Combinatorial transcriptional control of the lactose operon of Escherichia coli

Edited by Carol A. Gross, University of California, San Francisco, CA, and approved January 29, 2007
April 3, 2007
104 (14) 6043-6048

Abstract

The goal of systems biology is to understand the behavior of the whole in terms of knowledge of the parts. This is hard to achieve in many cases due to the difficulty of characterizing the many constituents involved in a biological system and their complex web of interactions. The lac promoter of Escherichia coli offers the possibility of confronting “system-level” properties of transcriptional regulation with the known biochemistry of the molecular constituents and their mutual interactions. Such confrontations can reveal previously unknown constituents and interactions, as well as offer insight into how the components work together as a whole. Here we study the combinatorial control of the lac promoter by the regulators Lac repressor (LacR) and cAMP-receptor protein (CRP). A previous in vivo study [Setty Y, Mayo AE, Surette MG, Alon U (2003) Proc Natl Acad Sci USA 100:7702–7707] found gross disagreement between the observed promoter activities and the expected behavior based on the known molecular mechanisms. We repeated the study by identifying and removing several extraneous factors that significantly modulated the expression of the lac promoter. Through quantitative, systematic characterization of promoter activity for a number of key mutants and guided by the thermodynamic model of transcriptional regulation, we were able to account for the combinatorial control of the lac promoter quantitatively, in terms of a cooperative interaction between CRP and LacR-mediated DNA looping. Specifically, our analysis indicates that the sensitivity of the inducer response results from LacR-mediated DNA looping, which is significantly enhanced by CRP.
The lac promoter (Plac) of Escherichia coli is one of the most extensively studied systems of molecular biology (16). The knowledge and insight gained from these studies have shaped much of how we now think about gene regulation. It is well known that E. coli cells repress the expression of the lac operon when glucose is abundant in the growth medium. Only when the glucose level is low and the lactose level is high is the operon fully expressed. Thus, the regulation of this operon represents an example of “combinatorial control” widely seen in prokaryotes and eukaryotes (7, 8). In this case, the combinatorial control is implemented molecularly by two transcription factors, the Lac repressor (LacR), which represses transcription and the cAMP receptor protein (CRP) which activates transcription. Activation by CRP requires the inducer cAMP, which is used by E. coli cells as a signal of glucose shortage (915). Repression by LacR is activated in a nearly all-or-none manner upon varying the amount of lactose or one of the several synthetic inducers in growth medium with poor carbon sources (16, 17). The fold-change in repression is very large (>1,000-fold) and has been shown to involve LacR-mediated DNA looping (5, 6, 1821).
Here we quantitatively investigate the competing effects of activation and repression on the Plac in vivo. We focus on two perplexing issues. (i) According to biochemical studies (2225), LacR–inducer interaction is only weakly cooperative. By what mechanism(s) does the observed induction response become so abrupt (26, 27)? (ii) Despite the well known role CRP plays in activating transcription (28), structural studies (29, 30) suggest that CRP enhances repression by facilitating the LacR-mediated DNA looping. Moreover, in vitro biochemical studies indicate that CRP stabilizes LacR–DNA binding (3133). What functional role(s) does CRP actually play in the control of this operon? We approached these issues by first identifying mutants of E. coli MG1655 that allowed us to directly control the activities of the activators and repressors by varying the levels of two inducers in the growth medium. We then characterized the promoter activity systematically for numerous combinations of the inducers. The gene expression data obtained clearly reveal the effect of CRP in enhancing the steepness of the inducer response. We developed a thermodynamic model of gene regulation (8, 3436), incorporating the known molecular mechanisms of LacR-induced DNA looping and its coupling to CRP through DNA bending (32, 33). The success of the model is manifested in its ability to describe the complex codependence of gene expression on the two inducer levels quantitatively by invoking a single parameter, the cooperativity between CRP and LacR-mediated DNA looping, with the fitted value of the cooperativity agreeing well with that determined from in vitro biochemical measurements (32, 33). Our study presents a proof of concept that the complicated web of interactions that couple repressors, activators, promoters, and DNA loops in vivo can be quantitatively dissected, provided that the right modeling together with a precise sequence of experiments on a systematically picked set of mutants are carried out.

Results

Repression by LacR.

