Synthesis, utilization and degradation of lactose operon mRNA in Escherichia coli

Modeling Gene Expression: Lac operon

Gene regulation is an essential process for cell development, having a profound effect in dictating cell functions. Bacterial genes are often regulated through inducible systems like the Lac operon which plays an important role in cell metabolism. An accurate model of its regulation can reveal the dynamics of gene expression. In this paper, a mathematical model of this system is constructed by focusing on regulation by the Lac repressor. The results show, as expected, that the concentration of lactose approaches zero while glucose concentration approaches the initial concentration of lactose by the action of β-galactosidase, expressed by the Lac operon. Addition of PD control improves stability of the system, with the phase margin increasing from 45° to 90°. Modeling the dynamics of gene expression in inducible operons like Lac operon can be essential for its applications in the production of recombinant proteins and its potential usage in gene therapy.

Quantifying heterogeneity of stochastic gene expression

The heterogeneity of stochastic gene expression, which refers to the temporal fluctuation in a gene product and its cell-to-cell variation, has attracted considerable interest from biologists, physicists, and mathematicians. The dynamics of protein production and degradation have been modeled as random processes with transition probabilities. However, there is a gap between theory and phenomena, particularly in terms of analytical formulation and parameter estimation. In this study, we propose a theoretical framework in which we present a basic model of a gene regulatory system, derive a steady-state solution, and provide a Bayesian approach for estimating the model parameters from single-cell experimental data. The proposed framework is demonstrated to be applicable for various scales of single-cell experiments at both the mRNA and protein levels and is useful for comparing kinetic parameters across species, genomes, and cell strains.

Strategy revealing phenotypic differences among synthetic oscillator designs

Considerable progress has been made in identifying and characterizing the component parts of genetic oscillators, which play central roles in all organisms. Nonlinear interaction among components is sufficiently complex that mathematical models are required to elucidate their elusive integrated behavior. Although natural and synthetic oscillators exhibit common architectures, there are numerous differences that are poorly understood. Utilizing synthetic biology to uncover basic principles of simpler circuits is a way to advance understanding of natural circadian clocks and rhythms. Following this strategy, we address the following questions: What are the implications of different architectures and molecular modes of transcriptional control for the phenotypic repertoire of genetic oscillators? Are there designs that are more realizable or robust? We compare synthetic oscillators involving one of three architectures and various combinations of the two modes of transcriptional control using a methodology that provides three innovations: a rigorous definition of phenotype, a procedure for deconstructing complex systems into qualitatively distinct phenotypes, and a graphical representation for illuminating the relationship between genotype, environment, and the qualitatively distinct phenotypes of a system. These methods provide a global perspective on the behavioral repertoire, facilitate comparisons of alternatives, and assist the rational design of synthetic gene circuitry. In particular, the results of their application here reveal distinctive phenotypes for several designs that have been studied experimentally as well as a best design among the alternatives that has yet to be constructed and tested.

Evolution of a genome-encoded bias in amino acid biosynthetic pathways is a potential indicator of amino acid dynamics in the environment

Overcoming the stress of starvation is one of an organism’s most challenging phenotypic responses. Those organisms that frequently survive the challenge, by virtue of their fitness, will have evolved genomes that are shaped by their specific environments. Understanding this genotype–environment–phenotype relationship at a deep level will require quantitative predictive models of the complex molecular systems that link these aspects of an organism’s existence. Here, we treat one of the most fundamental molecular systems, protein synthesis, and the amino acid biosynthetic pathways involved in the stringent response to starvation. These systems face an inherent logical dilemma: Building an amino acid biosynthetic pathway to synthesize its product—the cognate amino acid of the pathway—may require that very amino acid when it is no longer available. To study this potential “catch-22,” we have created a generic model of amino acid biosynthesis in response to sudden starvation. Our mathematical analysis and computational results indicate that there are two distinctly different outcomes: Partial recovery to a new steady state, or full system failure. Moreover, the cell’s fate is dictated by the cognate bias, the number of cognate amino acids in the corresponding biosynthetic pathway relative to the average number of that amino acid in the proteome. We test these implications by analyzing the proteomes of over 1,800 sequenced microbes, which reveals statistically significant evidence of low cognate bias, a genetic trait that would avoid the biosynthetic quandary. Furthermore, these results suggest that the pattern of cognate bias, which is readily derived by genome sequencing, may provide evolutionary clues to an organism’s natural environment.

