS by CRP (Figure 1G) in this I1-FFL. As the range of cAMP concentrations needed for activation of the galS promoter overlaps with the concentrations at which the promoter activity of galE and galP decreases (Figure 1C and F), one may hypothesize that the induction of the GalS repressor leads to the observed non-monotonic pattern.

Deletion of the galS gene results in monotonically increasing input function

We studied the possible contribution of the I1-FFL to the non-monotonic behavior by mapping the input function of galE and galP in an isogenic strain that had a genomic deletion of the galS gene (Box 1D) (Baba et al, 2006; see Materials and methods). We find that in the galS strain, galE and galP show monotonic input functions that increase with cAMP levels (Figure 1B and E). At low cAMP levels, this function is very similar to that of the wild-type strain and rises with cAMP levels at about the same rate as in the wild-type strain. However, whereas the wild type peaks and then decreases at high cAMP levels, the galS strain shows no peak and saturates at high cAMP levels. Thus, in a strain in which the I1-FFL is disrupted by deletion of the galS repressor, non-monotonic input function changes to a monotonic one.

Note that sensitivity to galactose is maintained in the galS strain (Figure 1B and E), owing to the presence of the second gal repressor, GalR. GalR is a constitutively expressed repressor, and, in contrast to GalS, is not part of the I1-FFL, as it is not regulated by CRP.

We also disrupted the I1-FFL by another means: we deleted the repressor binding sites from the target galE promoter (Box 1F) while keeping the repressor gene intact. We find that the input function of a reporter strain in which the GalS/GalR binding sites in the galE promoter were deleted is monotonic (Figure 1H). This experiment indicates that the non-monotonic behavior is due to Gal repressor action and not due to a hypothetical direct repression by CRP at high cAMP levels.

Deletion of galR maintains the non-monotonic shape of the input function

We also studied the input function of the galE promoter in an isogenic strain deleted for the galR gene (Box 1E). In this strain, the galS I1-FFL remains intact and the constitutive galR repressor is missing. We find that the galR strain preserves a non-monotonic shape for the galE input function, with expression that peaks at intermediate levels of cAMP (Figure 2A). The position of this peak changes with galactose concentrations: the peak position rises from 6 mM cAMP at low galactose to about 20 mM cAMP at high galactose levels (Figure 2A).

Figure 2

Input function of galE in a galR background shows non-monotonic behavior to cAMP. (A) Experimental measurements. (B) A simple model of I1-FFL (see equations (1), (2) and (3)) shows a good fit to the measured input function with parameters K₁=5 mM, K₂=5 mM and k_g=5 mM. The position of the peak (concentration of cAMP at which promoter activity is maximal) increases with the concentration of galactose (white dashed line).

Full figure and legend (123K)Figures & Tables index

We also find that the input function has a higher basal level than in the wild-type strain: the galR deletion strain shows expression of the galE promoter (even in the absence of galactose) that is at least two-fold higher than its most induced activity in the presence of GalR. This is consistent with earlier studies that indicated that GalR is the major repressor for galE and is responsible for most of its galactose sensitivity (Geanacopoulos and Adhya, 1997; Semsey et al, 2007).

The I1-FFL generates a monotonic input function in the mglB promoter

We also studied the input function of the mglB promoter, which controls the expression of the galactose ABC transporter genes and is regulated by the gal I1-FFL. We find that the input function of the mglB promoter is monotonic (Supplementary Figure 3A), rising continuously with cAMP levels. Thus, in addition to the non-monotonicity found in the galE and galP promoters, we find that the I1-FFL can also result in monotonic input functions. The monotonic mglB input function is maintained also in a galS strain in which the I1-FFL is disrupted (Supplementary Figure 3B). The difference between the galE/galP and the mglB input functions suggests that the I1-FFL can be designed to show either monotonic or non-monotonic behavior, depending on biochemical parameters. To address the effects of biochemical parameters on the gene input function, we now turn to a mathematical analysis of the I1-FFL.

A simple model for I1-FFL input functions

To model a simple I1-FFL and compare it to experimental data, we study the galE input function in a strain with deletion of galR (see Figure 2A). This strain provides a simple in vivo model for the I1-FFL motif as it contains a single repressor (GalS), rather than the two repressors (GalS and GalR) of the wild-type strain. To make a model that captures the essentials if not the full details of this system, we use the standard modeling approach based on equilibrium binding of transcription factors to their sites on a promoter, as reviewed in Bintu et al (2005) and Entus et al (2007). Consider an activator that binds a promoter with the dissociation constant k_A and a repressor that binds with the dissociation constant k_R. The promoter is transcriptionally active when the activator but not the repressor binds. The promoter activity is then described by a ratio of two polynomials corresponding to the partition function of the binding process, whose variables are the concentrations of an active activator A and an active repressor R: In the I1-FFL, the repressor level R increases with the activity of A (as CRP activates the galS gene). The repression activity of R is inhibited by the inducer (galactose), with half-effect at inducer concentration of k_g (equation (2)). These effects can be described most simply by the following equation that rises linearly with A and has a Michaelis–Menten-like effect of g: By plugging in the repressor level from equation (2) into equation (1) one obtains an expression for I1-FFL input function. This equation gives rise to non-monotonic behavior (equation (3)), because the denominator increases as a function of A², whereas the numerator increases as a function of A and thus the function first rises and then decreases as a function of A: We find that this model provides a good fit to the data for the galE input function in the galR strain (Figure 2A and B).