We first quantitatively characterized the activity of the Plac subject to various degrees of repression by the LacR for E. coli cells in the exponential growth phase. In our experiments, the activity of LacR was modulated by the synthetic gratuitous inducer isopropyl β-d-thiogalactopyranoside (IPTG) (37). We performed the β-galactosidase assays for wild-type E. coli MG1655 cells in M9 minimal medium with 0.5% glucose as the carbon source and up to 1 mM IPTG. Plac activity, defined here as the product of the β-galactosidase activity and the cell-doubling rate [see supporting information (SI) Methods], is plotted against the corresponding IPTG concentrations as the black crosses in Fig. 1a.
Fig. 1.
Dependence of Plac activity on the inducers. (a) The IPTG response for E. coli MG1655 and various ΔlacY mutants grown in minimal M9 medium with various amounts of IPTG and 0.5% glucose except for the cyan circles (0.5% glycerol). No cAMP was added to the medium except for the red triangles, which indicate that 1 mM cAMP was added. The lines are best fits to the Hill function (Eq. 1). (b) The cAMP response for E. coli MG1655 and various ΔcyaA mutants, grown in minimal M9 medium plus 0.5% glucose, 1 mM IPTG, and various amount of cAMP. The lines are best fits to the Hill function (Eq. 2).
The data points are fitted to the Hill function,
shown as the black line in Fig. 1a. The Hill function is used here (and elsewhere in Results) merely to extract the qualitative features of the promoter activity; the appropriate quantitative description of the data presented will be provided below in Analysis. The features of the IPTG-dependent promoter activity (the “IPTG response”) are conveyed by the best-fit Hill parameters listed in Table 1(row 1): The overall fold change, quantified by fIPTG ≈ 1,200, is in good agreement with previous studies (5, 6, 1820, 38, 39). However, the “sensitivity” of the response, quantified by the slope of the transition region in a log–log plot and given approximately by the Hill coefficient (mIPTG ≈ 4.5), is much larger than the expected behavior based on the known biochemistry (see below).
Table 1.
Hill parameters for the IPTG response
StrainbIPTG, MU/hrfIPTGCIPTG, μMmIPTG
MG16550.51,200 ± 8020 ± 44.5 ± 0.7
TK150 (ΔlacY)0.41,445 ± 185100 ± 182.6 ± 0.2
TK230 (Δcrp ΔlacY)0.05255 ± 19150 ± 152.0 ± 0.1
TK310 (ΔcyaA ΔcpdA ΔlacY), no cAMP0.02238 ± 2690 ± 52.0 ± 0.2
TK310, 1 mM cAMP0.71,600 ± 18070 ± 82.8 ± 0.1
Parameters derived from fit of the IPTG dependence of the Plac activity to the Hill form (Eq. 1) for various strains of E. coli derived from MG1655, grown in medium with 0.5% glucose and various amounts of IPTG. For the last row, 1 mM cAMP was also added to the growth medium. MU, Miller unit.
One factor contributing to the hypersensitivity observed is a positive-feedback effect due to the expression of lacY, which encodes the Lac permease, as previously reported (16, 39). We therefore deleted lacY from E. coli MG1655 to form strain TK150 (see SI Table 4), and repeated the β-galactosidase assays for this strain. Plac activities obtained are plotted as the cyan crosses in Fig. 1a. Fitting again to the Hill form yields the cyan line with the best-fit parameters shown in Table 1 (row 2). The IPTG response of the ΔlacY mutant exhibits a broader transition, with mIPTG ≈ 2.6.
Another possible cause of this hypersensitivity is a suggested cooperative interaction between the LacR and the activator CRP, which also binds in the promoter region (3133). To investigate this possibility, we deleted the crp gene from E. coli TK150 to form strain TK230 (SI Table 4) and repeated the β-galactosidase assays for this strain. Plac activities obtained are plotted as the green circles in Fig. 1a. Fitting again to the Hill form yields the green line with the best-fit parameters shown in Table 1 (row 3). The IPTG response of the Δcrp ΔlacY double mutant is broader still, with mIPTG ≈ 2.

Activation by CRP.

We next characterized the dependence of Plac activity to different degrees of activation by cAMP–CRP (the “cAMP response”). To avoid possible complications due to interaction between LacR and CRP, all experiments were performed under saturating IPTG concentration (1 mM) to disable LacR–operator interaction. This was complemented by direct deletion of LacR in some cases (see below). We also deleted lacY in all subsequent experiments to avoid possible feedback. In all cases discussed below where we directly compared the Plac activity of lacY and lacY+ cells, differences of no more than 2-fold were obtained (data not shown).

Control by cAMP.

One way to manipulate the cellular level of cAMP–CRP is to subject cells to different levels of cAMP in the medium and rely on the diffusion of cAMP into cells. This approach requires shutting off the endogenous synthesis of cAMP by the enzyme adenylate cyclase (AC), encoded by cyaA (4144). Setty et al. (28) attempted this approach by growing cells in medium with 0.2% glucose and various levels of cAMP, expecting that AC activity would be repressed via catabolite repression (10, 14, 15, 4549). However, they observed only a few-fold change in Plac activity despite large variations in the extracellular cAMP levels (0–20 mM) (27). The observed change was surprisingly small given that >50-fold difference in Plac activity was obtained between the wild-type and Δcrp strains (3). In fact, a nearly 10-fold difference in Plac activity can be seen by simply growing wild-type cells on various sugars [see SI Fig. 3 (blue bars)].

Effect of AC deletion.