Phenotypic deconstruction of gene circuitry

It remains a challenge to obtain a global perspective on the behavioral repertoire of complex nonlinear gene circuits. In this paper, we describe a method for deconstructing complex systems into nonlinear sub-systems, based on mathematically defined phenotypes, which are then represented within a system design space that allows the repertoire of qualitatively distinct phenotypes of the complex system to be identified, enumerated, and analyzed. This method efficiently characterizes large regions of system design space and quickly generates alternative hypotheses for experimental testing. We describe the motivation and strategy in general terms, illustrate its use with a detailed example involving a two-gene circuit with a rich repertoire of dynamic behavior, and discuss experimental means of navigating the system design space.

Dynamics and bistability in a reduced model of the lac operon

It is known that the lac operon regulatory pathway is capable of showing bistable behavior. This is an important complex feature, arising from the nonlinearity of the involved mechanisms, which is essential to understand the dynamic behavior of this molecular regulatory system. To find which of the mechanisms involved in the regulation of the lac operon is the origin of bistability, we take a previously published model which accounts for the dynamics of mRNA, lactose, allolactose, permease and beta-galactosidase involvement and simplify it by ignoring permease dynamics (assuming a constant permease concentration). To test the behavior of the reduced model, three existing sets of data on beta-galactosidase levels as a function of time are simulated and we obtain a reasonable agreement between the data and the model predictions. The steady states of the reduced model were numerically and analytically analyzed and it was shown that it may indeed display bistability, depending on the extracellular lactose concentration and growth rate.

Why the lysogenic state of phage lambda is so stable: a mathematical modeling approach

We develop a mathematical model of the phage lambda lysis/lysogeny switch, taking into account recent experimental evidence demonstrating enhanced cooperativity between the left and right operator regions. Model parameters are estimated from available experimental data. The model is shown to have a single stable steady state for these estimated parameter values, and this steady state corresponds to the lysogenic state. When the CI degradation rate (gammacI) is slightly increased from its normal value (gammacI approximately 0.0 min(-1)), two additional steady states appear (through a saddle-node bifurcation) in addition to the lysogenic state. One of these new steady states is stable and corresponds to the lytic state. The other steady state is an (unstable) saddle node. The coexistence these two globally stable steady states (the lytic and lysogenic states) is maintained with further increases of gammacI until gammacI approximately 0.35 min(-1), when the lysogenic steady state and the saddle node collide and vanish (through a reverse saddle node bifurcation) leaving only the lytic state surviving. These results allow us to understand the high degree of stability of the lysogenic state because, normally, it is the only steady state. Further implications of these results for the stability of the phage lambda switch are discussed, as well as possible experimental tests of the model.

Feedback regulation in the lactose operon: a mathematical modeling study and comparison with experimental data

A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented. This model takes into account the dynamics of the permease facilitating the internalization of external lactose; internal lactose; beta-galactosidase, which is involved in the conversion of lactose to allolactose, glucose and galactose; the allolactose interactions with the lac repressor; and mRNA. The final model consists of five nonlinear differential delay equations with delays due to the transcription and translation process. We have paid particular attention to the estimation of the parameters in the model. We have tested our model against two sets of beta-galactosidase activity versus time data, as well as a set of data on beta-galactosidase activity during periodic phosphate feeding. In all three cases we find excellent agreement between the data and the model predictions. Analytical and numerical studies also indicate that for physiologically realistic values of the external lactose and the bacterial growth rate, a regime exists where there may be bistable steady-state behavior, and that this corresponds to a cusp bifurcation in the model dynamics.

