Origin of bistability in the lac Operon

Multistability is an emergent dynamic property that has been invoked to explain multiple coexisting biological states. In this work, we investigate the origin of bistability in the lac operon. To do this, we develop a mathematical model for the regulatory pathway in this system and compare the model predictions with other experimental results in which a nonmetabolizable inducer was employed. We investigate the effect of lactose metabolism using this model, and show that it greatly modifies the bistable region in the external lactose (Le) versus external glucose (Ge) parameter space. The model also predicts that lactose metabolism can cause bistability to disappear for very low Ge. We have also carried out stochastic numerical simulations of the model for several values of Ge and Le. Our results indicate that bistability can help guarantee that Escherichia coli consumes glucose and lactose in the most efficient possible way. Namely, the lac operon is induced only when there is almost no glucose in the growing medium, but if Le is high, the operon induction level increases abruptly when the levels of glucose in the environment decrease to very low values. We demonstrate that this behavior could not be obtained without bistability if the stability of the induced and uninduced states is to be preserved. Finally, we point out that the present methods and results may be useful to study the emergence of multistability in biological systems other than the lac operon.     

Regulation of the galactose-inducible lac operon and the histidine utilization operons in pts mutants of Klebsiella aerogenes.

Galactose appears to be the physiological inducer of the chromosomal lac operon in Klebsiella aerogenes. Both lactose and galactose are poor inducers in strains having a functional galactose catabolism (gal) operon, but both are excellent inducers in gal mutants. Thus the slow growth of K. aerogenes on lactose reflects the rapid degradation of the inducer. Several pts mutations were characterized and shown to affect both inducer exclusion and permanent catabolite repression. The beta-galactosidase of pts mutants cannot be induced at all by lactose, and pts mutants appear to have a permanent and constitutive inducer exclusion phenotype. In addition, pts mutants show a reduced rate of glucose metabolism, leading to slower growth on glucose and a reduced degree of glucose-mediated permanent catabolite repression. The crr-type pseudorevertants of pts mutations relieve the constitutive inducer exclusion for lac but do not restore the full level of glucose-mediated permanent catabolite repression and only slightly weaken the glucose-mediated inducer exclusion. Except for weakening the glucose-mediated permanent catabolite repression, pts and crr mutations have no effect on expression of the histidine utilization (hut) operons.     

A mutant Ebg enzyme that converts lactose into an inducer of the lac operon.

Lactose is not itself an inducer of the lac operon, nor is it converted to an inducer by ebg+ beta-galactosidase of Escherichia coli. We report here the isolation of a mutant Ebg beta-galactosidase which is capable of converting lactose into an inducer of the lac operon.     

Studies on beta-galactoside transport in a Proteus mirabilis merodiploid carrying an Escherichia coli lactose operon

Merodiploid derivatives bearing an F-linked lac operon (i(+), o(+), z(+), y(+), a(+)) from Escherichia coli were prepared from a Proteus mirabilis strain unable to utilize lactose and from a lac deletion strain of E. coli. A suitable growth medium was found in which the episomal element in the P. mirabilis derivative was sufficiently stable to allow induction of the episome-borne lac operon and thus to permit a comparison of the activities and properties of E. coli lac products in the intracellular environments of P. mirabilis and E. coli. In both derivatives the episomal lac operon was shown to be repressed in the absence of inducer. Kinetics of induction with gratuitous inducer (isopropyl-1-thio-beta-d-galactoside) were similar for both beta-galactosidase activity (beta-d-galactoside galactohydrolase, EC 3.4.1.23) and beta-galactoside transport activity in both derivatives, although the ratio of galactoside transport to beta-galactosidase activity was approximately 1.6-fold higher in the E. coli derivative. Comparison of beta-galactosidase and M-protein (lac y gene product)-specific activities indicated coordinate expression of the induced lac operon in both derivatives. Quantitatively, the maximal beta-galactosidase specific activity was two or three times higher for the E. coli derivative. A significant sodium azide inhibition (65% inhibition by 10 mM sodium azide) of lactose permease-mediated transport of o-nitrophenyl-beta-galactoside from an outside region of high concentration to an inside region of very low concentration ("downhill transport") was observed for the P. mirabilis derivative. Identical conditions for the E. coli derivative yielded only about 15% inhibition. Active transport of thiomethyl-beta-galactoside was similar for both derivatives, the major difference being that active transport was more sensitive to azide poisoning in the P. mirabilis derivative. Preliminary examination of the thiomethyl-beta-galactoside derivatives following active transport did not demonstrate the accumulation of a phosphorylated product in either strain but did reveal an unidentified derivative present in the P. mirabilis merodiploid extract which was not detectable in the E. coli merodiploid.     