We reasoned that the small change in Plac activity obtained by Setty et al. (28) might have resulted from the incomplete repression of AC activity by glucose uptake; hence, we repeated the experiment with the deletion of cyaA. E. coli TK250 strain (ΔcyaA ΔlacY; see SI Table 4) was grown in M9 minimal medium with 0.5% glucose, 1 mM IPTG, and up to 10 mM cAMP. β-Galactosidase activity was assayed as described above. The resulting Plac activity displays a smooth sigmoidal dependence as shown in Fig. 1b (blue squares). [Almost identical results (data not shown) were obtained for the LacR-null mutant (strain TK320), indicating that LacR is indeed not a factor with saturating IPTG (1 mM) in the growth medium.] A ≈100-fold difference is seen between the low and high cAMP concentrations, comparable to the difference in Plac activity reported between the crp-null mutant and wild-type strains of E. coli (3). In contrast, Plac activity of the wild type (Fig. 1b, black symbols) as well as the ΔlacY mutant (data not shown) grown in glucose displayed only an ≈3-fold change over the same range of cAMP levels, similar to the before-mentioned finding by Setty et al. (28). As a negative control, we show in Fig. 1b (green circles) the promoter activity obtained for the crp strain (TK230); its lack of cAMP dependence indicates that the observed cAMP dependence for the crp+ strain was mediated primarily by cAMP–CRP. Additional negative controls on possible indirect effects of cAMP variations on Plac activity are shown in SI Fig. 4b. We found the variation of CRP expression and the nonspecific effects of CRP on Plac activity to be small (≈2-fold), compared with the 100-fold difference observed for the ΔcyaA mutants over the same range of cAMP concentrations.
The cAMP response exhibited by strain TK250 was analyzed by fitting to the Hill function,
and plotted as the blue line in Fig. 1b. The best-fit parameters are shown in Table 2(row 1). The sensitivity of the cAMP response, characterized by the Hill coefficient mcAMP ≈ 2, is in disagreement with the noncooperative nature of cAMP–CRP interaction (5053). This suggests a nonlinear relationship between the extracellular and intracellular cAMP concentrations in ΔcyaA strain and prompted us to look for additional factors regulating intracellular cAMP levels.
Table 2.
Hill parameters for the cAMP response
StrainbcAMP, MU/hrfcAMPCcAMP, μMmcAMP
TK250 (ΔcyaA ΔlacY)9.191 ± 5645 ± 432.1 ± 0.1
TK310(ΔcyaA ΔcpdA ΔlacY)5.9240 ± 13320 ± 321.0 ± 0.1
Prediction based on thermodynamics>2010–1,0001
The first two rows give the parameters derived from fit of cAMP response of cyaA mutants to the Hill function (Eq. 2). The last row gives the best estimates of these parameters according to the thermodynamic model and the known biochemical parameters (see SI Methods for details).

Effect of phosphodiesterase deletion.

One such factor is cAMP degradation catalyzed by the enzyme cAMP-phosphodiesterase (PDE) (5458), encoded by cpdA (59). We deleted the cpdA gene to obtain strain TK310 (ΔcyaA ΔlacY ΔcpdA) (see SI Table 4) and repeated the β-galactosidase assay and analysis. The cAMP response obtained (Fig. 1b, red circles) is more gradual than that of cpdA+ cells (blue squares). Fitting the data to the Hill form (Eq. 2) yielded the red line with the Hill parameters listed in Table 2 (row 2). Specifically, the Hill coefficient mcAMP ≈ 1 is consistent with the naïve expectation based on the noncooperative nature of cAMP–CRP interaction (5053).

Combinatorial Control.

We next investigated the codependence of Plac activity on the two regulators, LacR and cAMP–CRP. We showed above that the Δcrp ΔlacY strain (TK230) could be used to characterize the bare IPTG response, whereas the ΔlacY ΔcyaA ΔcpdA strain (TK310) could be used to characterize the bare cAMP response. To characterize the codependence of the promoter on IPTG and cAMP, we first verified that strain TK310 exhibited nearly the same IPTG dependence as TK230 in growth medium with no cAMP added; compare§ the red squares and green circles in Fig. 1a. Fitting the IPTG response of TK310 (red squares) to the Hill form (Eq. 1) yields the solid red line; the corresponding parameters are provided in Table 1 (row 4).
We repeated the β-galactosidase assay and analysis for TK310 cells grown in media with various combinations of IPTG and cAMP concentrations. As evidence of an interaction between IPTG-mediated and cAMP-mediated regulations, we show in Fig. 1a (red triangles) the IPTG response for TK310 strain in growth medium containing 1 mM cAMP. This response is nearly indistinguishable from the physiological Plac activity exhibited by cyaA+ cpdA+ cells in glycerol medium (cyan circles). The dashed red line is the best fit to the Hill function (Eq. 1), with parameters listed in Table 1 (row 5). Note that the overall fold-change (fIPTG) is increased from <250-fold when no cAMP was added in the medium to >1,500-fold with 1 mM cAMP in the medium. The latter fold-change is comparable to those obtained for wild-type E. coli cells grown in the absence or saturating concentration of IPTG (Fig. 1a, black crosses) (5, 6, 1820, 38, 39). Additionally, the sensitivity of the IPTG response increased from mIPTG ≈ 2.0 (Table 1, row 4) for TK310 cells grown in the absence of cAMP to mIPTG ≈ 2.8 (Table 1, row 5) for the same cells grown in 1 mM cAMP. Fitting the IPTG responses of these cells obtained at a variety of cAMP concentrations, we found a trend of increasing Hill coefficient (from 2 to 3) and fold-change (from 250- to 1,800-fold) for cAMP levels from 1 μM to 1 mM (see SI Fig. 5a). The complete codependence of Plac activity on IPTG and cAMP is shown as the 3D plot in SI Fig. 6a.