Transcription of single-copy hybrid lacZ genes by T7 RNA polymerase in Escherichia coli: mRNA synthesis and degradation can be uncoupled from translation

In Escherichia coli transcription of individual genes generally requires concomitant translation, and thus the decay of mRNAs cannot be studied without the complication of translation. Here we have used T7 RNA polymerase to transcribe in vivo lacZ genes carrying ribosome binding sites of variable efficiency. We show that neither cell viability nor growth rate is affected by the T7-driven transcription of these genes, provided that they are present as single chromosomal copy. Furthermore, transcription is now completely uncoupled from translation, allowing large amounts of even completely untranslated mRNAs to be synthesized. Taking advantage of these features, we discuss the influence of the frequency of translation upon the processing and degradation of the lac message.

Altered mRNA metabolism in ribonuclease III-deficient strains of Escherichia coli

The metabolism of mRNA from the lactose (lac) operon of Escherichia coli has been studied in ribonuclease (RNase) III-deficient strains (rnc-105). The induction lag for beta-galactosidase from the first gene was twice as long, and enzyme synthesis was reduced 10-fold in one such mutant compared with its isogenic rnc+ sister; in the original mutant strain AB301-105, synthesis of beta-galactosidase was not even detectable, although transduction analysis revealed the presence of a normal lac operon. This defect does not reflect a loss of all lac operon activity galactoside acetyltransferase from the last gene was synthesized even in strain AB301-105 but at a rate several times lower than normal. Hybridization analyses suggested that both the frequency of transcription initiation and the time to transcribe the entire operon are normal in rnc-105 strains. The long induction lag was caused by a longer translation time. This defect led to translational polarity with reduced amounts of distal mRNA to give a population of smaller-sized lac mRNA molecules. All these pleiotropic effects seem to result from RNase III deficiency, since it was possible to select revertants to rnc+ that grew and expressed the lac operon at normal rates. However, the rnc-105 isogenic strains (but not AB301-105) also changed very easily to give a more normal rate of beta-galactosidase synthesis without regaining RNase III activity or a faster growth rate. The basis for this reversion is not known; it may represent a "phenotypic suppression" rather than result from a stable genetic change. Such suppressor effects could account for earlier reports of a noninvolvement of RNase III in mRNA metabolism in deliberately selected lac+ rnc-105 strains. The ribosomes from rnc-105 strains were as competent as ribosomes from rnc+ strains to form translation initiation complexes in vitro. However, per mass, beta-galactosidase mRNA from AB301-105 was at least three times less competent to form initiation complexes than was A19 beta-galactosidase mRNA. RNase III may be important in the normal cell to prepare lac mRNA for translation initiation. A defect at this step could account for all the observed changes in lac expression. A potential target within a secondary structure at the start of the lac mRNA is considered. Expression of many operons may be affected by RNase III activity; gal and trp operon expressions were also abnormal in RNase III- strains.

Kinetic analysis of fraction I protein biosynthesis in young protoplasts of tobacco leaves

At maximum inhibition chloramphenicol reduced [35S] methionine incorporation into acid-insoluble materials of sterile protoplasts from young tobacco leaves 5-7 cm in length by 30% compared to 70% by cycloheximide, indicating that 30% of the [35S] methionine became incorporated into chloroplast proteins and 70% into cytoplasmic proteins. [35S] Methionine became incorporated into both the large and small subunits of Fraction I protein, the major soluble protein of chloroplasts. Rifampicin and streptolydigin inhibited [3H] uridine incorporation into the 23 and 16 S rRNAs of chloroplasts to a much greater extent than into the 25 and 18 S cytoplasmic rRNAs. Rifampicin inhibited [35S] metionine incorporation into Fraction I protein after the third hour of incubation; streptolydigin after 2 h, the former evidently preventing initiation of mRNA for the large subunit of Fraction I protein and the latter its elongation. About 2.5 h was required between initiation of the large subunit mRNA synthesis, and appearance of the protein. It was estimated that 45 min is required for transcription of the mRNA which has a half-life of 2 h and that 105 min is required for its translation into approximately 350 amino acids constituting the large subunit monomeric polypeptide. The effect of chloramphenicol, cycloheximide and 2-(4-methyl-2,6-dinitroanaline)-N-methyl propionamide, the latter an inhibitor of protein initiation by 80 S ribosomes, on kinetics of Fraction I protein synthesis indicate that protoplasts contain a pool of small subunit polypeptides and that 30 min is required to polymerize the approximately 100 amino acids constituting the primary structure.

