Sustained oscillations and threshold phenomena in an operon control circuit

A genetic regulatory model involving a positive feedback (via induction) and a negative feedback (via catabolite repression) is analyzed and applied to the problem of the lac operon regulation in E. coli. Damped and sustained oscillations of the limit cycle type are found along with threshold phenomena corresponding to multiple limit cycles or to multiple steady states, for values of the parameters compatible with experimental data. A comparison With the observations of Knorre and Goodwin is outlined.     

Two Mutations in the First Gene of the Histidine Operon of Salmonella typhimurium Affecting Control

Two strains with mutations in the first structural gene of the histidine operon of Salmonella typhimurium were characterized. (The first structural gene specifies the first enzyme of histidine biosynthesis, phosphoribosyltransferase, which is sensitive to feedback inhibition by histidine.) One mutation, hisG3934, results in a phosphoribosyltransferase which is no longer sensitive to feedback inhibition by histidine but is instead subject to inhibition by aspartic acid. The other mutation, hisG3935, allows the histidine operon to be partially repressed by several amino acids, including aspartic acid. Analysis of hisG3935 is consistent with the hypothesis that phosphoribosyltransferase is directly involved in the regulation of the histidine operon.     

A cis/trans Test of the Effect of the First Enzyme for Histidine Biosynthesis on Regulation of the Histidine Operon

Previous studies showed that when triazolalanine was added to a derepressed culture of a histidine auxotroph, repression of the histidine operon occurred as though histidine had been added (6). However, when triazolalanine was added to a derepressed culture of a strain with a mutation in the first gene of the histidine operon which rendered the first enzyme for histidine biosynthesis resistant to inhibition by histidine, repression did not occur. The studies reported here represent a cis/trans test of this effect of mutations to feedback resistance. Using specially constructed merodiploid strains, we were able to show that the wild-type allele is dominant to the mutant (feedback resistant) allele and that the effect operates in trans. We conclude that the enzyme encoded by the first gene of the histidine operon exerts its regulatory effect on the operon not by acting locally at its site of synthesis, but by acting as a freely diffusible protein.     

The Goodwin Oscillator and its Legacy

In the 1960’s Brian Goodwin published a couple of mathematical models showing how feedback inhibition can lead to oscillations and discussed possible implications of this behaviour for the physiology of the cell. He also presented key ideas about the rich dynamics that may result from the coupling between such biochemical oscillators. Goodwin’s work motivated a series of theoretical investigations aiming at identifying minimal mechanisms to generate limit cycle oscillations and deciphering design principles of biological oscillators. The three-variable Goodwin model (adapted by Griffith) can be seen as a core model for a large class of biological systems, ranging from ultradian to circadian clocks. We summarize here main ideas and results brought by Goodwin and review a couple of modeling works directly or indirectly inspired by Goodwin’s findings.

     

Histidine Mutants Requiring Adenine: Selection of Mutants with Reduced hisG Expression in SALMONELLA TYPHIMURIUM

A method is described for the selection of Salmonella typhimurium mutants with reduced levels of hisG enzyme activity. This method is based on the fact that the hisG enzyme catalyzes the consumption of ATP in the first step of histidine biosynthesis. Normally, this reaction is closely regulated, both by feedback inhibition and by repression of the operon. However, conditions can be set up that result in the uncontrolled use of adenine in histidine biosynthesis. Cells grown under these conditions become phenotypic adenine auxotrophs. Some revertant clones that no longer require adenine contain mutations in hisG, hisE, or the his-control region. The hisG mutations are of all types (nonsense, frameshift, missense, deletion and leaky types), and they map throughout the hisG gene.     

Quantitative analysis of the Hopf bifurcation in the Goodwin n-dimensional metabolic control system

We study, from a quantitative point of view, the Hopf bifurcation in an ODE model of feedback control type introduced by Goodwin (1963) to describe the dynamics of end-product inhibition of gene activity. We formally prove that the exchange of linear stability of the positive equilibrium in the n-dimensional Goodwin system with equal reaction constants coexists with a Hopf bifurcation of nontrivial periodic solutions emanating from this equilibrium, without any further restriction on the dimension n 3 or on the Hill coefficient . The direction of the bifurcation, and the stability and the period of the bifurcating orbits are estimated by means of the algorithm proposed by Hassard et al. (1981).Supported by MURST 40/60%     