Analysis

We have seen that the IPTG and cAMP responses of various mutant strains of E. coli MG1655 fitted well to Hill functions, with the Hill parameters summarized in Tables 1 and 2. However, the Hill function itself has been invoked so far without justification; it was merely a familiar form used to quantify key features of the response, e.g., the overall fold-change and sensitivity. Below we will analyze and interpret the results obtained in light of the rich knowledge on the molecular biology of the Plac and the biochemistry of the associated components using a thermodynamic model of transcriptional regulation (see refs. 8 and 36; see also the brief review in SI Methods).

Activation by cAMP–CRP Is Noncooperative.

The cAMP response found for strain TK310 (ΔcyaA ΔcpdA ΔlacY) exhibited a broad transition (Fig. 1b, red circles), well fitted by the Hill form (red line). This is in agreement with the thermodynamic model, which predicts the Hill form for response to simple activation by cAMP–CRP (SI Methods) (35). The Hill coefficient mcAMP ≈ 1 obtained is in good agreement with the biochemistry finding that it takes one cAMP molecule to activate the CRP dimer (5153).
The thermodynamic model further relates the other Hill parameters fcAMP and CcAMP to the biochemical parameters that describe CRP-mediated transcriptional activation (see SI Methods). The best estimates of fcAMP and CcAMP based on knowledge of the biochemical parameters are given in Table 2 (row 3). The available information is not sufficient for a quantitative comparison of the parameter CcAMP, whose value depends on the CRP–operator binding affinity in vivo as well as the relationship between the intra- and extracellular cAMP concentrations, both of which can be estimated only very crudely (SI Methods) (9, 60). The parameter fcAMP, which describes the maximal fold-change in the cAMP response, is given by the cooperativity of CRP and RNA polymerase interaction according to the thermodynamic model. Our result fcAMP = 240 ± 13 is significantly larger than the cooperativity factor of ≈20 obtained from in vitro biochemical measurements (61, 62). This discrepancy is analogous to one noted earlier by Beckwith et al. (3). It may have resulted from the accumulation of a number of small factors. For example, in addition to recruiting RNA polymerase, CRP was shown to stimulate the transition of promoter DNA from the closed to open conformation, thereby enhancing the transcription rate by ≈50% (61). In addition, the autoregulation of CRP expression may account for ≈2-fold difference (see SI Fig. 3), and another ≈2- to 3-fold difference may be attributed to the deletion of cpdA (Fig. 1b, compare the vertical ranges of the blue and red lines).

PDE Provides Insulation to Variations in cAMP.

We are not aware of any significant phenotype reported for cells with a PDE deletion. Only small differences of 2- to 3-fold in Plac activity were seen between the wild-type and ΔcpdA strains (SI Fig. 3, blue and red bars), and no systematic trend can be seen in the growth rates of the two strains (SI Fig. 3, numbers on top of the bars). However, the effect of cpdA expression on the cyaA mutant is striking. Comparison of the blue and red lines in Fig. 1b suggests that PDE expression insulates the cell from extracellular cAMP variations of up to 100 μM. This may be important for cells in environments where AC activity is significantly repressed.

LacR-Mediated DNA Looping Increases the Sensitivity of the IPTG Response.