Physiological studies of beta-galactosidase induction in Kluyveromyces lactis

We examined the kinetics of beta-galactosidase (EC 3.2.1.23) induction in the yeast Kluyveromyces lactis. Enzyme activity began to increase 10 to 15 min, about 1/10 of a cell generation, after the addition of inducer and continued to increase linearly for from 7 to 9 cell generations before reaching a maximum, some 125- to 150-fold above the basal level of uninduced cells. Thereafter, as long as logarithmic growth was maintained, enzyme levels remained high, but enzyme levels dropped to a value only 5- to 10-fold above the basal level if cells entered stationary phase. Enzyme induction required the constant presence of inducer, since removal of inducer caused a reduction in enzyme level. Three nongratuitous inducers of beta-galactosidase activity, lactose, galactose, and lactobionic acid, were identified. Several inducers of the lac operon of Escherichia coli, including methyl-, isopropyl- and phenyl-1-thio-beta-d-galactoside, and thioallolactose did not induce beta-galactosidase in K. lactis even though they entered the cell. The maximum rate of enzyme induction was only achieved with lactose concentrations of greater than 1 to 2 mM. The initial differential rate of beta-galactosidase appearance after induction was reduced in medium containing glucose, indicating transient carbon catabolite repression. However, glucose did not exclude lactose from K. lactis, it did not cause permanent carbon catabolite repression of beta-galactosidase synthesis, and it did not prevent lactose utilization. These three results are in direct contrast to those observed for lactose utilization in E. coli. Furthermore, these results, along with our observation that K. lactis grew slightly faster on lactose than on glucose, indicate that this organism has evolved an efficient system for utilizing lactose.     

Transport regulation of recombinant gene expression in E. coli and B. subtilis

Expression kinetics of the lactose (lac) operon in Escherichia coli are reviewed for both wild-type and recombinant cell cultures under chemostatic conditions. A unified model which involves regulation of active inducer (lactose) transport, promoter-operator regulated expression of the lac operon, glucose-mediated inducer exclusion, and catabolite repression is summarized and supporting data is shown to verify its accuracy. The synthesis of alpha-amylase with a recombinant form of Bacillus subtilis is also reviewed to point out generic features in transport regulation, the lac operon model providing a point of departure. While there are many similarities in the influence of transport on both regulating models, there are also important differences. In a chemostat system, the synthesis of alpha-amylase is nongrowth associated, while beta-galactosidase is a growth-associated enzyme. Nevertheless, transport regulation is an important feature in both instances.     

Glucose-lactose diauxie in Escherichia coli

Growth of Escherichia coli in medium containing glucose, at a concentration insufficient to support full growth, and containing lactose, is diauxic. A mutation in the gene, CR, which determines catabolite repression specific to the lac operon, was found to relieve glucose-lactose but not glucose-maltose diauxie. Furthermore, a high concentration of lactose was shown to overcome diauxie in a CR(+) strain. Studies on the induction of beta-galactosidase by lactose suggested that glucose inhibits induction by 10(-2)m lactose. Preinduction of the lac operon was found to overcome this effect. The ability of glucose to prevent expression of the lac operon by reducing the internal concentration of inducer as well as by catabolite repression is discussed.     

