Inducer exclusion, by itself, cannot account for the glucose-mediated lac repression of Escherichia coli

Abstract

The lac operon of Escherichia coli is repressed several 100-fold in the presence of glucose. This repression has been attributed to cAMP receptor protein-mediated inhibition of lac transcription and EIIA^Glc-mediated inhibition of lactose transport (inducer exclusion). The growing evidence against the first mechanism has led to the postulate that the repression is driven by inducer exclusion. Although inducer exclusion reduces the permease activity only 2-fold in fully induced cells, it could be more potent in partially induced cells. Here, we show that even in partially induced cells, inducer exclusion reduces the permease activity no more than 6-fold. Moreover, the repression is so small because these experiments are performed in the presence of chloramphenicol. Indeed, when glucose is added to a culture growing on glycerol and TMG, but no chloramphenicol, lac expression is repressed 900-fold. This repression is primarily due to reversal of the positive feedback loop, i.e., the decline of the intracellular TMG level leads to a lower permease level, which reduces the intracellular TMG level even further. The repression in the absence of chloramphenicol is therefore primarily due to positive feedback, which does not exist during measurements of inducer exclusion.

Significance

There is growing evidence that cAMP regulation, by itself, cannot account for glucose-mediated repression of the lac operon of E. coli. By measuring the magnitude of inducer exclusion, we show that even inducer exclusion, by itself, cannot account for glucose-mediated lac repression. Explanations of this repression must therefore be sought beyond the molecular mechanisms of cAMP regulation and inducer exclusion that dominate the discourse in the literature. We show that positive feedback plays the dominant role in mediating glucose-mediated lac repression in the presence of low concentrations of non-metabolizable inducer.

Introduction

When glucose is added to a culture of Escherichia coli cells growing in the presence of lactose (1) or low concentrations of the gratuitous inducer methyl-β-D-thiogalactoside (TMG) (2,3), expression of the lac operon is repressed several 100-fold. This so-called catabolite repression is usually attributed to two molecular mechanisms (4,5):

• •Inhibition of lac transcription mediated by 3′,5′-cyclic adenosine monophosphate (cAMP) (6,7): Upon addition of glucose, the concentration of intracellular cAMP, and hence its complex with the cAMP receptor protein (CRP), decreases, which inhibits recruitment of RNAP to the lac promoter, thus reducing the lac transcription rate.
• •Inhibition of lactose transport mediated by EIIA^Glc (8, 9, 10): The uptake of glucose by the phosphotransferase system (PTS) is accompanied by the formation of the dephosphorylated enzyme EIIA^Glc, which inactivates lactose permease (LacY) by binding to it, thus inhibiting lactose transport. This mechanism is called inducer exclusion.

Both mechanisms are well understood at the molecular level, but their contribution to catabolite repression remains the subject of vigorous debate (11, 12, 13).

Some early studies indicated that the cAMP-mediated mechanism, by itself, cannot account for catabolite repression (14,15). However, the most compelling evidence was obtained subsequently by Aiba and co-workers who showed that the intracellular cAMP levels during the first and second exponential growth phases of the glucose-lactose diauxie were nearly the same, addition of excess cAMP did not relieve the catabolite repression of a culture growing on glucose and lactose, and catabolite repression persisted in mutants with cAMP-independent lac expression (1).

The foregoing evidence against the role of cAMP in catabolite repression led some researchers to posit that catabolite repression is primarily due to inducer exclusion (1,4). This hypothesis, referred to henceforth as the inducer exclusion hypothesis, was supported by the following experiments. Catabolite repression does not occur if glucose is added to crr⁻ cells (lacking functional EIIA^Glc) or lacY-overexpressing cells growing on lactose (16). In these cases, it can be argued that inducer exclusion does not exist because the EIIA^Glc:LacY ratio is so small that most of the LacY molecules escape EIIA^Glc binding. Catabolite repression also does not occur if glucose is added to lacI⁻ cells (lacking functional Lac repressor) growing on lactose (1) or succinate (17), and wild-type cells growing on lactose (1) or succinate (2,3) plus high concentrations of a gratuitous inducer. In these cases, one can argue that inducer exclusion occurred (i.e., LacY was inactivated), but was ineffective in mediating lac repression because the repressor was inactivated by LacY-independent mechanisms. Specifically, lacI⁻ cells synthesize defective Lac repressor that cannot bind to the lac operator, and entry of gratuitous inducers at high concentrations is mediated primarily by passive diffusion rather than LacY (18,19). Taken together, these data suggest that inducer exclusion is necessary for catabolite repression since rendering it nonexistent or ineffective abolishes catabolite repression.

Although inducer exclusion may be necessary for catabolite repression, it is not sufficient because there is hardly any repression even if inducer exclusion exists and is effective, e.g., in the presence of active repressor and large EIIA^Glc:LacY ratios (Fig. S1). This conclusion follows from measurements of the magnitude of inducer exclusion ${\phi }_p$, defined as the fractional reduction of the LacY activity in the presence of glucose

$${\phi }_p=\frac{E_{p,t}-E_p}{E_{p,t}}=1-\frac{E_p}{E_{p,t}},$$ (1)

where $E_p$ and $E_{p,t}$ are the respective specific permease activities in the presence of glucose and a non-PTS substrate, such as glycerol, that cannot cause inducer exclusion (20). It is determined by exposing the cells to a mixture of glucose/glycerol + TMG + chloramphenicol, and measuring the subsequent intracellular TMG level denoted $T$ (see supplement for the complete list of notations). Since chloramphenicol blocks not only the synthesis of all proteins including LacY, but also the degradation of LacY (21), the specific LacY activity remains constant throughout the experiment, and $T$ approaches a steady-state value $\tilde{T}$. If the concentration of extracellular TMG is sufficiently small, $\tilde{T}$ is proportional to $E_p$ (Section S1), and Eq. 1 implies that ${\phi }_p$ can be calculated from the expression