The IPTG response of the Δcrp ΔlacY double mutant (TK230) exhibited a reduced sensitivity (Fig. 1a, green circles) compared with the lacY mutant (TK150; Fig. 1a, cyan crosses). The difference is due to the activated CRP in the latter strain (which has cyaA intact and, hence, synthesizes cAMP endogenously). We will discuss the effect of CRP shortly; for now, we first discuss the IPTG response in the absence of CRP, i.e., that of strain TK230. This response is well fitted by the Hill form (Fig. 1a, green line), with the Hill coefficient mIPTG ≈ 2.0 (Table 1, row 3). Although a cooperative IPTG response with Hill coefficient ≈ 2 is widely quoted in the molecular biology literature (26) and, moreover, a cooperative IPTG–LacR interaction was suggested based on a structural study of LacR (29), in vitro biochemical studies of IPTG–LacR binding in fact found a noncooperative IPTG–LacR interaction, which became only weakly cooperative (Hill coefficient = 1.4∼1.6) in the presence of operator DNA fragments (2225). We reasoned that the apparent cooperativity (mIPTG ≈ 2) observed in vivo might have resulted from LacR-mediated DNA looping known to occur in wild-type E. coli cells (6, 1820). The corresponding thermodynamic model is developed in SI Methods, with the following form of the IPTG response:
Although Eq. 3 is not of the Hill form, it resembles a spectrum of different Hill functions, with the maximal fold-change
and with the sensitivity also increasing with the parameters R and L0 (see SI Methods). The parameter R depends on the LacR concentration and LacR–operator affinity; it gives the fold-repression between zero and saturating IPTG levels in the absence of DNA looping (L0 = 0). The values of R ≈ 20–50 can be inferred from two previous studies by Oehler et al. (6, 21), who characterized the activities of Placs bearing various Lac operator mutations (see SI Methods). In the analysis below, we use R ≈ 50; results of similar quality (data not shown) can be obtained for R ≈ 20. The parameter L0 describes the enhancement in the “local concentration” of LacR molecules due to DNA looping (6, 35). There is currently no direct measurement of L0 for the Plac in the absence of CRP binding.
Before applying Eq. 3 to our results, we first discuss its form in the absence of DNA looping (L0 = 0). In a very recent report, Oehler et al. (62) used various mutants to characterize the IPTG responses of the Plac incapable of DNA looping. Their data are reproduced in SI Fig. 7a (red triangles and blue squares) and shown to fit well to Eq. 3 with L0 = 0 (solid line). The data are equally well fitted in SI Fig. 7b by the Hill form (Eq. 1) with an effective Hill coefficient of 1.5, in agreement with results of previous in vitro studies (24).
We next confront DNA looping by fitting the IPTG response of strain TK230 (Fig. 1a, green circles) to Eq. 3, with two fitting parameters KIPTG and L0. (The saturation value α0 is fixed by the promoter activity at 1 mM IPTG.) The best-fit curve (data not shown) is nearly indistinguishable from the green line in Fig. 1a, although Eq. 3 contains one fewer fitting parameter than Eq. 1. In particular, the observed sensitivity of the IPTG dependence is well reproduced. The best-fit parameters obtained are shown in Table 3(row 1). The value of the loop parameter simply reflects the maximal fold-change of the IPTG response as given by Eq. 4. The value of the IPTG–LacR dissociation constant KIPTG obtained is comparable to the results of in vitro biochemical studies (SI Methods) (4, 64, 65). Similarly, we found that the DNA looping model described the IPTG response of strain TK310 (ΔcyaA ΔcpdA ΔlacY) very well in medium with no cAMP. The corresponding best-fit parameters are given in Table 3 (row 2); the best-fit curve (data not shown) is nearly indistinguishable from the lower red line in Fig. 1a.
Table 3.
Parameters for model with DNA Looping.
StrainKIPTG, μML0
TK230 (Δcrp ΔlacY)15.7 ± 1.54.1
TK310 (ΔcyaA ΔcpdA ΔlacY)12.3 ± 1.43.7
TK250 (ΔcyaA ΔlacY)17.8 ± 1.75.0
Parameters derived from the fit of IPTG response of given strains to the thermodynamic model with DNA looping (Eq. 3).

Cooperativity Between CRP and LacR-Mediated DNA Looping Enhances the Sensitivity of the IPTG Response.

