Predicting the asymmetric response of a genetic switch to noise

We present a simple analytical tool which gives an approximate insight into the stationary behavior of nonlinear systems undergoing the influence of a weak and rapid noise from one dominating source, e.g. the kinetic equations describing a genetic switch with the concentration of one substrate fluctuating around a constant mean. The proposed method allows for predicting the asymmetric response of the genetic switch to noise, arising from the noise-induced shift of stationary states. The method has been tested on an example model of the lac operon regulatory network: a reduced Yildirim-Mackey model with fluctuating extracellular lactose concentration. We calculate analytically the shift of the system's stationary states in the presence of noise. The results of the analytical calculation are in excellent agreement with the results of numerical simulation of the noisy system. The simulation results suggest that the structure of the kinetics of the underlying biochemical reactions protects the bistability of the lactose utilization mechanism from environmental fluctuations. We show that, in the consequence of the noise-induced shift of stationary states, the presence of fluctuations stabilizes the behavior of the system in a selective way: Although the extrinsic noise facilitates, to some extent, switching off the lactose metabolism, the same noise prevents it from switching on.     

Bistability of the <Emphasis Type="Italic">lac</Emphasis> Operon During Growth of <Emphasis Type="Italic">Escherichia coli</Emphasis> on Lactose and Lactose + Glucose

The lac operon of Escherichia coli can exhibit bistability. Early studies showed that bistability occurs during growth on TMG/succinate and lactose + glucose, but not during growth on lactose. More recently, studies with lacGFP-transfected cells show bistability during growth on TMG/succinate, but not during growth on lactose and lactose + glucose. In the literature, these results are invariably attributed to variations in the destabilizing effect of the positive feedback generated by induction. Specifically, during growth on TMG/succinate, lac induction generates strong positive feedback because the permease stimulates the accumulation of intracellular TMG, which in turn, promotes the synthesis of even more permease. This positive feedback is attenuated during growth on lactose because hydrolysis of intracellular lactose by β-galactosidase suppresses the stimulatory effect of the permease. It is attenuated even more during growth on lactose + glucose because glucose inhibits the uptake of lactose. But it is clear that the stabilizing effect of dilution also changes dramatically as a function of the medium composition. For instance, during growth on TMG/succinate, the dilution rate of lac permease is proportional to its activity, e, because the specific growth rate is independent of e (it is completely determined by the concentration of succinate). However, during growth on lactose, the dilution rate of the permease is proportional to e ² because the specific growth rate is proportional to the specific lactose uptake rate, which in turn, proportional to e. We show that: (a) This dependence on e ² creates such a strong stabilizing effect that bistability is virtually impossible during growth on lactose, even in the face of the intense positive feedback generated by induction. (b) This stabilizing effect is weakened during growth on lactose + glucose because the specific growth rate on glucose is independent of e, so that the dilution rate once again contains a term that is proportional to e. These results imply that the lac operon is much more prone to bistability if the medium contains carbon sources that cannot be metabolized by the lac enzymes, e.g., succinate during growth on TMG/succinate and glucose during growth on lactose + glucose. We discuss the experimental data in the light of these results.     

lac operon induction in Escherichia coli: Systematic comparison of IPTG and TMG induction and influence of the transacetylase LacA

Most commonly used expression systems in bacteria are based on the Escherichia coli lac promoter. Furthermore, lac operon elements are used today in systems and synthetic biology. In the majority of the cases the gratuitous inducers IPTG or TMG are used. Here we report a systematic comparison of lac promoter induction by TMG and IPTG which focuses on the aspects inducer uptake, population heterogeneity and a potential influence of the transacetylase, LacA. We provide induction curves in E. coli LJ110 and in isogenic lacY and lacA mutant strains and we show that both inducers are substrates of the lactose permease at low inducer concentrations but can also enter cells independently of lactose permease if present at higher concentrations. Using a gfp reporter strain we compared TMG and IPTG induction at single cell level and showed that bimodal induction with IPTG occurred at approximately ten-fold lower concentrations than with TMG. Furthermore, we observed that lac operon induction is influenced by the transacetylase, LacA. By comparing two Plac-gfp reporter strains with and without a lacA deletion we could show that in the lacA⁺ strain the fluorescence level decreased after few hours while the fluorescence further increased in the lacA⁻ strain. The results indicate that through the activity of LacA the IPTG concentration can be reduced below an inducing threshold concentration—an influence that should be considered if low inducer amounts are used.     