Expression and regulation of lactose genes carried by plasmids

A number of plasmids carrying the lactose character have been studied. All of the plasmids examined so far code for proteins essential for lactose utilization, i.e., beta-galactosidase and galactoside permease. None of them carries enzymatically or immunologically detectable thiogalactoside transacetylase. The expression of the two enzymes is both negatively and positively controlled: they are inducible by different galactosides and are sensitive to catabolite repression. Since the plasmid-coded lactose systems have many features in common with the Escherichia coli lactose operon, it is suggested that the plasmids could have acquired the lactose genes from an E. coli chromosome.

Regulation of nitrate reductase at the transcriptional and translational levels in Escherichia coli

Nitrate reductase from Escherichia coli is induced by nitrate and derepressed by oxygen removal after a lag phase. Elimination of inducer, shift to aerobic conditions and addition of actinomycin D causes the decline in the rate of its synthesis, which eventually may stop. Kinetic analysis of the sensitivity of the biosynthetic process to oxygen, chloramphenicol, actinomycin D and rifampicin gave results which we interprete as evidence that oxygen (and possibly nitrate) affect simultaneously both the transcriptional and translational processes.

Analysis of enzyme induction in bacteria

The theoretical relations between the induced initiation and accumulation of lac mRNA and its translation are derived, taking the kinetics of repressor-operator dissociation and enzyme maturation into account. These relations are used to evaluate observed data on lac induction and to estimate a number of parameters that characterize the transcription and translation of the beta-galactosidase gene in the bacterium Escherichia coli B/r growing at three different rates (0.7-2.1 doublings/h).

Lag in adaptation to lactose as a probe to the timing of permease incorporation into the cell membrane

If bacteria are incapable of forming and incorporating proteins into the cytoplasmic membranes in all phases of the cell cycle, then not all cells from an asynchronous culture should be capable of growth when switched to a new carbon and energy source whose metabolism requires new membrane function. The transfer of an inducible culture to low lactose provides such a situation since the cells cannot grow unless galactoside permease can function to concentrate the lactose internally. From such experiments, it was concluded that the Y gene product of the lac operon is synthesized, incorporated, and can start functioning in active transport, at any time throughout the bulk of the cell cycle. Not only were the lags before growth re-ensued much shorter than would be expected if the membrane transport capability could only be developed in a small portion of the cycle, but brief pulses of a gratuitous inducer shortened the lags much further. Three types of Escherichia coli ML 30 culture were studied: cells that had exhausted the limiting glucose; cells taken directly from glucose-limited chemostats; and a washed suspension of highly catabolite repressed cells from cultures grown in high levels of glucose and gluconate. The growth studies reported here were performed on-line with a minicomputer. They represent at least an order of magnitude increase in accuracy in estimating growth parameters over previous instrumentation.

Induction kinetics of the L-arabinose operon of Escherichia coli

After addition of l-arabinose to growing Escherichia coli, the l-ribulokinase (EC 2.7.1.16) and l-arabinose isomerase (EC 5.3.1.4) first appear at about 0.7 and 1.4 min, respectively. These times are consistent with the distances of the genes from the ribonucleic acid polymerase initiation site in the operon. The kinetics of appearance of these enzymes as well as those of beta-galactosidase (EC 3.2.1.23) in the same strain are consistent with a peptide elongation rate of no less than 14 amino acids per second. A measurement of the average peptide elongation rate made by measuring the kinetics of radioactive amino acid appearance in completed polypeptides yielded a rate of about 12 amino acids per s. Convenient assays of the arabinose isomerase and ribulokinase are also given.