$${\phi }_p=1-\frac{{\tilde{T}}^{\text{glc}}}{{\tilde{T}}^{\text{gly}}},$$ (2)

where ${\tilde{T}}^{\text{glc}}$ and ${\tilde{T}}^{\text{gly}}$ denote the steady-state concentrations of intracellular TMG in the presence of glucose and glycerol, respectively. Henceforth, we shall refer to these experiments for determining ${\phi }_p$ as inducer exclusion experiments. With the help of such experiments, Mitchell et al. determined ${\phi }_p$ at various EIIA^Glc:LacY ratios (20). They found that when the EIIA^Glc:LacY ratio was small, there was no inducer exclusion (${\phi }_p=0$), which is consistent with the foregoing explanation of the data for crr⁻ and lacY-overexpressing cells. As expected, ${\phi }_p$ increased with the EIIA^Glc:LacY ratio, but it plateaued at a maximum value of only 0.5. Thus, only half of the LacY molecules were inactivated by inducer exclusion even when the repressor was active, and the concentration of EIIA^Glc was comparable to, or higher than, the concentration of LacY. It follows that inducer exclusion, by itself, cannot account for the 600-fold catabolite repression.

The foregoing data of Mitchell et al. (20) show that inducer exclusion is not sufficient for catabolite repression, but upon closer inspection they reveal two issues that could give us pause. First, the extracellular TMG concentrations used in their inducer exclusion experiments were so large that the steady-state intracellular TMG concentrations were almost independent of the permease level (rather than proportional to it). Under this condition, ${\phi }_p$ is underestimated because similar intracellular TMG levels are obtained in the presence of glucose and glycerol (${\tilde{T}}^{\text{glc}}\approx {\tilde{T}}^{\text{gly}}$) despite rather different permease levels (Section S1). Second, they varied the EIIA^Glc:LacY ratio in a nonphysiological manner because under physiological conditions, the intracellular EIIA^Glc levels are constant (5,22), and the LacY level changes depending on the lac induction level. However, in their experiments, the level of LacY, expressed from a lac-constitutive promoter, was constant and the EIIA^Glc level was varied.

We were therefore led to revisit the experiments of Mitchell et al. (20), i.e., we determined the variation of ${\phi }_p$ with the EIIA^Glc:LacY ratio, but under conditions that eliminated the two issues mentioned above. We find that even when the EIIA^Glc:LacY ratio is large, the LacY activity decreases no more than 6-fold in the presence of glucose. This is significantly higher than the 2-fold decline observed by Mitchell et al. (20), but still insufficient to account for the several 100-fold catabolite repression. It follows that inducer exclusion, by itself, cannot account for glucose-mediated catabolite repression; there is some other process that amplifies the 6-fold repression several 100-fold. We find that this process is enzyme synthesis, and it drives catabolite repression due to amplification by positive feedback.

Materials and methods

Chemicals

Reagent-grade glycerol, glucose, isopropyl β-D-thiogalactopyranoside (IPTG), and ortho-nitrophenyl-β-galactoside (ONPG) were obtained from Fisher Scientific; TMG was obtained from Sigma-Aldrich; and ¹⁴C-methyl-β-D-thiogalactoside ([¹⁴C]TMG) was procured from American Radiolabeled Chemicals, Inc. (ARC 0322).

Bacterial strains

Experimental strains were procured from the E. coli Genetic Stock Center (CGSC), Yale University. Wild-type E. coli K12 strain MG1655 (CGSC# 6300) was used for studies pertaining to the wild-type lac operon. We isolated Lac permease-deficient (cryptic) strain RA-Y66 by UV mutagenesis and ampicillin selection of the wild-type strain MG1655 (23). The procedure is outlined below.

MG1655 cells were irradiated with UV, killing more than 99.9% of cells from mid-exponential growth phase, followed by overnight growth in Luria-Bertani (LB) broth in the dark. Cells were subcultured in the morning in M9 minimal medium supplemented with 0.4% lactose. Ampicillin (50 μg mL⁻¹) was added to the medium and cells were allowed to grow for about two generations. This enriched the cells incapable of using lactose. Cells were spun and resuspended in LB broth for a second round of ampicillin selection the next day. Dilutions of enriched cultures were plated on minimal agar plates containing 0.4% glycerol, 0.1 mM IPTG, and 0.003% 5-bromo-4-chloro-3-indolyl-β-D-galactopyranoside (X-Gal). White or pale blue isolates were grown on glycerol in the absence and presence of 0.5 mM IPTG to measure the Lac permease and β-galactosidase activity by Miller assays (23). Strain RA-Y66 was identified as one of the cultures resulting in wild-type LacZ activity and lacking LacY activity in both culturing conditions. In our hands, this strain exhibited a growth rate (approximately 0.52 h⁻¹) and growth yield (0.40 gdw g⁻¹) similar to wild-type strain on non-PTS carbon source such as maltose. RA-Y66 was inducible with IPTG and exhibited ONPG and TMG uptake kinetics similar to the available lac⁻ strain JW4081 (CGSC# 10937).