Strain TK310, which exhibited the expected cAMP response in medium with 1 mM IPTG and the expected IPTG response in medium with no cAMP added, was used to investigate the combinatorial control of Plac activity by LacR and cAMP–CRP. According to the thermodynamic model, if there is no interaction between cAMP–CRP-mediated activation and LacR-mediated repression, then the codependence of Plac activity on IPTG and cAMP would simply be the algebraic product of the IPTG response and the cAMP response, i.e., the product of the red lines in Fig. 1. A manifestation of this product form is a simple vertical shift of the IPTG responses of the same strain at different cAMP concentrations in the log–log plots. However, this clearly cannot be the case for strain TK310, because both the sensitivity and the maximal fold-change of its IPTG response increase with increasing cAMP levels (Fig. 1a and SI Fig. 5; see also SI Fig. 8a for a direct comparison).
Various forms of interactions between CRP and LacR in the Plac region have been previously proposed or reported (29, 3133, 66, 67). Because CRP causes a 90–130° bend in DNA (20, 68, 69), the binding of CRP to its site in the Plac could potentially bring the Lac operators O1 and O3 into closer proximity, promoting the formation of DNA loop between them (SI Fig. 9) (29). The existence of this interaction is supported by a computational study based on the available LacR–operator and CRP–operator cocrystal structures (30). Moreover, Hudson and Fried (33) and Vossen et al. (34) found cooperativity in the formation of a ternary complex of CRP, LacR, and Plac DNA in vitro, with the simultaneous presence of LacR and cAMP–CRP increasing the affinity of both proteins for their respective binding sites by a cooperative factor (Ω) of 4- to 12-fold.
To see whether CRP-assisted DNA looping may quantitatively explain the observed codependency of Plac activity, we extended the thermodynamic model with DNA looping to include the CRP-dependent looping effect (SI Methods). The extended model predicts the IPTG response to have the same form as Eq. 3 but with the prefactor α0 replaced by the Hill function αcAMP for strain TK310 (Eq. 2 with parameters given by Table 2, row 2) and with the loop parameter L0 replaced by
where Ω is the cooperativity factor of the CRP–LacR–loop interaction.
To test the predictions of the extended thermodynamic model, we used Eq. 4 to infer the value of the loop parameter L from the maximal fold-change of the IPTG response at each cAMP value; the result is plotted as the circles in Fig. 2a. We then used Eq. 3 to compute the expected IPTG responses using these values of L. The results are shown as the dashed lines in Fig. 2b for several representative cAMP values, together with the experimental data for TK310 cells grown in media with the corresponding cAMP concentrations. Note that the dashed lines are not fits of the data to the model. The striking congruence between the dashed lines and the data points (for [cAMP] ≤ 1 mM) shows that the cAMP-dependent sensitivity, which requires a series of different Hill coefficients within the Hill function description (SI Fig. 5a), can be naturally described by the DNA looping model in terms of the cAMP-dependent loop parameter L with no other adjustable parameters.
Fig. 2.
Combinatorial control of Plac activity for strain TK310. (a) The cAMP-dependent loop parameter L is inferred from Eq. 4 by fixing the maximal fold-change fIPTG to be the ratio of α0 and the observed promoter activity in medium with no IPTG. α0 is generated by the bare cAMP response αcAMP by using the parameters in Table 2 (row 2). The result obtained (circles) is fitted to Eq. 5 by using a single fitting parameter, Ω = 10.3 ± 0.1, with CcAMP = 320 μM (Table 2, row 2) and L0 = 3.7 (Table 3, row 4). (b) The IPTG responses obtained at different cAMP levels (symbols) are plotted together with predictions of the CRP-assisted DNA-looping model (Eq. 3) with no adjustable parameters. We used R = 50 and KIPTG = 12.3 μM (Table 3, row 3), with values of L taken from a and αcAMP for α0 (Eq. 2 with parameters values given in Table 2, row 2).
To further examine whether the cAMP-dependence of L conforms to the known energetics of CRP-assisted DNA looping, we fitted the inferred values of L (Fig. 2a, circles) to Eq. 5 by allowing only the parameter Ω to vary. The result of the fit (Fig. 2a, solid line) described the data well, except again at the highest cAMP level (10 mM), where cell growth significantly slowed down and other effects (e.g., overexpression of nucleoid proteins) might significantly affect DNA bending and looping (70). The value of the best-fit parameter obtained, Ω = 10.3 ± 0.1, is in agreement with the 4- to 12-fold cooperativity found in vitro (SI Methods) (31, 33). SI Fig. 6b shows the 3D plot of the expected Plac activity according to the extended thermodynamic model. Collectively, these results provide strong quantitative support for the hypothesis of CRP-assisted repression by DNA looping (3133).
Finally, we repeated the analysis for the combinatorial control of TK250 cells which are cpdA+. Despite the unexpected cooperative nature of the cAMP response of this strain (Fig. 1b, blue symbols), with mcAMP ≈ 2, the IPTG responses at various cAMP levels (SI Fig. 10b) are still well described by Eq. 3 (with the best-fit values of KIPTG and L0 given in Table 3, row 3). Moreover, except for the highest cAMP concentrations again, the cAMP-dependence of the loop parameter L agrees well with the corresponding Hill function, with similar value of the cooperativity factor, Ω ≈ 9.7 (see SI Fig. 10a). These results indicate that cpdA expression affects only the activation of CRP by extracellular cAMP but not the interaction of cAMP–CRP with DNA looping itself.

Discussion

Systematic, quantitative characterization of gene expression may yield unique insights on the mechanisms of gene regulation. A major obstacle in this effort is to quantify the amount of active transcription factors in cells in a given environment. As attempted earlier by Setty et al. (28), we tackled this problem for the Plac by controlling the amount of inducers IPTG and cAMP extracellularly but with the cyaA mutant of E. coli, which cannot synthesize cAMP endogenously. One danger of this approach is the array of mechanisms the cell may employ to control the intracellular effector levels. We encountered two such mechanisms in our study. Through the positive feedback of the Lac permease, E. coli cells sensitize themselves to the presence of inducers of the LacR, whereas through the activity of PDE, E. coli cells appear to insulate themselves from low levels of cAMP in the environment. The LacY effect is well known for induction with lactose in the growth medium (16, 17). However, the PDE effect observed here is previously unknown. It may yield important clues toward a comprehensive understanding of cAMP transport and control central to carbon metabolism in E. coli.

DNA Looping Is Assisted by CRP.