Subpopulations of sensorless bacteria drive fitness in fluctuating environments

Populations of bacteria often undergo a lag in growth when switching conditions. Because growth lags can be large compared to typical doubling times, variations in growth lag are an important but often overlooked component of bacterial fitness in fluctuating environments. We here explore how growth lag variation is determined for the archetypical switch from glucose to lactose as a carbon source in Escherichia coli. First, we show that single-cell lags are bimodally distributed and controlled by a single-molecule trigger. That is, gene expression noise causes the population before the switch to divide into subpopulations with zero and nonzero lac operon expression. While “sensorless” cells with zero preexisting lac expression at the switch have long lags because they are unable to sense the lactose signal, any nonzero lac operon expression suffices to ensure a short lag. Second, we show that the growth lag at the population level depends crucially on the fraction of sensorless cells and that this fraction in turn depends sensitively on the growth condition before the switch. Consequently, even small changes in basal expression can significantly affect the fraction of sensorless cells, thereby population lags and fitness under switching conditions, and may thus be subject to significant natural selection. Indeed, we show that condition-dependent population lags vary across wild E. coli isolates. Since many sensory genes are naturally low expressed in conditions where their inducer is not present, bimodal responses due to subpopulations of sensorless cells may be a general mechanism inducing phenotypic heterogeneity and controlling population lags in switching environments. This mechanism also illustrates how gene expression noise can turn even a simple sensory gene circuit into a bet hedging module and underlines the profound role of gene expression noise in regulatory responses.

Is ignorance bliss for some bacterial cells? Single-cell analysis of the archetypical switch from glucose to lactose as a carbon source in E. coli shows that bacteria can exhibit stochastic bimodal responses to external stimuli because the corresponding sensory circuit is so lowly expressed that some cells are effectively blind to the stimulus.     

Substrate selectivity of the melibiose permease (MelY) from Enterobacter cloacae

We have examined the substrate selectivity of the melibiose permease (MelY) from Enterobacter cloacae in comparison with that of the lactose permease (LacY) from Escherichia coli. Both proteins catalyze active transport of lactose or melibiose with comparable affinity and capacity. However, MelY does not transport the analogue methyl-1-thio-β,d-galactopyranoside (TMG), which is a very efficient substrate in LacY. We show that MelY binds TMG and conserves Cys148 (helix V) as a TMG binding residue but fails to transport this ligand. Based on homology modeling, organization of the putative MelY sugar binding site is the same as that in LacY and residues irreplaceable for the symport mechanism are conserved. Moreover, only 15% of the residues where a single-Cys mutant is inactivated by site-directed alkylation differ in MelY. Using site-directed mutagenesis at these positions and engineered cross-homolog chimeras, we show that Val367, at the periplasmic end of transmembrane helix XI, contributes in defining the substrate selectivity profile. Replacement of Val367 with the MelY residue (Ala) leads to impairment of TMG uptake. Exchanging domains N6 and C6 between LacY and MelY also leads to impairment of TMG uptake. TMG uptake activity is restored by the re-introduction of a Val367 in the background of chimera N6(LacY)-C6(MelY). Much less prominent effects are found with the same mutants and chimeras for the transport of lactose or melibiose.     

beta-D-phosphogalactoside galactohydrolase of Streptococcus faecalis and the inhibition of its synthesis by glucose.

The lactose hydrolysing system of Streptococcus faecalis is described. It is closely related to that one of the group N streptocci as it consists of a beta-D-phosphogalactoside galactohydrolase (beta-Pgal). The uptake of methyl-beta-D-thiogalactoside (TMG), lactose, and glucose is maintained by the phosphoenolpyruvate-dependent phosphotransferase system (PTS) but the uptake of galactose is not. The induction time is 6--7 min. Inducers are lactose and galactose but not isopropyl-beta-D-galactoside (IPTG) and TMG. In the presence of glucose, mannose, and maltose no induction of beta-Pgal occurs but pyruvate and glycerol allow induction. The competitive inhibition of uptake of TMG by glucose suggests inducer exclusion by this sugar. TMG accumulates in the cells exclusively as a derivative.     