Culturing conditions

Cells were grown at 37°C (unless stated otherwise) in M9 minimal medium (23) containing 0.4% glycerol as the carbon source to ensure noninducing and nonrepressing conditions. Fully induced cells were obtained by growing the cells in the presence of 0.5 mM inducer IPTG for at least 10 generations. The cell density (gdw L⁻¹) was followed by measurement of optical density at 600 nm (OD₆₀₀) and the two were found to be related by the expression gdw L⁻¹ = 0.35 $\times {\text{OD}}_{600}$. At several time points during the exponential growth phase (OD₆₀₀ > 0.3, μ ≥ 0.42 h⁻¹), culture aliquots were subcultured in medium containing 0.4% glucose and allowed to grow for 30 min to 3 h to ensure that the glucose transport enzymes, being fully induced, exerted the maximum inducer exclusion effect. Cells were harvested at various enzyme levels by adding 50 μg mL⁻¹ chloramphenicol, after which the cells were spun and resuspended in M9 minimal medium containing 50 μg mL⁻¹ chloramphenicol and carbon source, namely 0.4% glycerol (absence of glucose) or 0.4% glucose (presence of glucose) to obtain the experimental suspensions that were subsequently used to estimate the lactose permease and β-galactosidase levels. Chloramphenicol, which inhibits not only protein synthesis but also degradation of permease molecules (21), was added to ensure that the enzyme levels did not change during the course of the experiment. No chloramphenicol was added in experiments involving growth on glucose.

Assay for induction level

The lac induction levels of the experimental suspensions were determined by the β-galactosidase assay (23). The specific β-galactosidase activity was measured in Miller units. One Miller unit corresponds to about 200 nmol ONPG hydrolyzed per minute per milligram cell dry weight.

Assay for permease activity

The specific activity of lactose permease was assayed by measuring the steady-state concentration of intracellular [¹⁴C]TMG using Miller's method (23), but the concentration of extracellular TMG was much lower (2.5 μM). At these low extracellular TMG concentrations, the specific permease activity is directly proportional to the steady-state concentration of intracellular TMG (Supporting Material), which in turn was measured as follows. At t = 0, [¹⁴C]TMG with a known specific radioactivity and 2.0 to 2.5 μM final concentration was added to the experimental suspensions of both wild-type and cryptic strains that had been pre-equilibrated at 30°C on a shaker-incubator. The intracellular TMG levels were found to reach steady state within 5 min of incubation (Fig. S4). Culture aliquots of 1 mL were therefore rapidly filtered and washed with 3 mL of medium after about 10 min of incubation at 30°C. The filters were dried in scintillation vials, resuspended in a scintillation cocktail (24), and the counts were measured with a liquid scintillation counter (PerkinElmer Tri-Carb 2810) for at least 30 min to minimize the counting errors. Cellular suspensions containing no radioactivity, and M9 medium containing only [¹⁴C]TMG were also filtered and counted. The observed counts per minute were obtained after subtracting the background counts and the counts due to nonspecific binding of TMG to the filter. The intracellular concentrations were calculated by assuming that the cellular water volume was 2.7 mL gdw⁻¹ (25).

Data analysis

Data were processed using Microsoft Office Excel 2007 and MATLAB 2016b (The MathWorks, Inc.). In particular, the transient data were fitted by the least-square cubic B-spline method (26) using splinetool in MATLAB, and the derivatives of the fitted splines were obtained using the fnder command in the splinetool toolbox.

Results

The magnitude of inducer exclusion has a weak dependence on the induction level

The theory shows that $\tilde{T}$, the steady-state intracellular TMG concentration suitably corrected for nonspecific accumulation by passive diffusion, is directly proportional to the specific LacY activity $E_p$ only if the extracellular TMG concentration is sufficiently small (Section S1). Consequently, we exposed cells induced to various levels to a relatively low extracellular TMG concentration (2.5 μM). However, under this condition, the determination of $\tilde{T}$ was prone to significant error in cells induced to <2% of fully induced levels because most of the TMG was accumulated by passive diffusion rather than LacY (Fig. 1). Our data are therefore confined to cells induced from 2% to 100% of fully induced levels. In such cells, $\tilde{T}$ is indeed proportional to $E_p$ because the steady-state intracellular TMG concentration in the presence of glycerol, denoted ${\tilde{T}}^{\text{gly}}$, is proportional to the induction level $E_g$ (Fig. 2 A), which in turn is proportional to $E_p$ because lacZ and lacY are coordinately expressed, and there is no inducer exclusion to distort the constant LacZ:LacY ratio.

Figure 1.

The transport of TMG by LacY is significant compared with its transport by passive diffusion only if cells are induced to $\ge 2$ % of fully induced cells. The steady-state intracellular TMG level in uninduced wild-type cells is the same as that observed in cryptic (lacY⁻) cells. Since cryptic cells transport TMG solely by passive diffusion, the same must be true of uninduced wild-type cells. However, the steady-state intracellular TMG level in cells induced to 2% of fully induced cells is significantly higher than that observed in cryptic and uninduced wild-type cells, thus indicating that a substantial part of their intracellular TMG is transported by LacY. The cpm mL⁻¹ OD₆₀₀⁻¹ on the primary y axis are corrected for the background activity and [¹⁴C]TMG nonspecifically bound to the filter. The corresponding intracellular concentrations on the secondary y axis are calculated as described in materials and methods. The error bars represent the standard error stemming from three or more repeated measurements.

Figure 2.