The innate regulation of Plac activity is revealed in E. coli cells bearing cyaA lacY cpdA triple deletion. We found that with a saturating amount of IPTG in the medium, the cAMP–CRP-mediated activation behaved in accordance with the thermodynamic model, given the noncooperative nature of the cAMP–CRP interaction. In addition, in the absence of cAMP, the LacR-mediated repression behaved in accordance with the thermodynamic model with DNA looping. Moreover, the codependence on IPTG and cAMP can be explained by the extended thermodynamic model with a single cooperativity parameter, Ω, whose value is of the order found by in vitro experiments. Both the quality of the fit and the simplicity of the model (i.e., one parameter for codependence) are superior compared with other simple but ad hoc models, as we show explicitly in SI Fig. 8). These results strongly support the hypothesis of CRP-assisted DNA looping (29, 31) and shed light on the seemingly conflicting roles CRP plays in the regulation of the Plac: CRP is an activator in that it increases gene expression at each IPTG level. However, it increases gene expression in a nonlinear way such that the maximal fold-change and the sensitivity of the IPTG response are both enhanced.

Hypersensitivity of IPTG Response Resulted from Multiple Factors.

Even in the absence of lacY-mediated feedback, Plac activity depended sensitively on the IPTG level with an apparent Hill coefficient of 2.5∼3 at physiological intracellular cAMP concentrations. This is rather remarkable given that the basic interaction of IPTG with the Lac tetramer is not cooperative at all in the absence of operator DNA (24). Whereas the involvement of DNA looping in the IPTG hypersensitivity is shown qualitatively by the experiment of Oehler et al. (62), the results and analysis of this study reveal the complex way in which this hypersensitivity is attained. First, the noncooperative IPTG–LacR binding becomes weakly cooperative (effective Hill coefficient of ≈1.5) in the presence of operator DNA (SI Fig. 7) (2225), due presumably to the allosteric coupling between inducer and operator binding (see SI Methods). The involvement of DNA looping then increases the cooperativity (effective Hill coefficient of ≈2), because both dimeric units of the Lac tetramer are required to bind specifically to operators to form DNA loops. Finally, in the physiological range of intracellular cAMP concentrations where CRP is activated, the cooperative interplay between DNA looping and CRP-mediated DNA bending further enhances the looping-induced cooperativity to the observed effective Hill coefficient of 2.5∼3.
As shown by Novick and Weiner (16) and by Ozbudak et al. (17), the hypersensitivity of Plac activity to the inducer of LacR is crucial for the bistable (i.e., the all-or-none) nature of E. coli's lactose utilization strategy (16, 17). The latter is the molecular basis of important physiological effects, such as the diauxie shift (71). It is interesting that hypersensitivity resulted in this case from an agglomeration of weak interactions. This distributed way of implementing an important molecular function (instead of, e.g., a highly cooperative LacR–inducer interaction) may reflect the serendipity of the evolutionary dynamics or, alternatively, a robust evolutionary strategy to preserve important system-level functions.

The Importance of Being Quantitative.

Critical to this study was the recognition of various “artifacts” produced by processes not directly related to the regulation of the Plac. The key discriminating feature we used was the quantitative comparison of the observed responses to the expectations of the thermodynamic model, in light of the known biochemical processes. Although fitting the experimental data to a Hill form is in itself not a very discriminating task, we find that the “reasonableness” of the numerical values of the fitting parameters, especially the apparent Hill coefficients of the responses, can be quite revealing. Nevertheless, the power of the quantitative analysis is by itself limited, because it can only suggest the existence of problems but does not identify the sources. It is through the quantitative comparison of the characteristics of a series of key mutants that the major conclusions of this study are established. It is important to note that some of our most discriminating mutants did not display much difference in the high/low states of expression but exhibited clear differences in the abruptness of the transition between states.
The Plac is one of the prototypical model systems of gene regulation. Classic studies on the regulation of this promoter have established numerous fundamental concepts as well as laying down the appropriate methodology for studying the molecular biology of gene regulation. Quantitative studies of the Plac can again play important roles in laying down the foundation of quantitative systems biology, whose goal is to understand the behavior of a “system” in terms of the relevant properties of its components. The Plac is admittedly a rather simple system. Nevertheless, we see from this study that system-level properties, such as the sensitivity of the IPTG response, resulted from a closely intertwined set of interactions among the molecular constituents. We demonstrated how this system can be dissected by careful quantitative characterization and targeted genetic manipulations, along with guidance from quantitative modeling and the knowledge of the biochemistry of the molecular constituents. The experience gained here may be of value to the study of other more complex biological systems.

Methods

Plasmids and Strains.

All strains used in this study were derived from E. coli K-12 MG1655 as listed in SI Table 4 and detailed in SI Methods. Chromosomal gene deletion was performed by using the method of Datsenko and Wanner (71), and transferred from one strain to another by using P1 transduction. All mutations were verified with PCR.

Cell Growth and β-Galactosidase Assay.