The model also allows an analytical solution for the position of the peak in the input function. To find the level of A (i.e. the cAMP concentration) at which the promoter activity is maximal, one needs to find the value of A where the derivative dP/dA is zero. The solution A_max rises with the dissociation constants and with the inducer level: The position of the maximum is thus proportional to the geometric mean of the dissociation constants k_A and k_R. Differences in these effective binding constants may explain the difference in the observed peak position between the galP promoter (peak 3 mM cAMP) and the galE promoter (peak 6 mM cAMP) (Figure 1A and D). In addition, the peak position is expected to increase with the level of galactose g. This agrees with the observed shift in the peak position to higher cAMP levels with increasing galactose levels (dashed white line in Figure 2B) in the experiments presented above.

The I1-FFL of the galE promoter in a galR strain might also include a self-inhibitory effect of the GalS on its own promoter. However, a theoretical analysis shows that this should not have a significant effect on the above analysis (see Supplementary Figure 4).

Theoretical analysis suggests necessary conditions for non-monotonic input functions

Finally, we consider additional possible effects that can shape the input function of the I1-FFL. The aim is to find conditions in which the I1-FFL can generate non-monotonic input functions for a wide range of parameters. We also sought to find conditions under which the I1-FFL shows monotonic functions.

We first add Hill-like kinetics to the model of the previous section, described by effective Hill coefficients h₁ and h₂: Here, h₁ is the apparent Hill coefficient describing the cooperativity of A action and h₂ is that for R. In the I1-FFL the activator A also activates the gene for R. Thus one has R A^h₃, if the promoter of the R gene is far from saturation, where h₃ is the apparent Hill coefficient for the action of A on the promoter of the gene for R. Non-monotonic behavior is always found in this case (Figure 3A), because when A activity is large, the last term in the denominator goes as A^{(h₁ + h₃h₂)}, whereas the numerator goes as A^h₁. For positive Hill coefficients, h₁+h₃h₂ always exceeds h₁, and hence the promoter function decreases at high levels of A activity. Only if the promoter of the R gene saturates at low levels of A activity, before the quadratic term in the denominator is significantly larger than the other terms, will non-monotonic behavior be lost. Thus, when both factors A and R can bind the promoter simultaneously, non-monotonic behavior is obtained for a wide range of parameters.

Figure 3

Models of I1-FFL demonstrate conditions in which non-monotonic or monotonic input functions are achieved. (A) Non-monotonicity emerges in I1-FFL given that simultaneous binding of the activator and repressor is possible. (B) Elimination of the I1-FFL eliminates the non-monotonic behavior. (C) A monotonic input function is found in the case of exclusive binding of A and R when the cooperativity coefficients on both arms of the FFL are similar (h₁=1, h₂=1, h₃=1). (D) A non-monotonic input function is found in the case of exclusive binding of A and R when the cooperativity of the indirect arm of the I1-FFL exceeds that of the direct arm (here, h₁=1, h₂=2, h₃=1) (see Materials and methods for model description).

Full figure and legend (235K)Figures & Tables index

An alternative promoter design is that binding of A and R cannot occur at the same time owing to steric hindrance. This has been suggested to apply to the gal promoters (Semsey et al, 2006), because upon binding to their two binding sites the repressors are assumed to form a loop that prevents the CRP from binding to the promoter. In this case, the promoter activity can be modeled without the interaction term in the denominator: Here, as above, A R^h₃ in the case of a non-saturated promoter for gene R. Non-monotonic behavior is found when h₂h₃>h₁, because the denominator outweighs the numerator at high values of A activity (Figure 3C, D). For example, in the case of the gal system, the present data for the galS promoter suggest that h₃2 and that this promoter does not seem to saturate at the measured activity levels of A (Figure 1G). The galE promoter seems to have h₁1, and thus h₂h₃>h₁ and non-monotonic behavior is found (Figure 1C).

In summary, when both activator and repressor can simultaneously bind the promoter, non-monotonic input functions only require that the R promoter remains unsaturated at high levels of A activity. When A and R cannot bind the promoter simultaneously, non-monotonic behavior requires, in addition to an unsaturated R promoter, that the combined cooperativity of the indirect arm of the I1-FFL—the product of the cooperativity of A on the R promoter and R on the Z promoter—exceeds that of the direct arm, given by the cooperativity of A on the Z promoter (Figure 3).