Variation of the steady-state intracellular [¹⁴C]TMG concentration and magnitude of inducer exclusion with the lac induction level, as measured by the specific β-galactosidase activity $E_g$ or the normalized induction level $E_g/E_{g,m}$, where $E_{g,m}$ is the specific β-galactosidase activity of fully induced cells. (A) When the lac induction level is increased, the steady-state intracellular [14C]TMG concentration attained in the presence of glycerol ${\tilde{T}}^{\text{gly}}$ increases linearly (●), while that attained in the presence of glucose ${\tilde{T}}^{\text{glc}}$ increases nonlinearly (○). The intracellular [¹⁴C]TMG concentrations were obtained by subtracting the average measured in cryptic cells. (B) When the lac induction level is increased, the ratio of steady-state intracellular [¹⁴C]TMG levels ${\tilde{T}}^{\text{glc}}/{\tilde{T}}^{\text{gly}}$ increases, but it plateaus at both large and small induction levels. The full curve shows the least-square cubic spline fit to the data obtained in three independent experiments (solid symbols). The dashed curve shows the magnitude of inducer exclusion ${\phi }_p=1-{\tilde{T}}^{\text{glc}}/{\tilde{T}}^{\text{gly}}$ calculated from the fit to the data for ${\tilde{T}}^{\text{glc}}/{\tilde{T}}^{\text{gly}}$.

If cells induced to the same level are exposed to extracellular TMG and glucose/glycerol, the existence of inducer exclusion implies that the specific LacY activity in the presence of glucose ($E_p$) is lower than that in the presence of glycerol ($E_{p,t}$). Since $\tilde{T}$ is proportional to $E_p$, we expect ${\tilde{T}}^{\text{glc}}<{\tilde{T}}^{\text{gly}}$, and Fig. 2 A shows that this is always the case, thus confirming that inducer exclusion always exists at all induction levels. However, the magnitude of inducer exclusion decreases with the induction level because the ratio ${\tilde{T}}^{\text{glc}}/{\tilde{T}}^{\text{gly}}=E_p/E_{p,t}$ increases with the induction level $E_g$ (full curve of Fig. 2 B). In fully induced cells, this ratio is 0.8, but still increasing and likely to plateau at 1.0 in hyper-induced cells. Moreover, the lower the induction level, the lower the ratio ${\tilde{T}}^{\text{glc}}/{\tilde{T}}^{\text{gly}}$, but it plateaus at 0.16, which corresponds to a mere 100/16 ≈ 6-fold reduction of the specific permease activity. It follows the magnitude of inducer exclusion ${\phi }_p=1-E_p/E_{p,t}$ decreases with the induction level, and never exceeds 0.84 (dashed curve of Fig. 2 B).

Although ${\tilde{T}}^{\text{glc}}/{\tilde{T}}^{\text{gly}}=E_p/E_{p,t}$ plateaus at low and high induction levels, our data were obtained only with cells induced from 2% to 100% of fully induced cells, and one could therefore argue that $E_p/E_{p,t}$ might depart from these limiting values if experiments were performed with cells induced to $<2\%$ or $>100\%$ of fully induced cells. We show below that our limiting values of $E_p/E_{p,t}$, equaling 1.0 in hyper-induced cells and 0.16 in hypo-induced cells, are consistent with the predictions of a mechanistic model of inducer exclusion. To see this, observe that before glucose is added to the experimental suspension, all the EIIA^Glc molecules are phosphorylated and all the permease molecules are active, i.e., not bound to EIIA^Glc. Let $E_{\text{IIA},t}^{\text{glc}}$ and $E_{p,t}$ denote the intracellular concentrations of phosphorylated EIIA^Glc and permease under these conditions. Upon addition of glucose, virtually all the EIIA^Glc molecules are dephosphorylated (27), and some of them bind to the free permease molecules in the stoichiometric ratio 1:1 (28,29), thus forming the inactive complex $E_p\circ E_{\text{IIA}}^{\text{glc}}$. The binding can therefore be represented by the reaction

$$E_p+E_{\text{IIA}}^{\text{glc}}\rightleftarrows E_p\circ E_{\text{IIA}}^{\text{glc}},K_d=\frac{E_p{E}_{\text{IIA}}^{\text{glc}}}{E_p\circ E_{\text{IIA}}^{\text{glc}}},$$ (3)

where $K_d$ is the dissociation constant. Now, in hyper-induced cells, the permease molecules are in excess, i.e., $E_{p,t}\gg E_{\text{IIA},t}^{\text{glc}}$. Hence the fraction of permease molecules inactivated by binding is negligibly small, i.e., $E_p\approx E_{p,t}$ and ${\tilde{T}}^{\text{glc}}/{\tilde{T}}^{\text{gly}}=E_p/E_{p,t}\approx 1$, which is consistent with the data for hyper-induced cells obtained by Mitchell et al. (20). In hypo-induced cells, we have $E_{p,t}\ll E_{\text{IIA},t}^{\text{glc}}$, which implies that the fraction of EIIA^glc molecules bound to permease is negligibly small, i.e., $E_{\text{IIA}}^{\text{glc}}\approx E_{\text{IIA},t}^{\text{glc}}$. Thus, the binding reaction reduces to the pseudo-first-order reaction

$$E_p\rightleftarrows E_p\circ E_{\text{IIA}}^{\text{glc}}$$

with dissociation constant $E_p/E_p\circ E_{\text{IIA}}^{\text{glc}}\approx K_d/E_{\text{IIA},t}^{\text{glc}}$, which implies that

$$\frac{E_p}{E_{p,t}}=\frac{E_p}{E_p+E_p\circ E_{\text{IIA}}^{\text{glc}}}=\frac{1}{1+E_p\circ E_{\text{IIA}}^{\text{glc}}/E_p}\approx \frac{1}{1+E_{\text{IIA},t}^{\text{glc}}/K_d}.$$ (4)

Because $E_{\text{IIA},t}^{\text{glc}}$ = 50 μM and $K_d$ = 10 ± 5 μM (29), we obtain $E_p$/$E_{p,t}$ = 1/6, which agrees with our data for hypo-induced cells shown in Fig. 2 B. Thus, the occurrence of limiting values in our data as well as the magnitudes of these limiting values are consistent with the predictions of the mechanistic stoichiometric binding model of inducer exclusion.