Lomofungin, an inhibitor of ribonucleic acid synthesis in yeast protoplasts: its effect on enzyme formation

Lomofungin, an antibiotic active against fungi, yeasts, and bacteria, rapidly inhibits synthesis of ribonucleic acid (RNA) but not protein by protoplasts of Saccharomyces strain 1016. With 40 mug of lomofungin/ml, RNA synthesis was almost completely halted after 10 min of incubation; protein synthesis continued for at least 40 min. Since lomofungin inhibits isolated RNA polymerases from yeast, but not in vitro protein synthesis, it is concluded that the primary action of lomofungin in yeast protoplasts is on RNA synthesis. Examination of the pulse-labeled RNA indicated that biosynthesis of both ribosomal precursor RNAs and messenger RNAs was severely inhibited after the protoplasts were incubated with lomofungin for 5 min, whereas formation of small-molecular-weight RNA (4 to 5s) was only slightly affected. Under these conditions, lomofungin almost completely prevented induction of alpha-glucosidase. Once the protoplasts had been induced, further production of the enzyme was not impaired by lomofungin until after 30 min of incubation, but was rapidly halted by cycloheximide (4 mug/ml). Lomofungin inhibition of invertase formation by protoplasts actively synthesizing the enzyme also became evident only after a lag of about 30 to 40 min, although synthesis was promptly halted by cycloheximide. These observations suggest the existence of relatively long-lived specific messenger RNAs for these enzymes.

Susceptibility of whole cells and spheroplasts of Pseudomonas aeruginosa to actinomycin D

Cells of Pseudomonas aeruginosa suspended in 0.2 M Mg(2+), 20% sucrose, 0.01 M tris(hydroxymethyl)aminomethane, or water partially release lipopolysaccharide. The release of alkaline phosphatase from the periplasmic space and the ability to form spheroplasts on lysozyme treatment is directly related to the lipopolysaccharide released during treatment with 0.2 M Mg(2+), 20% sucrose, or other agents. The synthesis of ribonucleic acid (RNA) by intact cells, magnesium-lysozyme spheroplasts, or 20% sucrose-lysozyme spheroplasts is not sensitive to actinomycin D, whereas RNA synthesis by intact cells or spheroplasts in the presence of ethylene-diaminetetraacetic acid (EDTA) is sensitive to actinomycin D. EDTA alone has an inhibitory effect on RNA synthesis by whole cell, by magnesium-lysozyme spheroplasts, and by 20% sucrose-lysozyme spheroplasts. The experimental data indicate that, although the cell wall is damaged by 0.2 M Mg(2+) or 20% sucrose treatment in the presence of lysozyme, the treated cells or spheroplasts are still resistant to actinomycin D. These results suggest that the cytoplasmic membrane should be considered as the final and determinative barrier to this antibiotic in this organism.

Polycistronic effects of catabolite repression on the lac operon

The catabolite repression caused by glucose and glucose-6-phosphate has been studied for both beta-galactosidase and thiogalactoside transacetylase, the products of the operator proximal and distal cistrons of the lac operon, respectively. We find that both cistrons are affected coordinately by this form of repression. We also find that a single alteration at the lac promoter region is sufficient to abolish sensitivity to repression of both cistrons. From this, we conclude that there is only one target site for catabolite repression in the lac operon.

Effect of gene induction on the rate of mutagenesis by ICR-191 in Escherichia coli

ICR-191, an acridine half-mustard known to cause frameshift mutations in bacteria, was used to induce Lac(-) mutations revertible by ICR-191. The reversion rates of several of these mutations were stimulated approximately twofold by the presence of lac inducer. The stimulatory effect of inducer was attributable to gene induction rather than some other effect of inducer, since inducer did not stimulate reversion in a regulator constitutive strain. The stimulatory effect was not observed unless the gene to be reverted was induced during the period of exposure to ICR-191. The presence of a strong polar (nonsense) mutation on the operator side of a frameshift mutation abolished the stimulatory effect of inducer on reversion of the frameshift mutation by ICR-191. (As expected, a nonpolar mutation on the operator side of the frameshift mutation did not affect inducer-stimulated reversion.) It was concluded that some aspect of transcription or translation, or both, in the neighborhood of the ICR-191-induced mutation stimulated reversion by ICR-191. A recA mutation had no effect on reversion by ICR-191 in the presence or absence of inducer. In one mutant, gene induction depressed reversion by ICR-191 about sevenfold. The difference between this exceptional strain and other mutants was not attributable to different genetic backgrounds but seemed to be an inherent difference in the original Lac(-) mutations.