Adaptive evolution of the lactose utilization network in experimentally evolved populations of Escherichia coli

Adaptation to novel environments is often associated with changes in gene regulation. Nevertheless, few studies have been able both to identify the genetic basis of changes in regulation and to demonstrate why these changes are beneficial. To this end, we have focused on understanding both how and why the lactose utilization network has evolved in replicate populations of Escherichia coli. We found that lac operon regulation became strikingly variable, including changes in the mode of environmental response (bimodal, graded, and constitutive), sensitivity to inducer concentration, and maximum expression level. In addition, some classes of regulatory change were enriched in specific selective environments. Sequencing of evolved clones, combined with reconstruction of individual mutations in the ancestral background, identified mutations within the lac operon that recapitulate many of the evolved regulatory changes. These mutations conferred fitness benefits in environments containing lactose, indicating that the regulatory changes are adaptive. The same mutations conferred different fitness effects when present in an evolved clone, indicating that interactions between the lac operon and other evolved mutations also contribute to fitness. Similarly, changes in lac regulation not explained by lac operon mutations also point to important interactions with other evolved mutations. Together these results underline how dynamic regulatory interactions can be, in this case evolving through mutations both within and external to the canonical lactose utilization network.     

Enzymatic adaptation by bacteria under pressure.

A study of enzymic adaptation under hydrostatic pressure by moderately barotolerant bacteria that can grow at pressure up to about 500 atm revealed that some adaptive processes are relatively insensitive to pressure, whereas others are sufficiently barosensitive to compromise survival capacity in situations requiring adaptation to new substrates under pressure. Examples of the former include adaptation of Escherichia coli to arabinose catabolism for growth and adaptation of Streptococcus faecalis to catabolism of lactose, ribose, or maltose. Examples of the latter include derepression of the lac operon in Escherichia coli and induction of penicillinase synthesis by Bacillus licheniformis. For both these barosensitive systems, pressure had little effect on enzyme levels in constitutive strains or in bacteria that had previously been induced at 1 atm. Moreover, it had no detectable effect on penicillinase secretion. However, pressures of 300 to 400 atm were found to reduce markedly rates and extents of enzyme synthesis by bacteria undergoing derepression or adaptation. This inhibitory effect of pressure was reflected in greater barosensitivity with extended lag and slower growth of initially unadapted Escherichia coli cells inoculated into minimal medium with lactose as sole source of carbon and fuel, and by major reductions in the minimal inhibitory concentrations of penicillin G for unadapted B. licheniformis cells inoculated into complex, antibiotic-containing media. Cyclic adenosine 5'-monophosphate did not reverse pressure inhibition of derepression of the lac operon, and catabolite repression was complete under pressure. However, derepression of the lac operon was more sensitive to pressure at low concentrations of inducer than at high concentrations. Apparent volume changes for derepression were 94 and 60 ml/mol at inducer concentrations of about 0.5 and 5 mM, respectively. Pressure was found not to be inhibitory for uptake of beta-galactosides; in fact, it was somewhat stimulatory. Therefore, results were interpreted in terms of inducer binding and subsequent conversion of an operator-inducer-repressor complex to inactive repressor and operator. Both reactions appeared to result in an increase in volume, the former more so than the latter. We found also that 200 atm was actually stimulatory for growth of Escherichia coli in minimal media, and the bacterium was in a sense barophilic.     