It is therefore reasonable to conclude that even in the presence of active repressor and large EIIA^Glc:LacY ratios, inducer exclusion—measured in the presence of glucose/glycerol + TMG + chloramphenicol—yields no more than 6-fold repression. However, as we show below, there is 900-fold repression when glucose is added to a culture growing on glycerol and TMG, but no chloramphenicol.

Strong catabolite repression can occur even in the presence of TMG

We can infer the potential for strong glucose-mediated catabolite repression in the presence of TMG by examining the extensive data obtained by Ozbudak et al. (3). They showed that if E. coli cultures were exposed to the nonrepressing carbon source, succinate, and various concentrations of extracellular TMG, but no chloramphenicol, bistability occurred when the extracellular TMG concentration was in the range 3 to 30 μM. Bistability also occurred if similar experiments were performed with a mixture of succinate and the repressing carbon source glucose, but the bistable region was now shifted to a higher range of extracellular TMG concentrations (100–1000 μM). These data suggest that if glucose is added to a culture growing exponentially on succinate and 30 to 100 μM TMG, the specific β-galactosidase activity will ultimately decrease several 100-fold.

Since glycerol, like succinate, is a nonrepressing carbon source, we reasoned that data similar to Fig. 3 would be obtained if succinate were replaced by glycerol. More precisely, we hypothesized that if glucose were added to a culture growing exponentially on glycerol and certain concentrations of extracellular TMG, but no chloramphenicol, the specific β-galactosidase activity would ultimately decrease to dramatically low levels. We found that this was indeed the case when the concentration of extracellular TMG was 100 μM. When induced or noninduced cells of wild-type E. coli were grown overnight on glycerol and 100 μM TMG, they became fully induced (∼3000 Miller units) regardless of their initial state. In contrast, if glucose (4 g L⁻¹) was added to a steady-state culture growing exponentially on glycerol and 100 μM TMG, the specific β-galactosidase activity and intracellular [¹⁴C]TMG concentration declined continuously from the high levels observed before the addition of glucose (Fig. 4). Importantly, this decline was biphasic. In the first 5 min, the intracellular TMG level declined ∼3-fold, but the specific β-galactosidase activity remained constant. This is probably due to inducer exclusion since its magnitude (3-fold) and time scale (5 min) are similar to those observed in the inducer exclusion experiments (Figs. 2 A and S4). However, after this rapid initial transient, the intracellular TMG concentration and specific β-galactosidase activity decreased simultaneously at a slow rate, and the latter activity ultimately decreased to $<3.5$ Miller units, which corresponds to ∼900-fold repression. With the help of a kinetic model, we show below that this slow evolution, which causes most of the ∼900-fold repression but does not occur in the inducer exclusion experiments of Fig. 2 A, is due to a dramatic shift of the steady-state induction level precipitated by positive feedback.

Figure 3.

For a Figure360 author presentation of this figure, see https://doi.org/10.1016/j.bpj.2022.01.016.

Schematic diagram showing the steady-state lac promoter activity, as measured by the green fluorescence intensity, during growth of E. coli cultures on succinate (squares) and succinate +1 mM glucose (circles) in the presence of various extracellular TMG concentrations (adapted from Ozbudak et al. [3]). The open (respectively, closed) symbols show the steady-state GFP intensity reached when the inoculum is uninduced (respectively, induced). When the extracellular TMG concentrations are 30 to 100 μM, cells grown on succinate are eventually induced, but cells grown on succinate + 1 mM glucose are eventually uninduced. It follows that if 1 mM glucose was added to a steady-state culture growing on succinate and 30 to 100 μM extracellular TMG, the lac promoter activity should decrease several 100-fold, which is similar in magnitude to the catabolite repression observed in the glucose-lactose diauxie.

Figure 4.

Strong catabolite repression in the presence of TMG. Wild-type cells were pre-grown at 30°C on glycerol and 100 μM [¹⁴C]TMG until they reached steady state, as indicated by the constant specific β-galactosidase activity (▵) and intracellular TMG level (○) at $t<0$. At $t$ = 0, 0.4% glucose was added, and the specific β-galactosidase activity (▲) and intracellular TMG level (●) were measured for seven generations. Within 5 min of glucose addition, the intracellular TMG level decreased 3-fold, whereas the specific β-galactosidase activity remained unchanged. Thereafter, both slowly decreased approximately 15-fold over the next 15 h.

Proposed kinetics of catabolite repression in the presence of TMG

Before proposing a kinetic model for the strong glucose-mediated repression observed in Fig. 4, it is useful to recall two key facts.

First, the inducer exclusion experiments show that the steady-state intracellular TMG concentrations ${\tilde{T}}^{\text{gly}}$, ${\tilde{T}}^{\text{glc}}$ are increasing functions of the induction level $E_g$, linear in the case of glycerol and nonlinear in the case of glucose (Fig. 2 A). Although these data were obtained at various fixed $E_g$, engineered by the addition of chloramphenicol, we expect similar data if $E_g$ changes quasi-statically due to the slow evolution of the enzymes in the absence of chloramphenicol (Section S3). Thus, the variation of the quasi-steady-state intracellular TMG levels, ${\tilde{T}}^{\text{gly}}$ and ${\tilde{T}}^{\text{glc}}$, with the slowly varying $E_g$, can be depicted graphically by the dashed linear line and full nonlinear curve in Fig. 5 A.