Accumulation of untranslated lactose-specific messenger ribonucleic acid during catabolite repression in Escherichia coli

When Escherichia coli K-12 Hfr.H was induced to synthesize beta-galactosidase in the presence of glucose, an untranslated lactose-specific mRNA (lac-mRNA), protected from decay, was found to accumulate progressively within the cells. The lac-mRNA accumulation was unaffected by the carbon source on which the cells had been grown before the induction. The amount of the lac-mRNA available for translation was affected by catabolite repression and 3':5'-cyclic AMP, but it remained unclear whether this was a direct effect on the formation of the lac-mRNA or a consequence of the effect on its translation.

Reinitiation of RNA synthesis on transcription of chromatin DNA by Escherichia coli RNA polymerase

The transcription of DNA in chromatin by Escherichia coli RNA polymerase resembles that of isolated DNA in two important respects: the release of nascent RNA and reinitiation of RNA synthesis is dependent on the salt concentration, and RNA synthesis is markedly stimulated by the addition of ribosomes.

Transient repression of the lac operon - the effect of a lac promoter deletion

Experiments have been done to show whether the lac promoter delection L1, which partly alleviates catabolite repression, also affects transient repression of lac. In stain L1/F'M15 all of the beta-galactosidase is synthesized from a chromosomal gene cis to L1, whereas 98% of the thiogalactosidase transacetylase is synthesized from an episomal gene cis to an intact i-p-o region. The addition of glucose to induced cultures of strain L1/F'M15 growing in glycerol medium caused extensive transient repression of transacetylase but almost no transient repression of beta-galactosidase. In control experiments with a diploid stain of genotype p(+)z(+)a(-)/F'p(+)z(-)a(+) the two enzymes suffered equal transient repression. Thus L1 substantially relieves transient repression.

Catabolite repression of the lac operon. Effect of mutations in the lac promoter

1. Several lac diploid strains of Escherichia coli were constructed and tested to discover whether mutations in the lac promoter alleviate catabolite repression. 2. In each of these diploids the chromosome carries one of the promoter mutations, L8, L29 or L1; so that the rate of synthesis of the enzymes of the lac operon is only 2-6% of the fully induced wild-type. Each diploid harbours the episome F'lacM15 that specifies the synthesis of thiogalactoside transacetylase under the control of intact regulator, promoter and operator regions, but has a deletion in the structural gene for beta-galactosidase. In each diploid more than 90% of the thiogalactoside transacetylase is synthesized from the episome, and 100% of the beta-galactosidase is synthesized from the chromosome, and comparison of the extent of catabolite repression that the two enzymes suffered indicated whether the chromosomal promoter mutation relieves catabolite repression. 3. In the strains in which the promoter carries either of the point mutations L8 or L29 the enzymes were equally repressed, suggesting that neither L8 nor L29 affects catabolite repression. 4. In a diploid strain harbouring the same episome but carrying deletion L1 on the chromosome, synthesis of beta-galactosidase suffered much less repression than that of thiogalactoside transacetylase. 5. In a diploid strain in which the chromosome carries L1 and also a second mutation that increases the rate of expression of lac to that permitted by L8 or L29, the synthesis of beta-galactosidase again suffered much less repression than the synthesis of thiogalactoside transacetylase. 6. The effect of L1 (which deletes the boundary between the i gene and the lac promoter) is ascribed to its bringing the expression of lac under the control of the promoter of the i gene. 7. Even in strains carrying L1, some catabolite repression persists; this is not due to a trans effect from the episome since it occurs equally in a haploid strain with L1.