The lac repressor

Few proteins have had such a strong impact on a field as the lac repressor has had in Molecular Biology. Over 40 years ago, Jacob and Monod [Genetic regulatory mechanisms in the synthesis of proteins, J. Mol. Biol. 3 (1961) 318] proposed a model for gene regulation, which survives essentially unchanged in contemporary textbooks. It is a cogent depiction of how a set of 'structural' genes may be coordinately transcribed in response to environmental conditions and regulates metabolic events in the cell. In bacteria, the genes required for lactose utilization are negatively regulated when a repressor molecule binds to an upstream cis activated operator. The repressor and its operator together form a genetic switch, the lac operon. The switch functions when inducer molecules alter the conformation of the repressor in a specific manner. In the presence of a particular metabolite, the repressor undergoes a conformational change that reduces its affinity for the operator. The structures of the lac repressor and its complexes with operator DNA and effector molecules have provided a physical platform for visualizing at the molecular level the different conformations the repressor and the molecular basis for the switch. The structures of lac repressor, bound to its operator and inducer, have also been invaluable for interpreting a plethora of biochemical and genetic data.     

DNA Sequence Analysis of Artificially Evolved Ebg Enzyme and Ebg Repressor Genes

The ebg system has been used as a model to study the artificial selection of new catalytic functions of enzymes and of inducer specificities of repressors. A series of mutant enzymes with altered catalytic specificities were previously characterized biochemically as were the changes in inducer specificities of mutant, but fully functional, repressors. The wild type ebg operon has been sequenced, and the sequence differences of the mutant enzymes and repressors have been determined. We now report that, contrary to our previous understanding, ebg enzyme contains 180-kD alpha-subunits and 20-kD beta-subunits, both of which are required for full activity. Mutations that dramatically affect substrate specificity and catalytic efficiency lie in two distinct regions, both well outside of the active site region. Mutations that affect inducer specificity of the ebg repressor lie within predicted sugar binding domains. Comparisons of the ebg beta-galactosidase and repressor with homologous proteins of the Escherichia coli and Klebsiella pneumoniae lac operons, and with the galactose operon repressor, suggest that the ebg and lac operons diverged prior to the divergence of E. coli from Klebsiella. One case of a triple substitution as the consequence of a single event is reported, and the implications of that observation for mechanisms of spontaneous mutagenesis are discussed.     

Ni2+-based immobilized metal ion affinity chromatography of lactose operon repressor protein from Escherichia coli

A two-step chromatographic sequence is described for the purification of native lactose operon repressor protein from Escherichia coli cells. The first step involves Ni(2+)-based immobilized metal ion affinity chromatography of the soluble cytoplasmic extract. This method provides superior speed, resolution and yield than the established phosphocellulose cation-exchange chromatographic procedure. Anion-exchange chromatography is used for further purification to >95% purity. The identity and purity of the lactose repressor protein were demonstrated using sodium dodecylsulphate polyacrylamide electrophoresis, crystallization, tryptic finger-printing mass spectrometry, and inducer binding assays. The purified lac repressor exhibited inducer sensitivity for operator DNA binding and undergoes a conformational change upon inducer binding. By all these extensive biochemical criteria, the purified protein behaves exactly as that described for the Escherichia coli lactose operon repressor.     

Bistable behavior in a model of the lac operon in Escherichia coli with variable growth rate

This work is a continuation from another study previously published in this journal. Both the former and the present works are dedicated to investigating the bistable behavior of the lac operon in Escherichia coli from a mathematical modeling point of view. In the previous article, we developed a detailed mathematical model that accounts for all of the known regulatory mechanisms in this system, and studied the effect of inducing the operon with lactose instead of an artificial inducer. In this article, the model is improved to account, in a more detailed way, for the interaction of the repressor molecules with the three lac operators. A recently discovered cooperative interaction between the CAP molecule (an activator of the lactose operon) and Operator 3 (which influences DNA folding) is also included in this new version of the model. The growth rate dependence on the rate of energy entering the bacteria (in the form of transported glucose molecules and of metabolized lactose molecules) is also considered. A large number of numerical experiments is carried out with this improved model. The results are discussed in regard to the bistable behavior of the lactose operon. Special attention is paid to the effect that a variable growth rate has on the system dynamics.