Figure 5.

Proposed model for the glucose-mediated catabolite repression shown in Fig. 4 and its comparison with data. Left: Hypothesized variation with the induction level $E_g$ of (A) the quasi-steady-state intracellular TMG levels ${\tilde{T}}^{\text{gly}}$, ${\tilde{T}}^{\text{glc}}$, (B) the specific rates of β-galactosidase synthesis $r_{E_g}^{\text{gly}}$, $r_{E_g}^{\text{glc}}$ and dilution ${\mu }^{\text{gly}}{E}_g$, ${\mu }^{\text{gly}}{E}_g$, and (C) the net rate of β-galactosidase synthesis $d{E}_g/dt$. The dashed and solid curves show these variations during growth of E. coli in the presence of glycerol + TMG and glucose + glycerol + TMG, respectively. Right: Observed variations with induction level $E_g$ of (D) the intracellular TMG level ${\tilde{T}}^{\text{glc}}$, (E) the rates of induction $r_{E_g}^{\text{glc}}$ and dilution ${\mu }^{\text{gly}}{E}_g$, and (F) the rate of change of induction level $d{E}_g/dt$. These variations are derived from the data in Fig 4.

Second, since β-galactosidase is relatively stable (30), the slow evolution of $E_g$ is governed by the rates of β-galactosidase synthesis and dilution due to growth, i.e.,

$$\frac{d{E}_g}{dt}=r_{E_g}^{⊡}\left({\tilde{T}}^{⊡}\left(E_g\right),C^{⊡}\right)-{\mu }^{⊡}{E}_g,$$ (5)

where the superscript $⊡$ specifies the experimental condition ($⊡=\text{gly}$ when the experiment is performed with glycerol + TMG; $⊡=\text{glc}$ when the experiment is performed with glucose + glycerol + TMG), $C^{⊡}$ denotes the intracellular cAMP level at the given experimental condition, and $r_{E_g}^{⊡}\left({\tilde{T}}^{⊡}\left(E_g\right),C^{⊡}\right)$, ${\mu }^{⊡}{E}_g$ denote the induction and dilution rates of β-galactosidase at the given experimental condition. Since $r_{E_g}^{⊡}\left({\tilde{T}}^{⊡},C^{⊡}\right)$ is an increasing function of the intracellular TMG level ${\tilde{T}}^{⊡}$ (19), and ${\tilde{T}}^G$ is an increasing function of $E_g$ (Fig. 2 A), $r_{E_g}^{⊡}\left({\tilde{T}}^{⊡}\left(E_g\right),C^{⊡}\right)$ is an increasing function of $E_g$, i.e., there is positive feedback and hence induction follows autocatalytic kinetics. If ${\mu }^{⊡}$ is constant, as was found to be the case in our experiments, the dilution rate follows first-order kinetics.

We begin by explaining lac induction in the presence of glycerol +100 μM TMG. We assume that under this condition, the synthesis rate $r_{E_g}^{\text{gly}}$ and the dilution rate ${\mu }^{\text{gly}}{E}_g$ have the graphs shown in Fig. 5 B as the dashed sigmoidal curve and dashed line, respectively. The disposition of the two graphs is such that they intersect at a single point, denoted ▪, which represents the steady state with specific β-galactosidase activity denoted ${\tilde{E}}_g^{\text{gly}}$. Moreover, for all $0\le E_g<{\tilde{E}}_g^{\text{gly}}$, the induction rate exceeds the dilution rate, and hence, $d{E}_g/dt=r_{E_g}^{\text{gly}}-{\mu }^{\text{gly}}{E}_g>0$ (Fig. 5 C). It follows that if an uninduced inoculum with $E_g\left(0\right)\approx 0$ is exposed to glycerol +100 μM TMG, the induction level $E_g$ increases monotonically until it reaches the steady-state value ${\tilde{E}}_g^{\text{gly}}$.

Next, we explain the strong glucose-mediated lac repression observed in Fig. 4. We assume that the addition of glucose to a steady-state culture growing on glycerol and 100 μM TMG has the following three effects:

• 1)Due to inducer exclusion, the intracellular TMG level decreases rapidly while the induction level remains essentially constant at its initial value ${\tilde{E}}_g^{\text{gly}}$, which is depicted in Fig. 5 A by the downward vertical arrow from ${\tilde{T}}^{\text{gly}}\left({\tilde{E}}_g^{\text{gly}}\right)$ to ${\tilde{T}}^{\text{glc}}\left({\tilde{E}}_g^{\text{gly}}\right)$. In addition, the intracellular cAMP level also rapidly declines from $C^{\text{gly}}$ to $C^{\text{glc}}$ (31).
• 2)Due to the decline of the intracellular TMG and cAMP levels, the induction rate decreases from $r_{E_g}^{\text{gly}}$ to $r_{E_g}^{\text{glc}}$, i.e., the graph of the induction rate shifts downward from the dashed to the full sigmoidal curve in Fig. 5 B.
• 3)Due to glucose uptake and metabolism, the specific growth rate increases, i.e., the line representing the dilution rate rotates counter-clockwise from the dashed to the full line in Fig. 5 B.