Phosphorylation of a sugar-specific protein component of the lactose transport system in Staphylococcus aureus

A sugar-specific component of the lactose transport system in Staphylococcus aureus, Factor III^lac, is phosphorylated as an intermediate in the over-all transfer of a phosphoryl group from PEP to lactose. P-III^lac is isolated and shown to be a substrate for the final phosphoryl transfer reaction to sugar, catalyzed by Enzyme II^lac.     

Coregulation of beta-galactoside uptake and hydrolysis by the hyperthermophilic bacterium Thermotoga neapolitana

Regulation of the beta-galactoside transport system in response to growth substrates in the extremely thermophilic anaerobic bacterium Thermotoga neapolitana was studied with the nonmetabolizable analog methyl-beta-D-thiogalactopyranoside (TMG) as the transport substrate. T. neapolitana cells grown on galactose or lactose accumulated TMG against a concentration gradient in an intracellular free sugar pool that was exchangeable with external galactose or lactose and showed induced levels of beta-galactosidase. Cells grown on glucose, maltose, or galactose plus glucose showed no capacity to accumulate TMG, though these cells carried out active transport of the nonmetabolizable glucose analog 2-deoxy-D-glucose. Glucose neither inhibited TMG uptake nor caused efflux of preaccumulated TMG; rather, glucose promoted TMG uptake by supplying metabolic energy. These data show that beta-D-galactosides are taken up by T. neapolitana via an active transport system that can be induced by galactose or lactose and repressed by glucose but which is not inhibited by glucose. Thus, the phenomenon of catabolite repression is present in T. neapolitana with respect to systems catalyzing both the transport and hydrolysis of beta-D-galactosides, but inducer exclusion and inducer expulsion, mechanisms that regulate permease activity, are not present. Regulation is manifest at the level of synthesis of the beta-galactoside transport system but not in the activity of the system.     

Positive feedback exists and drives the glucose-mediated repression in Escherichia coli

The expression of the lac operon of E. coli is subject to positive feedback during growth in the presence of gratuitous inducers, but its existence in the presence of lactose remains controversial. The key question in this debate is: Do the lactose enzymes, Lac permease and β-galactosidase, promote accumulation of allolactose? If so, positive feedback exists since allolactose does stimulate synthesis of the lactose enzymes. Here, we addressed the above question by developing methods for determining the intracellular allolactose concentration as well as the kinetics of enzyme induction and dilution. We show that, during lac induction in the presence of lactose, the intracellular allolactose concentration increases with the lactose enzyme level, which implies that lactose enzymes promote allolactose accumulation, and positive feedback exists. We also show that, during lac repression in the presence of lactose + glucose, the intracellular allolactose concentration decreases with the lactose enzyme levels, which suggests that, under these conditions, the positive feedback loop turns in the reverse direction. The induction and dilution rates derived from the transient data show that the positive feedback loop is reversed due to a radical shift of the steady-state induction level. This is formally identical to the mechanism driving catabolite repression in the presence of TMG + glucose.     

Differences in uncoupling effects associated with the uptake of lactose and dansyl-galactoside in Escherichia coli membrane: Active transport versus specific binding

Cytoplasmic membrane vesicles isolated from Escherichia coli take up dansyl-galactoside, a fluorescent competitive inhibitor of lactose transport, to much lower levels than lactose. An initial interpretation, based on the study of the fluorescent changes accompanying the energy-dependent uptake, was that it represented a one-to-one specific binding to the lac carrier protein which was not followed by transport. Recently, on the basis of a new estimation of the number of lac carrier in the membrane, it has been advanced that the uptake of dansyl-galactoside represents a nonspecific binding on the inner surface of the membrane following transport. We discriminate between the two interpretations by comparing the effects of lactose and dansyl-galactoside uptake on the electrochemical gradient of protons ($\text{Δ}\text{}\text{?}\text{gm}{}_{\mathrm{H}}\text{+}$), generated by the oxidation of substrates, and on the uptake of proline. Indeed, it is known that the rate of lactose transport is such that it leads, as a consequence of the lactose/H⁺ symport, to an observable decrease of $\text{Δ}\text{}\text{?}\text{gm}{}_{\mathrm{H}}\text{+}$, and secondary to this decrease to an inhibition of the uptake of proline transported at much lower rate. We show that the rates of uptake of lactose and dansyl-galactoside by the membrane vesicles are similar; yet the uptake of dansyl-galactoside does not lead to the uncoupling effects which are associated with the uptake of lactose. We discuss the possible reasons for the absence of this uncoupling effect, and we conclude that our data are incompatible with the notion that the energy-dependent uptake of dansyl-galactoside is associated with an active transport involving a dansyl-galactoside/H⁺ symport. On the contrary, the data substantiate the initial interpretation that the energy-dependent uptake of dansyl-galactoside reflects the binding to the lac carrier not followed by transport.     