A generalized numerical approach to steady-state enzyme kinetics: Applications to protein kinase inhibition

A generalized numerical treatment of steady-state enzyme kinetics is presented. This new approach relies on automatic computer derivation of the underlying mathematical model (a system of simultaneous nonlinear algebraic equations) from a symbolic representation of the reaction mechanism (a system of biochemical equations) provided by the researcher. The method allows experimental biochemists to analyze initial-rate enzyme kinetic data, under the steady-state approximation, without having to use any mathematical equations. An illustrative example is based on the inhibition kinetics of p56^lck kinase by an ATP competitive inhibitor. A computer implementation of the new method, in the modified software package DYNAFIT [Kuzmi?, P. (1996) Anal. Biochem. 237, 260–273], is freely available to all academic researchers.     

The yydFGHIJ operon of Bacillus subtilis encodes a peptide that induces the LiaRS two-component system

The Bacillus subtilis LiaRS two-component system (TCS) responds to perturbations of the cell envelope induced by lipid II-interacting antibiotics, such as vancomycin, ramoplanin, nisin, and bacitracin. Here, we characterize Tn7-generated mutations that induce the liaRS TCS. In addition to insertions in liaF, a known negative regulator of the LiaRS TCS, we identified two disruptions in the last two genes of the yydFGHIJ operon. This operon is predicted to encode a 49-amino-acid peptide (YydF), a modification enzyme (YydG), a membrane-embedded protease (YydH), and an ATP-binding cassette (ABC) transporter (YydIJ). Genome sequence comparisons suggest that the yydFGHIJ operon may have been acquired by horizontal transfer. Inactivation of the YydIJ transporter resulted in increased expression from the LiaR-dependent P_liaI promoter only in the presence of the yydFGH genes. Cells harboring the complete yydFGHIJ operon induced LiaR activity in cocultured cells lacking either this transporter or the complete operon. These results suggest that this operon is involved in the synthesis and export of a modified peptide (YydF*) that elicits cell envelope stress sensed by the LiaRS TCS.     

Stable Expression of hom-1-thrB in Corynebacterium glutamicum and Its Effect on the Carbon Flux to Threonine and Related Amino Acids

The hom-1-thrB operon encodes homoserine dehydrogenase resistant to feedback inhibition by L-threonine and homoserine kinase. Stable expression of this operon has not yet been attained in different Corynebacterium glutamicum strains. We studied the use of chromosomal integration and of a low-copy-number vector for moderate expression of the hom-1-thrB operon to enable an analysis of the physiological consequences of its expression in C. glutamicum. Strains carrying one, two, or three copies of hom-1-thrB were obtained. They showed proportionally increased enzyme activity of feedback-resistant homoserine dehydrogenase and of homoserine kinase. This phenotype was stably maintained in all recombinants for more than 70 generations. In a lysine-producing C. glutamicum strain which does not produce any threonine, expression of one copy of hom-1-thrB resulted in the secretion of 39 mM threonine. Additional copies resulted in a higher, although not proportional, accumulation of threonine (up to 69 mM). This indicates further limitations of threonine production. As the copy number of hom-1-thrB increased, increasing amounts of homoserine (up to 23 mM) and isoleucine (up to 34 mM) were secreted. Determination of the cytosolic concentration of the respective amino acids revealed an increase of intracellular threonine from 9 to 100 mM and of intracellular homoserine from 4 to 74 mM as the copy number of hom-1-thrB increased. These results suggest that threonine production with C. glutamicum is limited by the efflux system for this amino acid. Furthermore, the results show the successful use of moderate and stable hom-1-thrB expression for directing the carbon flux from aspartate to threonine.     

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.     

I. Cytochrome oscillations in continuous culture: Action of chloramphenicol on Saccharomyces carlsbergensis and Candida utilis

Oscillations in the A, B and C group cytochromes of Saccharomyces carsbergensis and Candida utilis have been observed in continuous culture following the addition and removal of chloramphenicol. With S. carlsbergensis reproduction of these oscillations proved difficult due to the fermentative nature of the yeast. With C. utilis at D = 0.1 h⁻¹ the oscillations in teh A group cytochromes were statistically significant and 3–6 times the standard deviation observed in steady sate. The oscillations provide evidence of a feedback loop controlling cytochrome synthesis and have a period of the same order of that predicted by Goodwin for the protein (enzyme) component of his model (viz. 6–8 h). With C. utilis the period of these oscillations was a function of the growth rate varying from approx. 10 h at a growth rate of 0.1 h⁻¹ (mean generation time 6.9 h) to 3 h at a growth rate of 0.3 h⁻¹ (mean generation time 2.3 h).     