Due to the first effect, the intracellular TMG and cAMP levels decline, but $E_g$ is essentially constant. Due to the second and third effects, the disposition of the induction and dilution curves changes such that they intersect at a new steady state, denoted ●, with an induction level ${\tilde{E}}_g^{\text{glc}}$ that is drastically lower than the steady-state induction level ${\tilde{E}}_g^{\text{gly}}$ attained during growth on glycerol + TMG (Fig. 5 B); moreover, for all ${\tilde{E}}_g^{\text{glc}}<E_g\le {\tilde{E}}_g^{\text{gly}}$, the dilution rate now exceeds the induction rate, and hence, $d{E}_g/dt<0$ (Fig. 5 C). It follows that the induction level $E_g$ decreases relentlessly from its initial value ${\tilde{E}}_g^{\text{gly}}$ to its new steady-state value ${\tilde{E}}_g^{\text{glc}}$. During this slow decline of $E_g$, the intracellular TMG level, which is in quasi-steady state, follows the curve labeled ${\tilde{T}}^{\text{glc}}$ in Fig. 5 A.

We show below that the transient data of Fig. 4 allow us to test the validity of the model proposed above.

Proposed kinetics of catabolite repression is consistent with observed kinetics

The decline of the quasi-steady-state intracellular TMG level with the slowly declining induction level is consistent with the predicted trend shown in Fig. 5 A. Indeed, if we plot the instantaneous intracellular TMG levels in Fig. 4 against the corresponding induction levels, we obtain the graph labeled ○ in Fig. 5 D. The dotted vertical arrow shows that immediately after the addition of glucose, the induction level remains unchanged at ${\tilde{E}}_g^{\text{gly}}$, but the intracellular TMG level decreases 3-fold from its previous steady-state value ${\tilde{T}}^{\text{gly}}\left({\tilde{E}}_g^{\text{gly}}\right)=18$ mM, denoted ▪, to the new quasi-steady-state value ${\tilde{T}}^{\text{glc}}\left({\tilde{E}}_g^{\text{gly}}\right)=6$ mM, a process analogous to inducer exclusion. Thereafter, the quasi-steady-state intracellular TMG level ${\tilde{T}}^{\text{glc}}\left(E_g\right)$ declines slowly in tandem with the induction level $E_g$ (full curve passing through the points labeled ○).

Next, we show that the dilution and induction rates calculated from the data in Fig. 4 are consistent with the picture in Fig. 5 B. To see this, observe that the evolution of the cell density after the addition of glucose provides the specific growth rate ${\mu }^{\text{glc}}$, and hence the dilution rate ${\mu }^{\text{glc}}{E}_g$. This dilution rate, which is derived from the data, appears in Fig. 5 E as the full line passing through the origin and the points labeled Δ. Given this dilution rate ${\mu }^{\text{glc}}{E}_g$, we can also determine the induction rate $r_{E_g}^{\text{glc}}\left(t\right)$ by calculating the rate of change of the specific β-galactosidase activity $d{E}_g/dt$ from the data, and substituting it in the relation

$$r_{E_g}^{\text{glc}}\left(t\right)=\frac{d{E}_g}{dt}+{\mu }^{\text{glc}}{E}_g\left(t\right)$$ (6)

obtained from Eq. 5. When this induction rate $r_{E_g}^{\text{glc}}\left(t\right)$, which is estimated from the data, is plotted against the corresponding induction level $E_g\left(t\right)$, we obtain the full sigmoidal curve passing through the points labeled ○ in Fig. 5 E. This sigmoidal induction rate curve intersects the dilution rate line at the point labeled ● with a very low specific β-galactosidase activity ${\tilde{E}}_g^{\text{glc}}$ (Fig. 5 E). Moreover, $d{E}_g/dt=r_{E_g}^{\text{glc}}-{\mu }^{\text{glc}}{E}_g<0$ for all ${\tilde{E}}_g^{\text{glc}}<E_g<{\tilde{E}}_g^{\text{gly}}$ (Fig. 5 F). Consequently, the induction level decreases monotonically from its initial value ${\tilde{E}}_g^{\text{gly}}$, denoted ▪, to the new steady-state value ${\tilde{E}}_g^{\text{glc}}$, denoted ●. This leads to the persistent decline of the quasi-steady-state intracellular TMG level from ${\tilde{T}}^{\text{glc}}\left({\tilde{E}}_g^{\text{gly}}\right)=6$ mM to the immeasurably small value ${\tilde{T}}^{\text{glc}}\left({\tilde{E}}_g^{\text{glc}}\right)$.

The kinetics derived from the experimental data (Fig. 5 D–F) are therefore consistent with the proposed model (Fig. 5 A–C), but it is worth making a final point relating the observed kinetics to the underlying molecular mechanisms. The simultaneous decline of the intracellular TMG level and induction rate immediately after the addition of glucose may lead one to conclude that the induction rate decreased due to the decline of the intracellular TMG level, but this conclusion is not valid. Indeed, Fig. 5 D shows that despite the 3-fold decline of the intracellular TMG level immediately after the addition of glucose, the induction rate remains independent of the intracellular TMG level for some time, i.e., the intracellular TMG concentration is at a saturating level even after its initial decline. It follows that the initial decline of the induction rate is not due to inducer exclusion; hence, it must be due to the decline of the cAMP level that is known to occur immediately after the addition of glucose (31). Although inducer exclusion plays no role in the initial decline of the induction rate, it may be crucial for the subsequent decline of the induction rate when the intracellular TMG level has dropped to sub-saturating levels at which the induction rate is extremely sensitive to variations of the TMG level (32,33).