Overnight cultures were grown in M9 minimal medium containing the standard concentrations of necessary antibiotics in a 37°C water bath until stationary phase. The carbon source was 0.5% glucose unless otherwise indicated. These cultures were diluted 100- to 1,000-fold into 24-well plates (Costar) containing the same growth medium plus various concentrations of IPTG and cAMP. The plates were grown with vigorous shaking in a humidity-controlled incubator maintained at 37°C, with OD600 measurements taken every 2 h in a Tecan Genios Pro plate reader. When OD600 of a sample reached 0.2–0.4, it was assayed for β-galactosidase activity. These assays were performed in triplicate or more according to Miller (73) and Griffith (74), with minor modifications detailed in SI Methods. The β-galactosidase activity obtained (A) was expressed in Miller units (73), and the promoter activity (α) reported was taken to be the product of A and the cell-doubling rate λ1/2. Serial dilution experiments were used to verify that the entire range of promoter activity reported in the figures lay within the linear responsive regime of the measurements (see SI Methods).

Abbreviations

LacR
Lac repressor
CRP
cAMP-receptor protein
IPTG
isopropyl β-d-thiogalactopyranoside
AC
adenylate cyclase
PDE
cAMP-phosphodiesterase.

Acknowledgments

We thank Bob Schleif, Bill Loomis, and Shumo Liu for pointing out conceptual flaws in early versions of our experiments and Nicolas Buchler, Antoine Danchin, Hernan Garcia, Kathleen Matthews, Stefan Oehler, Rob Philips, and Agnes Ullmann for valuable comments. This work was supported by Department of Energy Grant DE-FG02-03-ER63691, National Science Foundation Grant MCB-0417721, and National Institutes of Health Grant GM070915. T.K. and T.H. were supported by Center for Theoretical Biological Physics Grants PHY-0216576 and PHY-0225630 through the National Science Foundation Physics Frontier Centers program.

Supporting Information

Adobe PDF - 06717Fig3.pdf
Adobe PDF - 06717Fig3.pdf
Adobe PDF - 06717Table4.pdf
Adobe PDF - 06717Table4.pdf
Adobe PDF - 06717SuppText.pdf
Adobe PDF - 06717SuppText.pdf
Adobe PDF - 06717Fig4.pdf
Adobe PDF - 06717Fig4.pdf
Adobe PDF - 06717Fig5.pdf
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Adobe PDF - 06717Fig6.pdf
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Adobe PDF - 06717Fig11.pdf
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Information & Authors

Information

Published in

Go to Proceedings of the National Academy of Sciences
Go to Proceedings of the National Academy of Sciences
Proceedings of the National Academy of Sciences
Vol. 104 | No. 14
April 3, 2007
PubMed: 17376875

Classifications

Submission history

Received: August 7, 2006
Published online: April 3, 2007
Published in issue: April 3, 2007

Keywords

  1. DNA looping
  2. gene regulation
  3. lac promoter
  4. systems biology

Acknowledgments

We thank Bob Schleif, Bill Loomis, and Shumo Liu for pointing out conceptual flaws in early versions of our experiments and Nicolas Buchler, Antoine Danchin, Hernan Garcia, Kathleen Matthews, Stefan Oehler, Rob Philips, and Agnes Ullmann for valuable comments. This work was supported by Department of Energy Grant DE-FG02-03-ER63691, National Science Foundation Grant MCB-0417721, and National Institutes of Health Grant GM070915. T.K. and T.H. were supported by Center for Theoretical Biological Physics Grants PHY-0216576 and PHY-0225630 through the National Science Foundation Physics Frontier Centers program.

Notes

This article is a PNAS direct submission.
This article contains supporting information online at www.pnas.org/cgi/content/full/0606717104/DC1.
§
However, cpdA mutants show a 2-fold overall reduction in gene expression for unknown reasons.
We note that the increased in cooperativity by DNA looping was discussed recently by Vilar and Saiz (75) in the context of the lysis-lysogeny control of Phage λ. However, the mechanism of cooperativity there is the oligomerization of regulatory proteins made possible through DNA looping. In contrast here, the tetramerization of LacR is independent of DNA looping. What DNA looping enhances here is the sensitivity to IPTG rather than LacR.

Authors

Affiliations

Thomas Kuhlman
Center for Theoretical Biological Physics and
Zhongge Zhang
Division of Biological Sciences, University of California at San Diego, La Jolla, CA 92093-0374
Milton H. Saier, Jr.
Division of Biological Sciences, University of California at San Diego, La Jolla, CA 92093-0374
Center for Theoretical Biological Physics and

Notes

To whom correspondence should be addressed at: Center for Theoretical Biological Physics, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0374. E-mail: [email protected]
Author contributions: M.H.S. and T.H. designed research; T.K. and Z.Z. performed research; T.K. analyzed data; T.K. and T.H. wrote the paper; and M.H.S. provided training and references.

Competing Interests

The authors declare no conflict of interest.

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    Combinatorial transcriptional control of the lactose operon of Escherichia coli
    Proceedings of the National Academy of Sciences
    • Vol. 104
    • No. 14
    • pp. 5705-6090

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