Giuseppe Palomba and the Lotka-Volterra equations

The economics commonly credited with the introduction of the Lotka-Volterra equations into economics to examine cyclical problems is Richard Goodwin (1965). In this paper we show that the Italian economist Giuseppe Palomba had used these equationsmuch earlier (1939), and describe Palomba’s model in detail, pointing out his surprisinglymodern conclusions and suggestions for future work.      

Coupling of homotropic and heterotropic interactions in Escherichia coli aspartate transcarbamylase

Several types of conditions allow the disconnection of homotropic and heterotropic interactions in Escherichia coli aspartate transcarbamylase. A model that includes a concerted gross conformational change corresponding to the homotropic cooperative interactions between the catalytic sites and local “site by site” effects promoted by the effectors accounts for this disconnection as well as for the other known properties of the enzyme. However, the substrate concentration influences the extent of stimulation and feedback inhibition of the catalytic activity by the effectors. This result is explained by assuming that these effectors promote a “primary effect”, which is exerted locally “site by site”, and a “secondary effect”, which is mediated by the substrate. As predicted by the model, relaxed (R) forms of the enzyme show only the primary effect. In addition 2-ThioU-aspartate transcarbamylase, a modified form of the enzyme in which the homotropic cooperative interactions between the catalytic sites are selectively abolished, shows the same heterogeneity in CTP binding sites as normal aspartate transcarbamylase.     

Derepression and repression of the histidine operon: role of the feedback site of the first enzyme.

Thiazolealanine, a false feedback inhibitor, causes transient repression of the his operon previously derepressed by a severe histidine limitation in strains with a wild-type or feedback-hypersensitive first enzyme but not in feedback-resistant mutants. Since experiments reported here clearly demonstrate that thiazolealanine is not transferred to tRNAHis, it is proposed that this "transient repression" is effected through the interaction of thiazolealanine with the feedback site of the enzyme. Experiments in the presence of rifampin indicate that this thiazolealanine-mediated effect is exerted at the level of translation. We conclude that histidine (free), in addition to forming co-repressor, also represses the operon at the level of translation through feedback interaction with the first enzyme of the pathway (adenosine 5'-triphosphate phosphoribosyltransferase). Rates of derepression in feedback-resistant strains are roughly half of those observed in controls, suggesting a positive role played by a first enzyme with a normal but unoccupied feedback site. Some feedback-resistant mutants, in contrast to the wild type, were unable to exhibit derepression under histidine limitation caused by aminotriazole.     

Feedback-Resistant Acetohydroxy Acid Synthase Increases Valine Production in Corynebacterium glutamicum

Acetohydroxy acid synthase (AHAS), which catalyzes the key reactions in the biosynthesis pathways of branched-chain amino acids (valine, isoleucine, and leucine), is regulated by the end products of these pathways. The whole Corynebacterium glutamicum ilvBNC operon, coding for acetohydroxy acid synthase (ilvBN) and aceto hydroxy acid isomeroreductase (ilvC), was cloned in the newly constructed Escherichia coli-C. glutamicum shuttle vector pECKA (5.4 kb, Km^r). By using site-directed mutagenesis, one to three amino acid alterations (mutations M8, M11, and M13) were introduced into the small (regulatory) AHAS subunit encoded by ilvN. The activity of AHAS and its inhibition by valine, isoleucine, and leucine were measured in strains carrying the ilvBNC operon with mutations on the plasmid or the ilvNM13 mutation within the chromosome. The enzyme containing the M13 mutation was feedback resistant to all three amino acids. Different combinations of branched-chain amino acids did not inhibit wild-type AHAS to a greater extent than was measured in the presence of 5 mM valine alone (about 57%). We infer from these results that there is a single binding (allosteric) site for all three amino acids in the enzyme molecule. The strains carrying the ilvNM13 mutation in the chromosome produced more valine than their wild-type counterparts. The plasmid-free C. glutamicum ΔilvA ΔpanB ilvNM13 strain formed 90 mM valine within 48 h of cultivation in minimal medium. The same strain harboring the plasmid pECKAilvBNC produced as much as 130 mM valine under the same conditions.