Discussion

Comparison of our results with studies in the literature

Our work on lac expression in the presence of TMG differs from earlier work with respect to the goal as well as the method. Indeed, because the goal of earlier work was to understand the mechanism of bistability, the theoretical models focused on prediction of the steady states (3,34, 35, 36, 37), and the experiments were primarily concerned with measurement of the induction levels (2,3,38). However, our goal was to understand the mechanism of strong glucose-mediated catabolite repression, which led us to focus on the transients and to measure both the induction and inducer levels.

Our focus on the transients, and the kinetics derived from it, also provides a more conclusive validation of the model. Indeed, in the earlier work cited above, the authors proposed the model kinetics, but verified the model by checking the agreement between the observed and predicted steady states. This method is not conclusive because some other kinetics, distinct from those proposed in the model, can also yield the same steady states. We also proposed model kinetics (Fig. 5 A and B), but we verified the kinetics (Fig. 5 D and E) rather than the steady states predicted by them. Our approach therefore provides a more definitive validation of the model.

Relative roles of the various mechanisms that mediate catabolite repression

We have shown that upon addition of glucose to a culture growing exponentially on TMG + glycerol, the steady-state induction and inducer levels decline dramatically because the induction rate decreases due to the rapid decline of the intracellular TMG and cAMP levels, and the dilution rate increases due to the enhanced specific growth rate (Fig. 5). Importantly, the magnitude of each of these effects is rather small: inducer exclusion reduces the intracellular TMG levels no more than 6-fold (Fig. 2), the decline of the cAMP levels reduces the induction rate 3-fold (Fig. 5 B), and the dilution rate of the lactose enzymes increases only 2-fold (Fig. 5 B). Yet, these small effects, taken together, produce a massive 900-fold repression by shifting the steady-state induction level from ${\tilde{E}}_g^{\text{gly}}$ to ${\tilde{E}}_g^{\text{glc}}$. In what follows, we examine the root cause of this striking result.

The massive repression is mediated by the autocatalytic kinetics of enzyme synthesis. Indeed, our data show that if enzyme synthesis is abolished by adding chloramphenicol, the addition of glucose produces only a modest decline of the permease activity, which reflects the effect of inducer exclusion (Fig. 2). However, our model predicts that the repression reduces drastically even if enzyme synthesis exists, but its rate $r_{E_g}$ is independent of the induction level $E_g$, i.e., the graph of $r_{E_g}$ is a horizontal line rather than the increasing function shown in Fig. 5 E. This can be engineered in two ways: Render $r_{E_g}$ independent of $\tilde{T}$, as is the case in lac-constitutive mutants, or make $\tilde{T}$ independent of $E_g$ by adding excess TMG or IPTG to the culture (in which case inducer is transported primarily by diffusion rather than by LacY). In both cases, $r_{E_g}$ is expected to become independent of $E_g$, and addition of glucose should produce a very modest effect. This is consistent with experiments since there is practically no repression if glucose is added to lac-constitutive mutants (17), and wild-type cells exposed to excess TMG (2). Therefore, it is the existence of autocatalytic enzyme synthesis, as opposed to just enzyme synthesis, that is critical for glucose-mediated lac repression in the presence of small concentrations of the nonmetabolizable inducer TMG.

Implication for the glucose-lactose diauxie of E. coli

It is relevant to ask if autocatalytic induction kinetics are also critical for glucose-mediated lac repression in the presence of the metabolizable substrate lactose. The insights derived from this work suggest that the answer lies in the following two questions:

• 1)Does positive feedback exist during growth on lactose?
• 2)Does positive feedback act (in the reverse direction) when glucose is added to a culture growing on lactose?

If both questions yield an affirmative answer, autocatalytic induction kinetics also play a key role in the glucose-lactose diauxie.

Given what is known about the regulation of lac expression, the first question reduces to the experimentally testable question: Do the lactose enzymes (specifically, permease and β-galactosidase) promote the accumulation of allolactose? Indeed, since allolactose stimulates synthesis of the lactose enzymes, positive feedback exists precisely if the lactose enzymes promote the accumulation of allolactose, i.e., the intracellular allolactose level increases with the induction level as is the case for intracellular TMG (Fig. 5 D). In the sequel to this work (39), we show that this is indeed the case.

To address the second question, it is necessary to ask if upon addition of glucose to a culture growing on lactose, the concentrations of allolactose and β-galactosidase decline in tandem, in a manner analogous to the decline of intracellular TMG and β-galactosidase levels shown in Fig. 4. More importantly, the induction and dilution kinetics derived from the data should have forms similar to those shown in Fig. 5 E. This is also the case as shown in the sequel to this work (39).

The dynamics of glucose-mediated repression of the lac operon in the presence of lactose are therefore analogous to those observed in the presence of small concentrations of TMG.

Conclusions

In this work, we have shown that

• 1)Inducer exclusion, by itself, cannot account for catabolite repression because the repression due to inducer exclusion, which is determined by measuring TMG accumulation in cells exposed to glycerol/glucose, TMG, and chloramphenicol, is $<$ 6-fold.
• 2)When glucose is added to a culture growing on glycerol and small concentrations of TMG, but no chloramphenicol, the lac operon is repressed 900-fold which is almost entirely due to positive feedback. It follows that $<$ 6-fold repression observed in the inducer exclusion experiments is due to the presence of chloramphenicol which abolishes enzyme synthesis, and hence, positive feedback.
• 3)The abolition of positive feedback also explains the weak repression observed upon addition of glucose to lacI⁻ cells, and wild-type cells exposed to high concentrations of TMG.

Author contributions

R.K.A. and A.N. designed the study and experiments, R.K.A. obtained the experimental results, R.K.A. and A.N. analyzed the data, and R.K.A. and A.N. wrote the manuscript.

Editor: Stanislav Shvartsman.