Inhibition of growth of Escherichia coli by lactose and other galactosides

A study has been made of the inhibition of growth caused by the addition of lactose or other galactosides to lac constitutive Escherichia coli growing in glycerol minimal medium. The effect was greater at pH 5.9 and pH 7.9 than at pH 7.0. Inhibition of growth by lactose was observed also in the case of a β-galactosidase negative mutant. However, a lacY mutant, which has a defect in the entry of protons normally coupled with galactoside transport, showed only slight inhibition of growth on the addition of galactosides. In the case of the parental strain the addition of lactose resulted in a sharp fall in ΔpH across the cell membrane and a reduction in intracellular ATP, and the recovery was slow. Under the same conditions the lacY mutant showed a smaller and only transient effect. It is postulated that the sudden entry of protons associated with lactose uptake lowers the protonmotive force, reducing the ATP levels and inhibiting growth of the cells. This hypothesis would account also for the selection of lacY mutants found when E. coli is grown in the presence of isopropyl-β-d-thiogalactoside.     

Evolution of a regulated operon in the laboratory

The evolution of new metabolic functions is being studied in the laboratory using the EBG system of E. coli as a model system. It is demonstrated that the evolution of lactose utilization by lacZ deletion strains requires a series of structural and regulatory gene mutations. Two structural gene mutations act to increase the activity of ebg enzyme toward lactose, and to permit ebg enzyme to convert lactose into allolactose, an inducer of the lac operon. A regulatory mutation increases the sensitivity of the ebg repressor to lactose, and permits sufficient ebg enzyme activity for growth. The resulting fully evolved ebg operon regulates its own expression, and also regulates the synthesis of the lactose permease.     

The expression of β-galactosidase by Escherichia coli during continuous culture

We have used the technique of continuous culture to study the expression of β-galactosidase in Escherichia coli. In these experiments the cultures were grown on carbon-limited media in which half of the available carbon was supplied as glycerol, glucose, or glucose 6-phosphate, and the other half as lactose. Lactose itself provided the sole source of inducer for the lac operon. The steady-state specific activity of the enzyme passed through a maximal value as a function of dilution rate. Moreover, the rate at which activity was maximal (0.40 h^?1) and the observed specific activity of the enzyme at a given growth rate were found to be identical in each of the three media tested. This result was unexpected, since the steady-state specific activity can be shown to be equal to the differential rate of enzyme synthesis, and since it is known that glycerol, glucose, and glucose-6-P-cause different degrees of catabolite repression in batch culture. The differential rate of β-galactosidase synthesis was an apparently linear function of the rate of lactose utilization per milligram protein regardless of the composition of the input medium. That is, it is independent of the rate of metabolism of substrates other than lactose which are concurrently being utilized and the enzyme level appears to be matched to the metabolic requirement for it. If this relationship is taken to indicate the existence of a fundamental control mechanism, it may represent a form of attenuation of the rate of β-galactosidase synthesis which is independent of cyclic AMP levels.     

Design of the lac gene circuit revisited

The lactose (lac) operon of Escherichia coli serves as the paradigm for gene regulation, not only for bacteria, but also for all biological systems from simple phage to humans. The details of the systems may differ, but the key conceptual framework remains, and the original system continues to reveal deeper insights with continued experimental and theoretical study. Nearly as long lasting in impact as the pivotal work of Jacob and Monod is the classic experiment of Novick and Weiner in which they demonstrated all-or-none gene expression in response to an artificial inducer. These results are often cited in claims that normal gene expression is in fact a discontinuous bistable phenomenon. In this paper, I review several levels of analysis of the lac system and introduce another perspective based on the construction of the system design space. These represent variations on a theme, based on a simply stated design principle, that captures the key qualitative features of the system in a largely mechanism-independent fashion. Moreover, this principle can be readily interpreted in terms of specific mechanisms to make predictions regarding monostable vs. bistable behavior. The regions of design space representing bifurcations are compared with the corresponding regions identified through bifurcation analysis. I present evidence based on biological considerations as well as modeling and analysis to suggest that induction of the lac system in its natural setting is a monostable continuously graded phenomenon. Nevertheless, it must be acknowledged that the lac stability question remains unsettled, and it undoubtedly will remain so until there are definitive experimental results.     