To explain the monotonic behavior found in the mglB promoter, the present theory offers several possibilities. Monotonic behavior can be found if k_R, which reflects the threshold of the repressor, is high enough (e.g. weak affinity to its site in the promoter). This is because the repressor then has only a limited effect within its physiological concentration range, and the peak level is pushed to very high A levels beyond the physiological range. An alternative scenario for monotonic behavior occurs if A and R bind with similar cooperativity but interfere with each others' binding (Figure 3C). Support for this possibility lies in the structure of the mglB promoter in which partial overlap between the repressors and activator binding sites is observed (Box 1G).

Reporter strains

GFP reporter plasmids for galE, galP, mglB and galS in the wild-type background (MG1655) are from the fluorescent reporter library given in detail in Zaslaver et al (2006). A mutated reporter plasmid for galE was obtained by deleting the GalS/GalR binding sites (Keseler et al, 2005; Karp et al, 2007) in the promoter region on the plasmid (Baseclear Labservices). The deleted sequences are tgtgtaaacgattccac around -60 bp from initiation of transcription and tatgagagttctggttaccggtggtagcggttaca at around +50 bp. Isogenic galS and galR strains were obtained by transducing the deletions from the Keio knockout collection derived from the BW25113 strain (Baba et al, 2006) into MG1655 by P1 transduction. The genomic deletion was verified by PCR. Kanamycin resistance was eliminated from the deleted strain using FLP recombinase, as described (Datsenko and Wanner, 2000). We then transformed the galS and galR strains with the reporter plasmids for galE, galP, mglB and galS.

Growth conditions and measurements

Reporter strains (five different reporter strains+promoterless control strain pUA66 in each experiment) were grown overnight in M9 minimal medium containing 0.4% glucose, 0.2% casamino acids and 50 g/ml kanamycin at 37°C. Using a robotic liquid handler (FreedomEvo, Tecan), 96-well plates were prepared with 150 l of M9 minimal medium containing 0.2% glucose, 0.05% casamino acids, 25 g/ml kanamycin and 96 different combinations of the system inducers (8 levels of serially diluted cAMP (1:1.5) and 12 levels of serially diluted D-galactose (1:1.4)). The wells were inoculated with the reporter strain at a 1:600 dilution from the overnight culture. This high dilution factor allowed a prolonged exponential phase. Wells were then covered with 100 l of mineral oil (Sigma) to prevent evaporation, a step that we previously found not to significantly affect aeration or growth (Ronen et al, 2002; Zaslaver et al, 2004), and transferred into an automated incubator. Cells were grown in an incubator with shaking (6 Hz) at 30°C for about 20 h. Every 8 min the plate was transferred by the robotic arm into a multiwell fluorimeter (Infinite F200, Tecan) that read OD (600 nm) and GFP fluorescence (535 nm). Plasmid copy number did not vary measurably over the growth conditions (Kaplan et al, 2008).

Data analysis

Promoter activity for each well was calculated from the OD and GFP measurements after subtracting the OD and GFP backgrounds as described (Kaplan et al, 2008). GFP background was obtained for each well from the promoterless control strain U66. Promoter activity was calculated by computing the rate of accumulation of GFP per unit time divided by the OD (dGFP/dt/OD) (Ronen et al, 2002). The promoter activity was averaged over a window of 80 min (1 cell cycle at exponential growth). Over this window, promoter activity varied less than 20%. Each input function was normalized to its maximal level and smoothed with a median filter (medfilt2 of Matlab 7.0). Growth rate (dOD/dt/OD/ln(2) in units of doublings/h) over this time window was very similar for all conditions (0.60.03 doublings/h).

Model input functions

The model input functions presented in Figure 3 were obtained using Matlab 7.1. A grid of equally spaced logarithmic scale axes from 10^-1 to 10¹ was used for both the activator inducer y (so that A activity is A=y) and the inhibitor signal x of the repressor R so that R activity is inversely proportional to x. In the case in which the repressor is not regulated by the activator (no I1-FFL), R₀=K_RX/x. In the cases in which R is activated by A (I1-FFL), R is, for an unsaturated promoter design, proportional to A so that R₁=K_RXA/x. In the case in which R activation by A is unsaturated and cooperative, the repressor can be described as R₂=K_RXA^h/x. If the Z repressor allows simultaneous binding of activator and repressor with no I1-FFL (Figure 3A), one has P=A/(1+A+R₀+AR₀). Simultaneous binding of activator and repressor with I1-FFL (Figure 3B) corresponds to P=A/(1+A+R₁+AR₁). An I1-FFL with exclusive binding with similar cooperativity of activator and repressor (Figure 3C) is described by P=A/(1+A+R₁). An I1-FFL with exclusive binding with cooperativity of the repressor binding (h=2) (Figure 3D) is modeled by P=A/(1+A+R₁²). An I1-FFL with exclusive binding with cooperativity of the activator–repressor interaction using R₂ (Figure 3E) is modeled by P=A/(1+A+R₂).