The melibiose permease system of Escherichia coli K12

The melibiose permease system of E. coli K12 has been explored using a strain deficient in lactose permease: 300 P. The accumulation of 1-S-methyl-beta-D-thiogalactopyranoside (TMG) was observed. The uptake system was inducible by melibiose and a number of analogs at 30 degrees C. At higher temperatures the differential rate of synthesis decreases until becoming negligible at 42 degrees C. The uptake tends toward a steady state which corresponds to an accumulation several hundredfold over the sugar concentration in the medium. At a given temperature the steady state level was proportional to the initial rate of uptake whatever the degree of induction and the substrate concentration. Lowering the temperature decreased the initial rate of uptake but increased the steady state level. This uptake system was pH dependent with better efficiency at pH 8. It was also dependent on the presence of sodium or lithium ions active at 5 mM whereas potassium at 170 mM enable only about half maximal uptake. The uptake in a medium with choline chloride was less than one fifth of optimal activity. Addition of Li+ brought about half maximal activation at approximately 0.5 mM. The activation consists mainly in a decrease of apparent Km. The emphasis of this study was put on the similarities and differences with lactose permease which is able to transport the same sugar to approximately the same extent. Inducer specificities and substrate specificities were compared and a method of measuring the two activities in the same cells was devised.     

Role of Na+ and Li+ in thiomethylgalactoside transport by the melibiose transport system of Escherichia coli.

Thiomethyl-beta-galactoside (TMG) accumulation via the melibiose transport system was studied in lactose transport-negative strains of Escherichia coli. TMG uptake by either intact cells or membrane vesicles was markedly stimulated by Na+ or Li+ between pH 5.5 and 8. The Km for uptake of TMG was approximately 0.2 mM at an external Na+ concentration of 5 mM (pH 7). The alpha-galactosides, melibiose, methyl-alpha-galactoside, and o-nitrophenyl-alpha-galactoside had a high affinity for this system whereas lactose, maltose and glucose had none. Evidence is presented for Li+-TMG or Na+-TMG cotransport.     

Regulation of the glucose:H+ symporter by metabolite-activated ATP-dependent phosphorylation of HPr in Lactobacillus brevis.

Lactobacillus brevis takes up glucose and the nonmetabolizable glucose analog 2-deoxyglucose (2DG), as well as lactose and the nonmetabolizable lactose analoge thiomethyl beta-galactoside (TMG), via proton symport. Our earlier studies showed that TMG, previously accumulated in L. brevis cells via the lactose:H+ symporter, rapidly effluxes from L. brevis cells or vesicles upon addition of glucose and that glucose inhibits further accumulation of TMG. This regulation was shown to be mediated by a metabolite-activated protein kinase that phosphorylase serine 46 in the HPr protein. We have now analyzed the regulation of 2DG uptake and efflux and compared it with that of TMG. Uptake of 2DG was dependent on an energy source, effectively provided by intravesicular ATP or by extravesicular arginine which provides ATP via an ATP-generating system involving the arginine deiminase pathway. 2DG uptake into these vesicles was not inhibited, and preaccumulated 2DG did not efflux from them upon electroporation of fructose 1,6-diphosphate or gluconate 6-phosphate into the vesicles. Intravesicular but not extravesicular wild-type or H15A mutant HPr of Bacillus subtilis promoted inhibition (53 and 46%, respectively) of the permease in the presence of these metabolites. Counterflow experiments indicated that inhibition of 2DG uptake is due to the partial uncoupling of proton symport from sugar transport. Intravesicular S46A mutant HPr could not promote regulation of glucose permease activity when electroporated into the vesicles with or without the phosphorylated metabolites, but the S46D mutant protein promoted regulation, even in the absence of a metabolite. The Vmax but not the Km values for both TMG and 2DG uptake were affected. Uptake of the natural, metabolizable substrates of the lactose, glucose, mannose, and ribose permeases was inhibited by wild-type HPr in the presence of fructose 1,6-diphosphate or by S46D mutant HPr. These results establish that HPr serine phosphorylation by the ATP-dependent, metabolite-activated HPr kinase regulates glucose and lactose permease activities in L. brevis and suggest that other permeases may also be subject to this mode of regulation.